Global estimation method, system, device and terminal of wave-induced turbulent mixing model

Abstract

The application belongs to the technical field of circulation mixing coefficient estimation, and discloses a global estimation method, system, device and terminal of a wave-induced turbulent mixing model, the global estimation method of the wave-induced turbulent mixing model comprising: estimating the global three-dimensional structure of the internal tide-induced turbulent mixing coefficient based on the wave-induced turbulent mixing coefficient, the internal tide information extracted by the satellite altimeter and the WOA13 temperature and salinity data; determining the structure of the global internal wave spectrum; and estimating the distribution characteristics of the global annual average internal wave-induced turbulent mixing coefficient BVIW. The internal tide information extraction comprises: obtaining, processing and filtering satellite along-track sea surface height anomaly data, performing tidal harmonic analysis on the filtered data, and obtaining the internal tide harmonic constant of the global ocean tidal frequency M2. According to the derived mixing coefficient, new mixing is not created, but a mixing process that is not available under the existing framework and is rich in physical connotation is created, and the important significance of wave mixing to the circulation is given.

Description

Technical Field

[0001] This invention belongs to the field of circulation mixing coefficient estimation technology, and particularly relates to a global estimation method, system, device and terminal for a wave-generated turbulence mixing model. Background Technology

[0002] Currently, the semi-empirical, semi-theoretical mixing model proposed by Prandtl in the early 20th century is an effective approach for estimating turbulent transport fluxes. It borrows the concept of molecular free path from molecular kinetic theory, proposing a scalar quantity called turbulent mixing length, and derives the relationship between turbulent stress and mean velocity shear by referring to the relationship between molecular viscous stress and velocity shear. In practical applications of this shear relationship, industry practice only considers the shear of large-scale circulation in the model, neglecting the effects of small- and medium-scale fluctuations (ocean waves + internal waves). However, the ocean is a complex dynamic system, and the shear source of the turbulent mixing term in the circulation system should have multi-scale motion characteristics, with fluctuations being the largest energy source contributing to turbulence in these systems. Existing technology lacks a global estimation method that incorporates fluctuation-generated turbulent mixing models. This leads to significant simulation discrepancies between theory and reality, often resulting in overestimation of sea surface temperature and underestimation of hydrothermal intensity in simulations.

[0003] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: the existing technology does not have a global estimation method based on an independently developed wave-generated turbulence mixing model.

[0004] The challenges in addressing these issues and shortcomings lie in how to reasonably incorporate the effect of the wave field into the turbulent mixing term and how to estimate the global mixing coefficient distribution using existing data.

[0005] The significance of solving the above problems and defects is that it avoids the dilemma of arbitrary parameter adjustment and allows for reasonable consideration of the influence of different motion systems on the ocean circulation mixing term, especially the internal wave mixing which has a significant effect. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a global estimation method, system, device, and terminal for a wave-generated turbulence mixing model.

[0007] This invention is implemented as follows: a global estimation method for a wave-generated turbulence mixing model, the global estimation method for the wave-generated turbulence mixing model comprising:

[0008] Step 1: Based on the wave-generated turbulent mixing coefficient, combined with the internal tide information extracted from the satellite altimeter and the WOA13 temperature and salinity data, estimate the global three-dimensional structure of the internal tide-generated turbulent mixing coefficient;

[0009] Step 2: Determine the structure of the global internal wave spectrum; estimate the distribution characteristics of the global annual average internal wave generated turbulence mixing coefficient (BVIW).

[0010] Furthermore, in step one, the turbulent mixing coefficient generated by the wave is as follows:

[0011]

[0012]

[0013] Furthermore, in step one, the method for extracting internal tide information includes: performing high-pass filtering on altimeter SSH data along the track with a cutoff wavenumber of 200km-400km to remove the barotropic tide portion; and then performing harmonic analysis to extract the internal tide of M2.

[0014] Furthermore, the method for extracting internal moisture information includes the following steps:

[0015] (1) Acquire data on sea surface height anomalies along the satellite orbit and perform data supplementation processing;

[0016] (2) High-pass filtering is applied to the processed data to select fluctuations along the track with a spatial wavelength within 200km;

[0017] (3) Perform tidal harmonic analysis on the filtered data to obtain the intidal harmonic constant with global ocean tidal frequency M2.

[0018] Furthermore, the process of supplementing the acquired data includes:

[0019] For any missing points in time or space, interpolation is performed using the nearest available results to fill in the gaps.

[0020] Furthermore, the estimation of the internally generated turbulent mixing coefficient includes:

[0021] Based on the M2 endocytic data extracted from altimeters and the WOA13 temperature and salinity data, the mixing coefficient B generated by the global endocytic wave orbit shearing was obtained. VIW The distribution of the surface data and the theoretical model were used to invert the deep-sea mixing coefficient.

[0022] Furthermore, in step two, the construction of determining the global internal spectrum includes:

[0023] The global internal undulation spectrum is estimated by combining the standardized internal wave spectral model GM spectrum with the global M2 internal tidal fluctuations, and the high-frequency band B is calculated. VIW :

[0024]

[0025] The fluctuation spectrum, kinetic energy spectrum, and total energy spectrum of the internal wave per unit mass are as follows:

[0026] F ξ (ω,j)=b 2 N0N -1 (ω2 -f 2 )ω -2 E(ω,j)

[0027] F μ (ω,j)=F μ1 +F μ2 =b 2 N0N(ω 2 +f 2 )ω -2 E(ω,j);

[0028]

[0029] According to the expression of the GM79 spectrum, the expression of the internal wave energy density E(ω,j) is:

[0030] E(ω,j)=B(ω)·H(j)·E;

[0031] in,

[0032] By correcting the dimensionless parameter E in the GM spectrum using inland tide amplitude data extracted from the altimeter, the sea surface undulation spectrum for the entire field is obtained:

[0033]

[0034] Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the following steps:

[0035] Based on the wave-generated turbulence mixing coefficient, combined with the internal tide information extracted from the satellite altimeter and the WOA13 temperature and salinity data, the global three-dimensional structure of the internal tide-generated turbulence mixing coefficient is estimated.

[0036] Determine the structure of the global internal wave spectrum; estimate the distribution characteristics of the global annual average internal wave generated turbulence mixing coefficient (BVIW).

[0037] Another objective of this invention is to provide an information data processing terminal for implementing the global estimation method of the wave-generated turbulence mixing model.

[0038] Another object of the present invention is to provide a global estimation system for a wave-generated turbulence mixing model that performs the global estimation method of the aforementioned wave-generated turbulence mixing model, the global estimation system for the wave-generated turbulence mixing model comprising:

[0039] The global 3D structure estimation module is used to estimate the global 3D structure based on the wave-generated turbulence mixing coefficient, combined with the internal tide information extracted by the satellite altimeter and WOA13 temperature and salinity data.

[0040] The distribution characteristics estimation module is used to determine the structure of the global internal wave spectrum and estimate the distribution characteristics of the global annual average internal wave-generated turbulence mixing coefficient (BVIW).

[0041] Combining all the above technical solutions, the advantages and positive effects of this invention are as follows: the invention does not create new mixtures according to the derived mixing coefficients, but rather a mixing process that is not present in the existing framework and has rich physical connotations. This avoids the dilemma of arbitrary parameter tuning of models and has important practical significance for improving the simulation and forecasting capabilities of ocean models. Attached Figure Description

[0042] Figure 1 This is a roadmap for estimating the mixing coefficient of autonomous internal wave-generated turbulence provided in an embodiment of the present invention.

[0043] Figure 2 This is a flowchart of the global estimation method for the wave-generated turbulence mixing model provided in this embodiment of the invention.

[0044] Figure 3 This is a schematic diagram of the semi-empirical, semi-theoretical Prandtl hybrid model provided in the embodiments of the present invention.

[0045] Figure 4 This is the 0th order provided in the embodiments of the present invention. A schematic diagram comparing the frequency ratio approximation and the old hybrid model.

[0046] Figure 5 These are the 0th and 1st order provided in the embodiments of the present invention. Approximate diagram of frequency ratio.

[0047] Figure 6 This is a schematic diagram comparing the ideal mixing coefficients of density gradient strength and depth provided in an embodiment of the present invention.

[0048] Figure 7 This is a schematic diagram of Wunsch's classification of ocean dynamic systems into four motion categories and the mixing of other motion categories with the total circulation, provided in an embodiment of the present invention.

[0049] Figure 8 This is a global orbital map of the T / PJ satellite altimeter provided in an embodiment of the present invention.

[0050] Figure 9 This is a schematic diagram of the global M2 intidal amplitude distribution based on 200km of T / PJ track data provided in this embodiment of the invention, in meters.

[0051] Figure 10(a) shows the different modes B at full depth in a typical mid-latitude Pacific Ocean provided by the embodiments of the present invention. VIW Cross-sectional view.

[0052] Figure 10(b) shows the distribution over the upper 100m provided in an embodiment of the present invention.

[0053] Figure 11(a) shows the sea surface undulations at different depths in the mid-latitude Atlantic Ocean provided by the embodiment of the present invention. VIW The cross-sectional distribution.

[0054] Figure 11(b) is a schematic diagram of the distribution over the upper 100m provided in an embodiment of the present invention.

[0055] Figure 12(a) shows the different modes B at full depth in a typical mid-latitude Pacific Ocean provided by the embodiments of the present invention. VIW Cross-sectional view.

[0056] Figure 12(b) is a schematic diagram of the distribution over the upper 100m provided in an embodiment of the present invention.

[0057] Figure 13(a) shows the different modes B at full depth in a typical mid-latitude Atlantic Ocean provided by the embodiments of the present invention. VIW Cross-sectional view.

[0058] Figure 13(b) shows the 400mB provided in the embodiment of the present invention. VIW Cross-section, the black line is a schematic diagram of buoyancy frequency.

[0059] Figure 14(a) shows the full water depth at different latitudes (B) at 186°E provided in the embodiment of the present invention. VIW Cross-sectional view.

[0060] Figure 14(b) shows the 100m B at different latitudes provided in the embodiments of the present invention. VIW Cross-sectional view.

[0061] Figure 15(a) shows the full water depth at different latitudes (B) at 330°E provided in the embodiment of the present invention. VIW Cross-sectional view.

[0062] Figure 15(b) shows the 100m B at different latitudes provided in the embodiments of the present invention. VIW Cross-sectional view.

[0063] Figure 16(a) is a schematic diagram of the full-depth BVIW profile at 186°E 3*ωM2 frequency doubling provided in an embodiment of the present invention.

[0064] Figure 16(b) is a schematic diagram of the 186°E 5*ωM2 frequency-doubled full-depth BVIW profile provided in an embodiment of the present invention.

[0065] Figure 16(c) is a schematic diagram of the full-depth BVIW profile at 186°E 7*ωM2 frequency doubling provided in an embodiment of the present invention.

[0066] Figure 17(a) is a vertical average distribution diagram of the mixing coefficient with latitude provided in the embodiment of the present invention.

[0067] Figure 17(b) is a schematic diagram of the turbulent mixing generation mechanism in the Northwest Pacific provided by an embodiment of the present invention.

[0068] Figure 18 This is a planar distribution map of the tidal mixing coefficient within a typical water layer up to 200m above the surface, provided by an embodiment of the present invention.

[0069] Figure 19 This is a schematic diagram of the kinetic energy spectrum (black straight line) at 140m from the internal ocean wave observation spectrum of the Ocean Storms Experiment (47.5°N, 139.25°W) in the Pacific Ocean (47.5°N, 139.25°W) provided in an embodiment of the present invention, and the kinetic energy spectrum estimated based on the GM spectrum (red dashed line). The shaded area represents the energy density factor oscillation in the range of 0.5E-2E.

[0070] Figure 20 This is a schematic diagram of the 350m isodense surface undulation spectrum in the sea area 800km offshore of Santiago provided in an embodiment of the present invention.

[0071] Figure 21 This is a planar distribution map of the mixing coefficient of typical water layers worldwide, provided by an embodiment of the present invention.

[0072] Figure 22 This is a diagram of turbulence observation stations and global topography provided in this embodiment of the invention. The numbers in the diagram represent schematic diagrams of different observation plans.

[0073] Figure 23 This is a schematic diagram of the input of external mechanical energy for 12 deep-water turbulence observation stations provided in an embodiment of the present invention.

[0074] Figure 24(a) is a schematic diagram showing the relationship between external mechanical energy input and turbulent dissipation provided in an embodiment of the present invention.

[0075] Figure 24(b) is a schematic diagram showing the relationship between external mechanical energy input and turbulent dissipation provided in an embodiment of the present invention.

[0076] Figure 25 This is a schematic diagram comparing terrain roughness (left coordinate) and turbulent dissipation (right coordinate) provided in an embodiment of the present invention.

[0077] Figure 26(a) is a comparison diagram of six deep-sea mixing locations provided in the embodiments of the present invention.

[0078] Figure 26(b) is a comparison chart of six groups of deep-sea dissipation rates provided in the embodiments of the present invention.

[0079] Figure 26(c) is a comparison chart of the six calculated mixing coefficients BVIW and Osborn80 estimates provided in the embodiments of the present invention. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0081] To address the problems existing in the prior art, this invention provides a global estimation method, system, device, and terminal for a wave-generated turbulence mixing model. The invention will now be described in detail with reference to the accompanying drawings.

[0082] like Figures 1-2 As shown, the global estimation method for the wave-generated turbulence mixing model provided in this embodiment of the invention includes:

[0083] S101, based on the wave-generated turbulent mixing coefficient, combined with the internal tide information extracted by the satellite altimeter and the WOA13 temperature and salinity data, estimates the global three-dimensional structure of the internal tide-generated turbulent mixing coefficient;

[0084] S102, determine the structure of the global internal wave spectrum; estimate the distribution characteristics of the global annual average internal wave generated turbulence mixing coefficient (BVIW).

[0085] The turbulent mixing coefficients provided in this embodiment of the invention are as follows:

[0086]

[0087]

[0088] The method for extracting internal moisture information provided in this embodiment of the invention includes:

[0089] The altimeter SSH data along the track is high-pass filtered with a cutoff wavenumber of 200km-400km to remove the barotropic tidal component; then harmonic analysis is performed to extract the internal tidal volume of M2.

[0090] The method for extracting internal moisture information provided in this embodiment of the invention includes the following steps:

[0091] (1) Acquire data on sea surface height anomalies along the satellite orbit and perform data supplementation processing;

[0092] (2) High-pass filtering is applied to the processed data to select fluctuations along the track with a spatial wavelength within 200km;

[0093] (3) Perform tidal harmonic analysis on the filtered data to obtain the intidal harmonic constant with global ocean tidal frequency M2.

[0094] The data supplementation provided in this embodiment of the invention includes:

[0095] For any missing points in time or space, interpolation is performed using the nearest available results to fill in the gaps.

[0096] The estimation of the internally tidal turbulent mixing coefficient provided in this embodiment of the invention includes:

[0097] Based on the M2 endocytic data extracted from altimeters and the WOA13 temperature and salinity data, the mixing coefficient B generated by the global endocytic wave orbit shearing was obtained. VIW The distribution of the surface data and the theoretical model were used to invert the deep-sea mixing coefficient.

[0098] The construction of determining the global internal wave spectrum provided in this embodiment of the invention includes:

[0099] The global internal undulation spectrum is estimated by combining the standardized internal wave spectral model GM spectrum with the global M2 internal tidal fluctuations, and the high-frequency band B is calculated. VIW :

[0100]

[0101] The fluctuation spectrum, kinetic energy spectrum, and total energy spectrum of the internal wave per unit mass are as follows:

[0102] F ξ (ω,j)=b 2 N0N -1 (ω 2 -f 2 )ω -2 E(ω,j)

[0103] F μ (ω,j)=F μ1 +F μ2 =b 2 N0N(ω 2 +f 2 )ω -2 E(ω,j);

[0104]

[0105] According to the expression of the GM79 spectrum, the expression of the internal wave energy density E(ω,j) is:

[0106] E(ω,j)=B(ω)·H(j)·E;

[0107] in,

[0108] By correcting the dimensionless parameter E in the GM spectrum using inland tide amplitude data extracted from the altimeter, the sea surface undulation spectrum for the entire field is obtained:

[0109]

[0110] The technical solution of the present invention will be further described below with reference to specific embodiments.

[0111] Example 1:

[0112] This invention designs multiple sets of numerical experiments to answer the question of whether internal wave breaking and mixing plays a key role in maintaining deep-sea stratification, and to answer whether turbulent mixing caused by internal wave orbital velocity shear instability (hereinafter referred to as internal wave-induced turbulent mixing) has a key impact on the simulation of the upper ocean. The first part mainly describes the establishment of the wave-induced turbulent mixing theoretical model independently developed by the author's team and the estimation of global three-dimensional coefficients. Figure 1 This lays the foundation for the second part of the study on the impact of upper ocean turbulent mixing on ocean circulation.

[0113] The first section is arranged as follows: Section 1.1 introduces the mixing coefficient of wave-generated turbulence in the Prandtl mixing model; Section 1.2 provides a saturated equilibrium estimate of the mixing coefficients of wave-generated turbulence, vortex, and circulation under systems science; Section 1.3 estimates the distribution of the mixing coefficient of internal tidal turbulence based on satellite altimeter data; Section 1.4 provides a global estimate of the mixing coefficient of internal wave-generated turbulence based on altimeter internal tidal data and the GM model spectrum; Section 1.5 will summarize the invention.

[0114] 1.1 Derivation of mixing coefficients for wave-induced turbulence based on Prandtl mixing model

[0115] 1.1.1 Semi-empirical and semi-theoretical Prandtl hybrid model

[0116] Previous methods using internal wave energy models have verified the important role of internal wave breaking and mixing. However, many parameterization issues in internal wave energy models require careful study. This invention aims to address the problem of how to directly estimate non-breaking internal wave turbulent mixing based on residual turbulent transport flux combined with observational data.

[0117] In the early 20th century, Prandtl proposed a semi-empirical, semi-theoretical mixing model, which is an effective approach to estimating turbulent transport fluxes. Borrowing the concept of molecular free path from molecular kinetic theory, he proposed a scalar quantity called the turbulent mixing length, and by referring to the relationship between molecular viscous stress and velocity shear, he deduced the relationship between turbulent stress and average velocity shear.

[0118] For simplicity, near a certain point o in the fluid, the local coordinate system {o; x1, x2, x3} of the average motion of the framework of this invention is defined. Figure 3Its x1 coordinate axis points in the direction of the average velocity, the x2 coordinate axis is the direction of the greatest velocity change on the vertical plane of the average flow velocity, and the x3 coordinate axis, which forms a right-handed frame with the former two, is the direction of the least velocity change on the vertical plane of the average flow velocity. Thus, this invention has...

[0119] In turbulent motion, a mixing length equivalent to the molecular mean free path is introduced. Within this distance, the fluid mass will not collide with other fluid masses, thus maintaining its physical properties such as constant momentum. Consider two fluid layers parallel to the x2 = x2 coordinate plane within the fluid, with their boundary surfaces being... Because there is a turbulent disturbance velocity component in the x2 coordinate axis direction Thus, let 1 and 2 denote the momentum fluxes of the upper and lower fluid layers, respectively, thereby generating turbulent stress on the coordinate plane x2 = x2. The momentum fluxes of fluid layers 1 and 2 are respectively

[0120]

[0121] Thus, the turbulent stresses on the x2=x2 coordinate plane are equal to their average exchange residue.

[0122]

[0123] in Indicates the mixing viscosity coefficient of dynamic turbulent flow. Represents the viscous number of turbulent mixing;

[0124] This represents the average velocity along the x1 coordinate axis. This represents the average (characteristic) perturbation velocity in the direction perpendicular to the x1 coordinate axis within the mainstream plane, i.e., in the direction of the x2 coordinate axis. This represents the average (characteristic) perturbation mixing length along the x2 coordinate axis.

[0125] In the Prandtl mixture model, the introduced average perturbation velocity and mixed length It still needs to be determined based on the actual situation, through experimental analysis and theoretical assumptions.

[0126] This invention has

[0127]

[0128] Where σ is the Prandtl number for relative velocity mixing in a warm-salt mixture, which is equal to 0.5 in the neutral case. In the next section, this invention will give the expression for the mean turbulent disturbance velocity in the sense of wave-induced turbulence. and average mixing length The analysis results and theoretical assumptions.

[0129] 1.1.2 Expression of mixing coefficients for wave-generated turbulence based on Prandtl mixing model

[0130] Under the four-category classification principle of ocean motion, waves mainly include ocean waves at the sea surface and internal waves near the density strata. In this section, this invention will provide a unified analytical estimate of the wave-generated turbulence mixing coefficient according to the Prandtl mixing model, based on the analytical representation of "typical-simple" ocean waves and internal waves given in the appendix.

[0131] (1) Analytical estimation of the mixing coefficient of wave-generated turbulence

[0132] Here, the present invention will first give the average turbulent disturbance velocity. and average mixing length The theoretical representation is as follows: Using the range of motion of turbulent water particles as a measure of the average mixing length of wave-generated turbulence, it can be written as...

[0133]

[0134] The water quality point fluctuation h SW It can be written as

[0135]

[0136] The velocity increment of the "typical-simple" wave velocity shear modulus over an average mixing length is taken as a measure of the average disturbance velocity of wave-generated turbulence. Thus, this invention has...

[0137]

[0138] Based on the definition of kinematic viscosity, this invention includes a wave-generated turbulence mixing coefficient.

[0139]

[0140] and

[0141]

[0142] (2) Analytical estimation of the mixing coefficient of internally generated turbulent flow

[0143] Here, the present invention will first give the turbulent average mixing length. and average perturbation velocity The theoretical approach is as follows: using the range of motion of turbulent water particles as a measure of the mean mixing length of internally generated turbulence, it can be written as...

[0144]

[0145] The water quality point fluctuation h IWIt can be represented as

[0146]

[0147] The velocity increment calculated over an average mixing length using the "typical-simple" internal wave velocity shear mode is taken as a measure of the average disturbance velocity of the internal wave-generated turbulence. Thus, this invention has...

[0148]

[0149] Based on the definition of kinematic viscosity, this invention includes an internally generated turbulent mixing coefficient.

[0150]

[0151] and

[0152]

[0153] 1.1.3 Verification of the Simulation Effect of the Ideal Condition for the Mixing Coefficient of Wave-Generated Turbulent Flow

[0154] Here, the present invention first provides an accurate order to 0 based on the Prandtl mixture model. The mixing coefficients of wave-generated turbulence based on frequency ratios are compared with previous results. Then, the results are given with accuracy up to the first order. The basic values ​​and vertical distribution of the mixing coefficients of wave and internal wave-generated turbulence with frequency ratio.

[0155] (1) Accurate to order 0 Test of the mixing coefficient of wave-generated turbulence based on frequency ratio

[0156] Will Substituting a frequency ratio of 0 into the wave result, this invention has an accuracy to order 0. Frequency ratio of wave-generated turbulence mixing coefficient

[0157]

[0158] and

[0159]

[0160] Compared with previous semi-empirical results based on Prandtle

[0161]

[0162] and

[0163]

[0164] There are only minor differences.

[0165] Ideally, the two results should be compared. Figure 4 Based on the 0th-order approximation, using the single-wave approximation with a period T of 10s, the wave number K = 0.0402 and the significant wave height Hs = 2m. The classical calculation results are significantly larger than the new results; depending on K, the classical results near the sea surface are 2 to 6 times larger than the new results.

[0166] (2) Accurate to the first order Test of turbulent mixing coefficient based on frequency ratio fluctuation

[0167] This invention has accuracy down to the first order. Frequency ratio of wave-generated turbulence mixing coefficient

[0168]

[0169] and

[0170]

[0171] Under ideal conditions, using the 0th-order approximation formula and the 1st-order approximation formula for ocean waves, and also employing the single-wave approximation with a period T of 15s, the wave number K = 0.0179 and the significant wave height Hs = 2m. By selecting different values ​​of T within the interval [2, 20], the two approximations become closer when T is larger (K ​​is smaller).

[0172] This invention has accuracy down to the first order. Internal wave turbulence mixing coefficient of frequency ratio

[0173]

[0174] and

[0175]

[0176] Under ideal conditions, the vertical distribution of the mixing coefficient was plotted based on the first-order approximation formula of the internal wave. Choosing different values ​​of T and using the single-wave approximation, with a period T of 250s, the wave number K = 6.4389 × 10⁻¹⁰. -5 m -1 The wave height Hs = 5m. The vertical distribution of the internal wave mixing coefficient with density (rho) and buoyancy frequency (f) was plotted, and the location of the strongest density stratum was marked in the figure.

[0177] 1.2 Saturated Equilibrium Estimation of Mixing Coefficients of Wave-Generated Turbulence under Systems Science

[0178] 1.2.1 Research Background

[0179] In the previous section, this invention reviewed the semi-empirical, semi-theoretical expression of the mixing coefficient for wave-generated turbulence and conducted a comparative study of the old and new Bv models. This semi-empirical theory has considerable uncertainty in determining the mixing length and artificially defines the parameter representations. The ocean is a complex dynamic system. Moving beyond this semi-empirical framework, this invention, starting from the turbulence saturation theory within the framework of systems science, explores whether it can derive a mixing coefficient expression based on turbulence characteristic quantities. This invention will review previous conclusions and re-evaluate the saturation equilibrium estimation of the mixing coefficients of waves, vortices, and circulations caused by wave-generated turbulence.

[0180] Current research proposes studying the mixing effects of other motions on the overall ocean circulation from the perspective of interactions among all ocean motion types. Wunsch's two aspects of ocean dynamic systems—the classification of motion types and their interactions—can be further elaborated and expanded upon using knowledge of systems science.

[0181] It first divides ocean motion into turbulence, waves, mesoscale eddies, and the general ocean circulation. Simultaneously, it provides a unique characterization of the mixing effects of other motion types on the general ocean circulation, pointing out that ocean waves are the most important energy transfer channel between the atmosphere and the ocean, and indicating that the mixing effects on the general circulation, besides the influence of molecular forces, mainly include three modules: the wave + turbulence module, the internal wave module, and the mesoscale eddy module. This is similar to the mixing module proposed in this invention, but this invention also has its unique aspects. The following review summarizes how this invention discusses the modules of mixing effects and their specific expressions from a systems science perspective.

[0182] 1.2.2 Classification of motion types and derivation of governing equations for the marine dynamic system

[0183] Existing technology 1 introduces the concept of systems science, taking the molecular forces (mainly including viscous-conductive-diffusion forces and surface tension), gravity, geostrophic force, tidal force, and thermo-chemical forces shown by the Boussinesq approximation of the ocean motion equations as the main controlling forces of ocean motion. It uses the presence or absence of time-varying terms in the equations containing these controlling forces as the basis for distinguishing equilibrium states. This invention can classify ocean motion into four categories at two levels: turbulence, wave motion, vortex motion, and circulation, based on the principle of control mechanism division according to the subsystems of a complex system, rather than the principle of spatiotemporal scale distribution.

[0184] Here, wave and vortex are specifically used to refer to a pair of motions controlled by gravity and respectively in dynamic and static equilibrium. They are only referred to as "gravity" in cases where confusion may arise.

[0185] When defining the Reynolds averaging operation according to the time-space scale or the set of motion classes, considering that the latter has complete ergodic determinism while the former has a large ergodic uncertainty, this invention will adopt the latter as the rigorous definition of the motion decomposition Reynolds averaging operation.

[0186] For simplicity, this invention starts with the Boussinesq approximation of the ocean motion control equations. The three defined Reynolds averages are applied sequentially to the starting control equations and their decomposed residual motion control equations, yielding control equation sets for turbulent, wave, vortex, and circulation motions. In these four sets of equations, the interaction of motions is precisely characterized as three types of terms: 1) velocity shear and temperature-salinity gradient generation terms from the latter (larger scale) motion on the current motion; 2) nonlinear interaction terms of the current motion itself; and 3) residual mixed terms of transport flux from the former (smaller scale) motion on the current motion. In fact, the control equations for the four types of motions are decompositions of the ocean motion starting control equations, and the latter are synthesiss of the former. Thus, the ocean motion control equations and the decomposed control equations for the four types of motions are actually self-consistent and consistent.

[0187] (1) Combination-average representation of fundamental characteristic quantities of turbulence for mixing coefficients of waves, vortices and circulation.

[0188] Mixing is an important aspect of the interaction of ocean motions, and its mathematical and physical description is fully contained in the derived set of governing equations for the ocean dynamic system.

[0189] The equations of motion for the wave subsystem of the ocean dynamic system.

[0190]

[0191]

[0192]

[0193]

[0194]

[0195] Equations of motion for the vortex subsystem of the marine dynamic system

[0196]

[0197]

[0198]

[0199]

[0200]

[0201] Equations of motion of the circulation subsystem of the marine dynamic system

[0202]

[0203]

[0204]

[0205]

[0206]

[0207] In all three subsystems, there are mixed terms in the momentum, temperature, and salinity equations. Taking circulation as an example, the mixed terms in the momentum, temperature, and salinity equations of the system are respectively...

[0208]

[0209]

[0210]

[0211] The mixing effect on the circulation subsystem can be obtained as a three-term sum of the averaged turbulent transport flux residue (flux divergence) on the wave and vortex sets, the averaged wave transport flux residue on the vortex sets, and the vortex transport flux residue. This mixing term is an inevitable result of the non-overlapping motion class classification, the full coverage of ocean motion, and the deterministic ergodicity of the Reynolds average defined by the motion set definition. It is beneficial for this invention to conduct analytical studies on the mixing effects of turbulence, waves, and vortices in ocean dynamic systems.

[0212] 1.2.3 Combination-Average Representation of Basic Characteristic Quantities of Turbulent Circulation Mixing Coefficient

[0213] Considering that turbulence has a three-dimensional, isotropic, and saturated equilibrium as its basic motion form, and that transport processes are large eddy behaviors, this invention can be expressed using the universal Fourier closed-form representation of turbulent transport flux.

[0214]

[0215] The basic characteristic quantities of the mixing coefficient are given. In the following representations, the kinetic energy and kinetic energy dissipation rate with a horizontal line represent the basic characteristic quantities under the basic motion mode of turbulence. FD It is in dimensional form Universal representation of the spatiotemporal scale of large eddies: The dimensional parameters written in CVD These are dimensionless universal coefficients derived from a large number of fitting results (Baumert et al. 2005).

[0216]

[0217] Prandtl number of universal Fourier closed representation of transport flux in the neutral case σ0 equal

[0218] Taking the combination-average representation of the basic characteristic quantities of the turbulent circulation mixing coefficient as an example

[0219]

[0220]

[0221]

[0222] This result indicates that the turbulent mixing term for circulation actually consists of two parts. The first part is proportional to the circulation velocity shear and the temperature-salinity gradient, and its turbulent mixing coefficient has a combination of fundamental characteristic quantities with a wave-vortex ensemble average.

[0223]

[0224] The second part is a combination-average representation of other motion-related descriptors unrelated to circulation, which reduces the problem to analytically solving for the fundamental characteristics of turbulence.

[0225] 1.2.4 The fundamental characteristic equations of turbulence and their theoretical and experimental relationships

[0226] In order to obtain the fundamental characteristic quantities of turbulence, namely kinetic energy and kinetic energy dissipation rate, this invention requires a set of equations describing their changes or theoretical and experimental relationships in the sense of saturated equilibrium.

[0227] (1) The theoretical relationship between the k-equation of turbulent kinetic energy and the basic characteristic quantities

[0228] The required fundamental characteristic quantity of turbulence: kinetic energy equation (derivation process is detailed in the appendix).

[0229]

[0230] in The single parameter introduced is the squared shear modulus of the wave-vortex-circulation composite motion velocity with density gradient correction. The density gradient correction term is a new quantity added in this invention based on the Osborn (1980) relation.

[0231] Under saturated equilibrium, the statistics of turbulence should be time- and space-invariant. Thus, according to the kinetic energy equation, this invention has a theoretical relationship of fundamental characteristic quantities.

[0232] or

[0233] According to Osborn's 1980 discussion, the term following the square root is simply 0.15 of the preceding term; therefore, this invention can always be considered as...

[0234] or

[0235] Given that the wave-descriptor in this composite motion has a larger magnitude and a smaller scale, the introduced single parameter can be approximated as a wave-dominant form. Thus, the theoretical relations of the fundamental characteristic quantities of wave-generated turbulence under the saturated equilibrium sense can be approximately written as follows:

[0236] or

[0237] Even in the sense of saturated equilibrium, to determine a set of fundamental characteristic quantities, this invention still requires another independent relationship between them. At this point, the invention first considers another fundamental characteristic quantity: the kinetic energy dissipation rate equation and another theoretical relationship, also in the sense of saturated equilibrium.

[0238] (2) Equation for turbulent kinetic energy dissipation rate ε and experimental relationship between basic characteristic quantities

[0239] The kinetic energy dissipation rate equation can be simplified as follows (see appendix for detailed derivation).

[0240]

[0241] The usual way to close the equation by the last two terms on the right-hand side is to transform it into generating terms. and the second-order dissipation term of the molecule The density gradient-corrected velocity shear generation term, proportional to the kinetic energy equation, is respectively... and molecular dissipation term -ε

[0242] Thus, the closed kinetic energy dissipation rate equation can be written in simplified form.

[0243]

[0244] Given that the theoretical relations of the fundamental characteristic quantities obtained by this equation under saturated equilibrium are insufficient to obtain nontrivial fundamental characteristic quantities together with the previously derived theoretical relations, this invention has to abandon this closed-loop result and turn to the measurement and analysis results that rely on the kinetic energy dissipation rate.

[0245] (3) Experimental relationships of fundamental turbulent characteristic quantities under saturated equilibrium

[0246] Since the latter half of the last century, researchers have developed in-situ measurement techniques for turbulent kinetic energy dissipation rates and conducted extensive studies on wave-generated turbulent mixing in the sea surface and density gradient layers. Considering that waves in the wave-vortex-circulation composite motion have larger velocity and density values ​​and smaller spatial scales, this invention can introduce a normalized relationship for the velocity shear mode, corrected for a unified turbulent dissipation rate and density gradient, for both ocean waves and internal waves.

[0247]

[0248] and

[0249]

[0250] Where x3 = DMAX represents the depth of the sea surface layer or density gradient layer. and or and These are the undetermined coefficients and exponents of the normalized experimental relationship of turbulent dissipation rates in the sea surface layer or density gradient layer, respectively.

[0251] The undetermined index can be determined using either wave-generated turbulent kinetic energy dissipation rate measurements near the sea surface layer or internal wave-generated turbulent kinetic energy dissipation rate measurements at the density gradient layer. Fitting results from a mixture of ocean and internal wave data show that the index can be uniformly determined as follows:

[0252]

[0253] This result indicates that ocean waves in the surface layer and internal waves in the density stratum, both belonging to the wave class, share the same wave-generated turbulence mechanism, which determines the same exponent value. Thus, this invention provides experimental relationships for the fundamental characteristic quantities of wave-generated turbulence (including ocean waves and internal waves) under saturation conditions.

[0254]

[0255] 1.2.5 Theoretical and Experimental Estimation of Fundamental Characteristic Quantities of Wave-Generated Turbulence under Saturated Equilibrium

[0256] This invention provides a single-parameter representation of the fundamental characteristic quantities of wave-generated turbulence under saturated equilibrium, solving for both theoretical and experimental relationships.

[0257]

[0258] and

[0259]

[0260] Thus, the present invention has an undetermined coefficient relating the depth of the sea surface layer or density gradient layer to the mixing length.

[0261]

[0262] or

[0263]

[0264] Therefore,

[0265]

[0266]

[0267] and

[0268]

[0269] This is the theoretical-experimental estimate of the fundamental characteristic quantities and mixing length in the sense of saturated equilibrium.

[0270] 1.2.6 Saturated Equilibrium Estimation of Mixing Coefficients of Wave-Generated Turbulence for Waves, Vortexes, and Circulation

[0271] The estimation of the mixing coefficient in the sense of saturated equilibrium is actually the determination of the supremum of the turbulent mixing coefficient. The present invention will provide such analytical estimates of the turbulent mixing coefficient for waves, vortices, and circulations respectively.

[0272] Taking the supremum analytical estimation of the mixing coefficient of the circulation from wave-generated turbulence as an example, the derived fundamental characteristic quantities of wave-generated turbulence are substituted into the expression of the mixing coefficient of the circulation from turbulence.

[0273]

[0274] This invention has

[0275]

[0276] and

[0277]

[0278] Similarly, taking the Reynolds average over the ensemble of fluctuations based on the fundamental motion patterns of time-stable and horizontally uniform fluctuations, and considering that the single parameter is always greater than zero and its density correction part averages zero, the mixing coefficient of turbulence on circulation can be written as:

[0279]

[0280] and

[0281]

[0282] 1.3 Global estimation of mixing coefficient of internal tidal turbulence based on satellite altimeter

[0283] 1.3.1 Research Background

[0284] Many factors influence ocean mixing, and tides are a significant one. Barotropic currents flowing through mid-ocean ridges and seamounts create baroclinic tides of the same frequency. Within stratified oceans, internal waves with tidal frequencies, known as internal tides, play a crucial role in the dissipation of global ocean energy and are one of the main mechanical energy sources for ocean mixing. They are vital for the balance of global ocean kinetic energy and heat content, as well as nutrient transport. Studies have found that the 18.6-year tidal cycle influences the climate of the North Pacific through ocean mixing, causing corresponding cyclical changes in the North Pacific. Tidal mixing in the Indonesian waters can lead to a weakening of the ENSO intensity in the eastern Pacific.

[0285] The internal wave mixing discussed in Section 1.3 is based on the wave-generated turbulent mixing coefficient derived in Section 1.2. Combined with the internal tide information extracted from the satellite altimeter and the WOA13 temperature and salinity data, the global three-dimensional structure of the internal tide-generated turbulent mixing coefficient is estimated.

[0286] 1.3.2 Extraction Method

[0287] There are five main methods commonly used to extract moisture from the interior of M2 using an altimeter:

[0288] ① Perform harmonic analysis on the time series of sea surface height (SSH) at a fixed measurement point to extract the amplitude of the M2 tidal constituent (including barotropic tide and internal tide); perform a moving average of the extracted amplitude along the track to obtain a smoothed amplitude, which is the amplitude of the barotropic tide; subtract the barotropic tide amplitude from the total amplitude to obtain the amplitude of the M2 internal tide.

[0289] ② Perform harmonic analysis on the SSH time series of fixed measurement points to extract the amplitude of M2 tidal constituents (including barotropic tides and internal tides); obtain the smoothed fitted amplitude, i.e., the amplitude of barotropic tides, by using polynomial fitting along the track; subtract the amplitude of barotropic tides from the total amplitude to obtain the amplitude of M2 internal tides.

[0290] ③ Perform high-pass filtering on the altimeter SSH data along the track (cutoff wave number is 200km-400km) to remove the barotropic tidal portion; then perform harmonic analysis to extract the internal tide of M2.

[0291] ④ Harmonic analysis was used to directly extract the internal tide signal from the sea surface height anomaly (SLA) signal along the track. The SLA data along the track was based on the SSH data with some corrections, and the barotropic tide signal was removed using the Global Tidal Wave Model (GOT99). Therefore, the amplitude and lag angle of the internal tide can be directly extracted by harmonic analysis.

[0292] ⑤ Harmonic analysis was performed using the confusion frequencies of each major tidal constituent to obtain the tidal level signal of the M2 tidal constituent; spatial high-pass filtering was performed to obtain the sea surface signal caused by the M2 internal tide; wavenumber spectrum analysis was performed to obtain the number of superimposed plane waves according to the number of peaks in the wavenumber spectrum.

[0293] The internal moisture signals obtained in the first and second methods are fluctuations in amplitude and lag angle caused by the interference of multiple internal moistures, while the internal moisture signals obtained in the third and fourth methods are the amplitude and lag angle of the internal moisture. The fifth method is much more complicated than the third and fourth methods in terms of processing steps.

[0294] Each of the above methods has its advantages and disadvantages. For the computational requirements of this invention, the third method is selected.

[0295] 1.3.3 Data Processing

[0296] The selected satellites are the TOPEX / POSEIDON (T / P) altimeter satellite, jointly launched by NASA and the French Space Agency's National Centre for Space Studies, as well as the subsequent Jason-1 and Jason-2 satellites.

[0297] The T / PJ satellite altimeter has a repeat measurement period of 9.9156 days, an interval of 5.75 km between two consecutive points along its orbit, a maximum distance of 315 km between two adjacent orbits along the latitudinal direction, and an extractable tidal information accuracy of 2.4 cm. Its orbit covers the region from 66.15°S to 66.15°N. The T / P satellite primarily carries a US dual-frequency Ku-band / 13.6 GHz and C-band / 5.3 GHz radar altimeter and a French single-frequency Ku-band / 13.65 GHz solid-state radar altimeter.

[0298] The sea surface height anomaly data along the orbit of the T / PJ satellite selected in this invention comes from AVISO (Archivings Validation and Interpretation of Satellite Oceanographic Data). The time span is from August 1992 to October 2014. To facilitate further analysis, this data was first supplemented. For missing temporal or spatial points, neighboring results were used for interpolation. To remove barotropic information from the orbital data, high-pass filtering was first applied, selecting fluctuations with a spatial wavelength within 200 km. Through these processing methods, data from 258,834 orbital satellite stations with regular temporal and spatial distributions were ultimately selected. The spatial range of these stations is approximately 66°N-66°S, 180°W-180°E, and the time span includes 254 satellite periods (…). Figure 8The sea surface height anomaly data along the track comes from AVISO (Archivings Validation and Interpretation of Satellite Oceanographic Data).

[0299] Tidal harmonic analysis was performed on the above data to obtain the intratidal harmonic constant with a global ocean tidal frequency of M2, and its amplitude results are as follows: Figure 9 As shown in the figure, strong M2 internal tides mainly occur in the waters surrounding Indonesia, the Hawaiian Islands, the 140°W area of ​​the South Pacific, and the western Indian Ocean. This is primarily due to the combined effects of steep local seafloor topography and strong seawater stratification.

[0300] Following analytical model sensitivity and validation experiments, and based on the previously processed T / PJ altimeter surface undulation data and WOA13 temperature and salinity data, the global three-dimensional internal tidal turbulence mixing coefficient can be analytically estimated. This invention primarily focuses on analyzing the characteristics of typical upper ocean water layers based on the calculation results.

[0301] Figure 18 The planar distribution map of the tidal mixing coefficient within a typical water layer at 200m globally shows that the distribution of the tidal mixing coefficient is largely consistent with the distribution of the tidal amplitude, with larger values ​​around 0 (10). -6 m 2 / s). As the depth increases to 20m, the mixing coefficient generally increases, reaching a maximum of O(10^2 / s). -5 m 2 / s). As the depth increases to 50m, the background value continues to increase, reaching a relative peak. Below 100m, there is a significant decreasing trend. This indicates that the spatial distribution of internal tidal orbital shear mixing is mainly controlled by external mechanical energy. With increasing depth, the stratification becomes larger and the mixing coefficient becomes higher, mainly controlled by stratification. The figure also shows that the external mechanical energy input and its corresponding turbulent kinetic energy dissipation rate are not a simple linear relationship; the internal wave mixing intensity is related to other factors. This also reveals the connotation that the theoretical model of this invention wants to express based on observation.

[0302] 1.4 Global estimation of mixing coefficient of internal wave-generated turbulence based on altimeter internal tide data and GM spectrum

[0303] In the previous section, this invention obtained the global distribution of the mixing coefficient of tidal turbulence within M2 based on satellite altimeter data. However, the contribution of the mixing coefficient of internal wave-generated turbulence cannot be ignored due to the contribution of gravity waves in the high-frequency band (which may be the main contributor in some sea areas). This invention mainly focuses on the realization of the high-frequency stochastic internal wave-generated turbulence mixing coefficient. This invention first studies the construction of the global internal wave spectrum; estimates the distribution characteristics of the global annual average internal wave-generated turbulence mixing coefficient (BVIW); and conducts verification experiments based on classical mixing experiments.

[0304] 1.4.1 Construction of the global internal wave spectrum

[0305] Based on the mixing coefficient formula for internally generated turbulents in the unified wave solution, this invention finds that the main parameters dependent on the mixing coefficient are the internal wave fluctuation spectrum, frequency, stratification, and horizontal wavenumber. Among these, the most challenging aspect is the global internal wave energy spectrum. Despite decades of development in internal wave dynamics, numerical calculation of the global internal wave energy spectrum is still not achievable. This is primarily because the global internal wave fluctuation spectrum cannot be directly obtained from observations, nor can its spatiotemporal variations be accurately determined based on excitation, nonlinear, and dissipation processes. Therefore, this invention can only construct the full-field internal wave fluctuation spectrum using data and existing universal GM spectra of ocean internal waves.

[0306] This invention uses the standardized internal wave spectral model GM spectrum combined with the global M2 endocytic fluctuations to estimate the global internal fluctuation spectrum, thereby enabling the calculation of high-frequency band B. VIW .

[0307]

[0308] The internal wave spectrum is constructed based on the classic mid-latitude oceanic GM spectrum. Since the GM spectrum assumes the internal wave field is horizontally isotropic, the horizontal wave number can be represented by kh without considering values ​​in different directions. kh can be uniquely determined by the dispersion relation using frequency and mode (ω, j). This invention uses the GM79 spectrum as the basis for constructing the internal wave fluctuation spectrum, improving upon some unreasonable assumptions and parameter selections in the GM72 and GM75 spectra.

[0309] The fluctuation spectrum, kinetic energy spectrum, and total energy spectrum of the internal wave per unit mass are as follows:

[0310] F ξ (ω,j)=b 2 N0N -1 (ω 2 -f 2 )ω -2 E(ω,j)

[0311] F μ (ω,j)=F μ1 +F μ2 =b 2 N0N(ω 2 +f2 )ω -2 E(ω,j) (4-72)

[0312]

[0313] F of the internal wave fluctuation spectrum ξ The sea surface portion F of (ω,j) ξ0 (ω,j) is the surface undulation spectrum Φ required in the theoretical model of this invention. IW (k1,k2). To correctly understand and apply this important spectral result, it is essential to understand its physical background and experimental basis. Observations show that the wave field within the main thermocline of the mid-latitude ocean possesses the following fundamental properties:

[0314] ①The internal wave field is basically isotropic in the horizontal direction.

[0315] ②The energy flux of the internal wave field is vertically symmetric. The upstream and downstream energy fluxes of the internal wave are statistically equal.

[0316] ③ The long-term average internal wave field energy density exhibits stability and horizontal uniformity. However, actual observations suggest that this energy density oscillates with a factor of 2 to 3, with a variation period of approximately 10 days.

[0317] Assume that ocean internal wave pulsations are formed by the superposition of waves of different frequencies, wave numbers, and amplitudes in a random linear fashion. The influence of other mean motions besides internal waves is not included.

[0318] According to the expression of the GM79 spectrum, the expression of the internal wave energy density E(ω,j) is:

[0319] E(ω,j)=B(ω)·H(j)·E (4-73)

[0320] in,

[0321]

[0322] B(ω) in (ω) 2 -f 2 ) -1 / 2 To ensure that the internal wave spectrum has near-inertial spikes, observational data was used to verify the correlation modal number j. * =3; e-reflection of N(z) b = 1.3 km; sea surface buoyancy frequency N0 = 5.2 × 10 -3 s -1 (i.e., 3 c / h); dimensionless energy parameter E = 6.3 × 10 -5 The inertial frequency at latitude 30° is f = 7.3 × 10⁻⁶. -5 s -1 .

[0323] The model spectra (5-71) to (5-73) can be used to calculate the second moment of the internal wave field.

[0324] This invention applies the above GM79 spectrum to the ocean area of ​​the Mid-latitude Pacific Ocean Storm Experiment. Figure 9 The kinetic energy spectrum F calculated by depth processing theory for a certain layer was found to be... μ (ω, j) (red dashed line) agrees well with the observed kinetic energy spectrum (black solid line). , It exhibits a spectral slope that is -2 to the power of 2. The observation data in the figure are taken from Muller and Briscoe (1999).

[0325] Similarly, Cairns and Williams (1976) observed the fluctuation spectrum F at 350m off the coast of San Diego, California. ξ (ω, j) also exhibits a similar spectral slope.

[0326] In existing technologies, the dimensionless coefficient E represents an "energy parameter," which is an approximate constant, generally within three times the standard value. This invention proposes that this parameter implicitly contains the magnitude of changing potential energy, which is proportional to the square of the undulation. Therefore, by correcting the dimensionless parameter E in the GM spectrum based on the internal tide amplitude data extracted from the altimeter, the entire sea surface undulation spectrum can theoretically be obtained.

[0327]

[0328] According to altimeter data The value of ω ranges approximately from 0.25 to 4, which is consistent with previous theoretical values. When ω is far from f, equation (5-74) can be written as:

[0329]

[0330] Therefore, the high-frequency band only lacks the structure of the f-peak, and the spectral slope is still -2. This design of the GM spectrum is also consistent with the observational understanding of this invention.

[0331] The aforementioned model spectrum provides the basis for most dynamic calculations. It is important to note that the model spectrum assumes the observed waves are linear internal waves, which is an untested assumption in certain parts of the wavenumber-frequency space.

[0332] 1.4.2 Estimation of Global Internal Wave Mixing Coefficient Based on Constructed Internal Wave Fluctuation Spectrum

[0333] Based on the revised internal wave surface undulation spectrum formula, internal tide height data, and WOA13 temperature and salinity data from the previous section, this invention obtains the global distribution of internal wave-generated turbulence mixing coefficients in the GM section. From the planar results, the internal wave mixing coefficient distribution in the GM section shows some consistency with the internal tide mixing distribution; that is, the mixing coefficient is larger in areas with rougher terrain, with larger values ​​reaching 1×10⁻⁶. -2 m 2 The mixing coefficient is around / s, because small-scale internal waves are easily broken in areas with rough terrain. With increasing depth, the mixing coefficient generally increases, with the GM band being 1-2 orders of magnitude larger than the low-frequency band, which is consistent with the observations of this invention. Simultaneously, this invention found that the internal wave mixing in the GM band has a relatively large value in the Southern Ocean. It is generally believed that the strong mixing in the Southern Ocean is caused by the Antarctic Circumpolar Current. The analytical results of this invention implicitly include the influence of the Circumpolar Current on the internal thermohaline structure, so the theoretical solution also shows this observational fact quite well. With increasing depth, the mixing coefficient in the GM band gradually increases in areas with rough terrain, while it gradually decreases in other flat areas, unlike the M2 internal tidal mixing where the mixing coefficient is largest near the seasonal thermocline.

[0334] In summary, based on the internal wave undulation spectrum, M2 internal tide data extracted from altimeters, and WOA13 temperature and salinity data, the distribution of the global internal wave shear-generated turbulence mixing coefficient (BVIW) in the GM band was obtained. The deep-sea mixing distribution, derived from surface data and theoretical models, is controlled by many external and internal factors, with different contributions in different frequency bands. The calculation results show that low-frequency mixing is mainly controlled by the temperature and salinity structure of seawater as the depth increases, while high-frequency mixing is jointly controlled by external mechanical energy and the temperature and salinity structure of seawater. The mixing coefficient is larger in areas with rough topography. These preliminary conclusions are generally consistent with offshore observations and common sense.

[0335] 1.4.3 Verification Experiment Based on Classical Turbulence Observations

[0336] (1) Verification of the theoretical model based on deep-sea turbulence observations and statistical characteristics of external mechanical energy

[0337] After the aforementioned sensitivity tests and global distribution theoretical calculations, the authors collected direct observation data of deep-sea turbulence over the past few decades as verification comparison data for the theoretical mixing coefficient BVIW. The data came from the Ocean Turbulence Database of the University of California. Figure 22 The diagram shows the locations of 31 stations in the direct turbulence observation experiment and the global topography. Among them, 20 stations, including NATRE, BBTRE97, HOME, LADDER, SOFINE, and MIXET, have observation profiles larger than 1000m and are represented by purple dots in the figure; 10 stations, including COARE, FLUX STATS, and TROPIC HEAT, have relatively shallow observation data and are represented by red dots in the figure. For detailed information on all stations, please refer to Appendix 4.

[0338] Before comparative verification, this invention extracted 12 deep-water stations with a relatively large number of observation samples (>15) and statistically analyzed their mechanical energy input from the external input of internal waves. Figure 23 The wind and tide input data come from the calculations in Chapter 3. It is not difficult to see from the global input of external mechanical energy that the contribution of internal tides to external mechanical energy is relatively large in mixed experiments such as HOME and BBTRE97. The global results also show that the contribution of internal tides is relatively large, about 5 times that of the wind field. Therefore, the input of internal tide energy can approximately represent the overall level of external mechanical energy input to the internal wave system.

[0339] The scatter plots of the dissipation rates of internal tides and wind inputs with the total water depth integral at some of the aforementioned stations in the prior art 2 study also prove the point of this invention, namely, that the correlation between internal tide input and internal wave dissipation is relatively strong, basically showing a positive proportional relationship, while the proportional relationship between wind input and internal wave dissipation is not very obvious. This statistical characteristic suggests that the theoretical model of this invention, which uses internal tides as the basis for internal wave mixing calculation, conforms to the statistical laws of turbulence, and is an index quantity that is clearly related to internal wave dissipation. The internal wave dissipation observed on the vertical axis in Figure 24 can be approximately calculated using the turbulent dissipation rate, D = ε / (1-Γ). Figure 24(a) is a graph that separates the external mechanical energy into statistics, and Figure 24(b) is a statistical graph of the overall external mechanical energy, which also confirms the aforementioned point of this invention, that internal tides can approximate the overall law. The dissipation at each deep-water station increases with the increase of internal tide input. The data from stations such as BBTRE on the 1:1 line represent the local balance between internal wave generation and dissipation. The data at the 20% dissipation line indicates that a portion of the input internal wave energy is transmitted to the surrounding sea area and cannot be entirely contributed to local internal wave mixing. The statistics from multiple stations in Figure 24(b) suggest that if the mixing rate is only estimated using external mechanical methods, this invention cannot estimate which sea areas are in a state of local equilibrium and which are propagating outwards. Therefore, the method of parameterizing the mixing rate based on the internal tidal energy input has significant uncertainty. Thus, estimating the global mixing rate using this method requires first assuming the dissipation ratio, which may yield very good results locally. As shown in the figure, the local dissipation ratio can be basically determined. Global issues will require careful study in future research. This invention proposes that the dissipation ratio can be classified based on topographic spectrum, high-mode, and low-mode internal waves, but this will not be described in detail here.

[0340] Besides the input of external mechanical energy, topographic roughness is often considered an important factor controlling the magnitude of internal wave mixing rate, and it is generally believed that the contribution of internal tides is mainly controlled by topography. Topographic roughness data are from existing technologies. Dissipation rate data are averaged across the entire water depth at the selected stations. Statistical analysis based on turbulent dissipation rate observation data and topographic roughness from the same 12 deep-water stations yielded the following results. Figure 25 .

[0341] Figure (25) shows that stations with higher roughness have a higher vertically average turbulent kinetic energy dissipation rate. Even at deep-water stations, the bottom topography still has a significant impact on the turbulent dissipation rate, not just the generally accepted impact on bottom boundary layer mixing. Topography affects internal wave mixing across the entire water depth, which supports the use of the undulation of the inner tidal surface as the basis for calculating internal wave mixing in this invention. The black numbers in the figure represent the proportion of dissipation to input energy, which decreases rapidly with increasing roughness. For example, at supercritical topography (HOME), dissipation accounts for only 5% of the internal wave radiation energy; in generally rough sea areas (BBTRE97, MIXET1), internal wave generation and dissipation are locally balanced, so the statistical points are on the 1:1 line. EXITS3 is an exception. Studies suggest that its dissipation is transmitted from elsewhere, but the topographic changes are too great, causing all the energy to be dissipated.

[0342] (2) Verification of the theoretical model profile structure based on classical turbulence observations

[0343] The M2 internal tide and GM internal wave mixing profile of the test sea area were estimated based on the theoretical solution. The results were compared and analyzed with the data measured by the turbulence meter in the experiment, which verified the aforementioned theoretical results.

[0344] Existing technology 2 selected six stations from the above locations for a comparative study of direct observation and fine-scale parameterization. The profile analysis in this section also selected the same stations for comparative study.

[0345] Figure 26(a) shows the location and topographic map of the six mixed stations. Each profile in Figure 26(b) is an average calculation based on each profile. The deviation of each station from the average is represented by a 95% confidence interval. The confidence intervals for observation and parameterization are represented by shaded areas and vertical lines, respectively.

[0346] Figure 26(b) shows the results of six deep-sea mixing experiments, including HOME. The dotted lines represent VMP measurements, and the segmented vertical lines represent results based on fine-scale stretching parameterization. In Figure 26(c), the red dotted lines represent the mixing coefficient estimated by Osborn based on VMP observations, the blue dotted lines represent the calculated BVIW of the M2 internal tide, and the orange dotted lines represent the calculated BVIW of the internal wave in the GM segment. This invention found that the theoretical results and the observed results are very similar in trend and magnitude. The vertical average deviation between the calculated BVIW of the internal wave in the GM segment and the estimated results by Osborn is within 2 × 10⁻⁶. -5 m 2 Approximately / s. In the aforementioned experiments, this invention found that the mixing coefficient formula is sensitive to certain parameters. Therefore, in order to avoid parameter adjustment, surface undulations, stratification, etc., are selected based on actual data and GM79 theoretical values ​​to avoid the arbitrariness and non-reproducibility of the verification experiment.

[0347] These sets of experiments demonstrate that the analytical model of this invention has a certain degree of rationality in the experimental water layer, and can reproduce the results of offshore observations relatively well. It can be initially used as an improved scheme in the vertical mixing scheme, and its application effect can be further verified in the circulation model.

[0348] This approach is unprecedented in the field of internal wave mixing coefficient research. Its main idea is to use known information about the ocean surface combined with the relationship between the sea surface and the interior to obtain unknown parameters of the interior.

[0349] The new method for obtaining mixing coefficients under the new dynamics framework of systems science has the following implications: it provides new directions for the study of mixing sources, including vortex mixing, etc.

[0350] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A global estimation method for a wave-generated turbulence mixing model, characterized in that, The global estimation methods for the wave-generated turbulence mixing model include: Based on the wave-generated turbulence mixing coefficient, combined with the internal tide information extracted from the satellite altimeter and the WOA13 temperature and salinity data, the global three-dimensional structure of the internal tide-generated turbulence mixing coefficient is estimated. Determine the structure of the global internal wave spectrum; estimate the global annual average internal wave-generated turbulence mixing coefficient B. VIW Distribution characteristics; The turbulent mixing coefficients generated by the fluctuations are as follows: The estimated mixing coefficient of intidal turbulence was obtained by using M2 intidal data extracted from altimeters and WOA13 temperature and salinity data, yielding the mixing coefficient B generated by global intidal wave orbit shear. VIW The distribution of the data was obtained through inversion using surface data and theoretical models. The global internal turbulence spectrum was estimated using the standardized internal wave spectral model GM spectrum combined with the global M2 internal tidal fluctuations. The dimensionless parameter E in the GM spectrum was corrected using internal tidal amplitude data extracted from altimeters. Combined with WOA13 temperature and salinity data, the internal wave-generated turbulence mixing coefficient B was determined. VIW Calculated using the following formula:

2. The global estimation method for the wave-generated turbulence mixing model as described in claim 1, characterized in that, The method for extracting internal tide information includes: performing high-pass filtering on altimeter SSH data along the track with a cutoff wavenumber of 200km-400km to remove the barotropic tide portion; and then performing harmonic analysis to extract the internal tide of M2.

3. The global estimation method for the wave-generated turbulence mixing model as described in claim 1, characterized in that, The method for extracting internal moisture information includes the following steps: (1) Acquire data on sea surface height anomalies along the satellite orbit and perform data supplementation processing; (2) High-pass filtering is applied to the processed data to select fluctuations along the track with a spatial wavelength within 200km; (3) Perform tidal harmonic analysis on the filtered data to obtain the intidal harmonic constant with global ocean tidal frequency M2.

4. The global estimation method for the wave-generated turbulence mixing model as described in claim 3, characterized in that, The process of supplementing the acquired data includes: for missing time or space measurement points, interpolating and supplementing them using nearby results.

5. The global estimation method for the wave-generated turbulence mixing model as described in claim 1, characterized in that, The construction of the global internal wave spectrum includes: estimating the global internal wave spectrum using the standardized internal wave spectrum model GM spectrum combined with the global M2 endocytic fluctuations, and calculating the high-frequency band B. VIW : The fluctuation spectrum, kinetic energy spectrum, and total energy spectrum of the internal wave per unit mass are as follows: According to the expression of the GM79 spectrum, the expression of the internal wave energy density E(ω,j) is: E(ω,j)=B(ω)·H(j)·E; B(ω)=2π -1 fω -1 (oh 2 -f 2 ) -1 / 2 , in, By correcting the dimensionless parameter E in the GM spectrum using inland tide amplitude data extracted from the altimeter, the sea surface undulation spectrum for the entire field is obtained:

6. A computer device, characterized in that, The computer device includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform a global estimation method for a wave-generated turbulence mixing model as described in any one of claims 1 to 5.

7. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the global estimation method of the wave-generated turbulence mixing model as described in any one of claims 1 to 5.

8. A global estimation system for a wave-generated turbulence mixing model that implements the global estimation method for the wave-generated turbulence mixing model according to any one of claims 1 to 5, characterized in that, The global estimation system for the wave-generated turbulence mixing model includes: The global 3D structure estimation module is used to estimate the global 3D structure based on the wave-generated turbulence mixing coefficient, combined with the internal tide information extracted by the satellite altimeter and WOA13 temperature and salinity data. The distribution characteristics estimation module is used to determine the structure of the global internal wave spectrum and estimate the distribution characteristics of the global annual average internal wave-generated turbulence mixing coefficient (BVIW).

Images