An analysis method for energy exchange between mesoscale eddy and near-inertial internal wave

Abstract

The application discloses a kind of marine mesoscale vortex and near-inertial internal wave energy exchange analysis method, belong to the technical field of ocean dynamics, including the following steps: S1, determining target mesoscale vortex area, obtaining high-resolution three-dimensional flow field data and preprocessing to obtain standardized three-dimensional flow field data;S2, by frequency domain filtering separation processing extracts near-inertial flow component and background flow component;S3, by sliding time average processing, obtain Reynolds stress component;S4, by spatial derivative calculation and strain rate derivation processing, obtain horizontal direction strain rate component;S5, substitute energy exchange equation, obtain energy exchange rate;S6, combined with seawater density, complete depth and time integration processing, obtain net energy exchange and realize energy transfer direction discrimination.The above method is used, realize the high-precision quantitative analysis of marine mesoscale vortex and near-inertial internal wave energy exchange direction and intensity and accurate discrimination of transfer direction.

Description

Technical Field

[0001] This invention relates to the field of marine dynamics technology, and in particular to a method for analyzing the energy exchange between mesoscale eddies and near-inertial internal waves in the ocean. Background Technology

[0002] Energy exchange between mesoscale eddies and near-inertial internal waves is the core mechanism of ocean energy cascade, which is crucial for driving ocean turbulent mixing, maintaining circulation structure, and regulating the global climate system. This type of technology is based on satellite remote sensing, on-site observation, or ocean reanalysis flow field data. It often uses frequency domain filtering to separate flow field components and kinetic energy difference estimation to attempt to analyze the energy transfer relationship between mesoscale eddies and near-inertial internal waves. The output results are mainly used in ocean circulation simulation, turbulent mixing mechanism research, and global climate system regulation law analysis.

[0003] However, when quantifying the energy exchange process between mesoscale eddies and near-inertial internal waves, a quantitative description of the coupling mechanism between Reynolds stress and background current strain rate is generally lacking, resulting in the following shortcomings: First, traditional methods estimate energy exchange solely through kinetic energy differences, completely ignoring the dynamic control effect of the strain field. The simplified calculation formulas used cannot capture the modulation effect of the anisotropy of near-inertial internal wave velocity fluctuations on energy transfer, leading to an overestimation of the energy exchange intensity in the eddy normal strain-dominated region by more than 20%, and a significant systematic bias in the calculation of the energy exchange rate. Second, in determining the direction of energy transfer, only the sign of energy changes is relied upon, without considering the coupling effect between the strain field and near-inertial velocity fluctuations, which easily leads to misjudgment of the eddy-wave energy transfer direction, directly causing a systematic underestimation of the energy input term in the ocean energy cascade model. Third, the above-mentioned biases and misjudgments ultimately lead to serious distortion in the ocean energy balance analysis, severely restricting the parameterization accuracy of the energy input in the ocean circulation model, and failing to provide accurate and reliable quantitative technical support for the study of multi-scale energy interactions in the ocean. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves, thereby solving the aforementioned technical problems.

[0005] To achieve the above objectives, this invention provides a method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves, comprising the following steps:

[0006] S1. Determine the target mesoscale eddy region based on satellite remote sensing and typhoon data, acquire high-resolution three-dimensional flow field data covering the target mesoscale eddy region and complete data preprocessing to obtain standardized three-dimensional flow field data.

[0007] S2. Based on the standardized three-dimensional flow field data of S1, frequency domain filtering and separation processing are performed to extract the near-inertial flow component and background flow component through bandpass filters, so as to obtain the near-inertial flow meridional / zonal velocity and the background flow meridional / zonal velocity.

[0008] S3, based on the near-inertial flow meridional / zonal velocity of S2, the Reynolds stress components are obtained by sliding time averaging.

[0009] S4. Based on the background meridional / zonal velocity of S2, the horizontal strain rate component is obtained through spatial derivative calculation and strain rate derivation.

[0010] S5, based on the Reynolds stress component of S3 and the horizontal strain rate component of S4, are quantitatively calculated by substituting them into the preset energy exchange equation to obtain the energy exchange rate between the mesoscale eddy and the near-inertial flow.

[0011] S6. Based on the energy exchange rate of S5, the depth and time are integrated by combining the seawater density to obtain the net energy exchange between the mesoscale eddy and the near-inertial internal wave and to determine the direction of energy transfer.

[0012] Preferably, in step S1, based on the spatiotemporal range characteristics of the target mesoscale eddy region, the spatiotemporal range of the high-resolution three-dimensional flow field data is set to be larger than the target mesoscale eddy region. At the same time, the high-resolution three-dimensional flow field data is interpolated to the ocean standard layer in the depth direction to complete the data standardization preprocessing and obtain standardized three-dimensional flow field data containing meridional and zonal flow velocity information.

[0013] Preferably, the high-resolution three-dimensional flow field data mentioned in S1 is satellite altimeter remote sensing data, ocean reanalysis dataset, or ocean field observation data.

[0014] Preferably, the specific steps of S2 include:

[0015] S21. Based on the standardized three-dimensional flow field data of S1, extract the original meridional and zonal velocity field data with a duration of no less than thirty days. Perform depth averaging on the original velocity field data to obtain the baroclinic velocity. Subtract the corresponding baroclinic velocity from the original velocity field data to obtain the zonal component of the baroclinic velocity. and meridional components ;

[0016] S22, Based on the center latitude of the target mesoscale vortex region Calculate its corresponding inertial frequency. The calculation formula is:

[0017] ;

[0018] in, This is the Earth's rotational angular velocity;

[0019] S23, at the inertial frequency of S22 The core parameter is used to design the passband frequency range as follows: bandwidth is A fourth-order Butterworth bandpass filter;

[0020] S24, the baroclinic flow velocity of S21 , The input is a fourth-order Butterworth bandpass filter, which filters to obtain the near-inertial flow radial component. and latitudinal components ;

[0021] S25, The preset low-pass filter cutoff frequency is: The baroclinic flow velocity , The filter is then applied again to a fourth-order Butterworth bandpass filter to obtain the background flow radial component. and latitudinal components .

[0022] Preferably, the specific steps of S3 include:

[0023] S31, Near-inertial flow radial component based on S24 and latitudinal components Calculate the self-multiplication and cross-multiplication values ​​of the flow velocity, respectively. , and ;

[0024] S32, inertial frequency based on S22 Calculate the period of inertia The calculation formula is:

[0025] ;

[0026] And the moving average window covering three near-inertial periods was determined as... ;

[0027] S33, S31's , and According to window length The Reynolds stress components are obtained by performing a time-moving average. , and .

[0028] Preferably, the specific steps of S4 include:

[0029] S41, Longitude based on the target mesoscale vortex region and latitude The latitude and longitude grid spacing of the flow field data is converted to metric actual distance using the following formula:

[0030] ; ;

[0031] in This is the difference in longitude. This is the difference in latitude. , Latitude and longitude;

[0032] S42, Transfer the background flow radial component of S25 and latitudinal components And the actual metric distance of S41 and The spatial partial derivatives are calculated using a second-order central difference scheme. The formula is as follows:

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] in, Background flow zonal component First-order partial derivative along the x-direction; Background flow zonal component First-order partial derivative along the y-direction; Background flow through component First-order partial derivative along the x-direction; Background flow radial component First-order partial derivative along the y-direction;

[0038] S43, Spatial partial derivatives obtained based on S42 , , , Calculate the normal strain rate components in the horizontal direction. and tangential strain rate components The calculation formula is:

[0039] ;

[0040] .

[0041] Preferably, the specific steps of S5 include:

[0042] S51, the Reynolds stress components from step S33 , , Strain rate components of S43 , As input parameters to the equation, an energy exchange equation is constructed, and the equation formula is as follows:

[0043] ;

[0044] in, Energy exchange rate;

[0045] S52. Substitute the input parameters into the energy exchange equation in S51 and perform point-by-point and time-by-time calculations to obtain the output parameter, energy exchange rate. Energy exchange rate A physical quantity that varies with space, time, and depth.

[0046] Preferably, the specific steps of S6 include:

[0047] S61. Collect seawater temperature, salinity, and pressure data in the target mesoscale eddy region, and input them into the seawater state equation UNESCOEOS-80 to calculate the seawater density as a function of space, time, and depth. ;

[0048] S62. Determine the depth range of influence of the target mesoscale eddy. and time range And based on the energy exchange rate of S52 Seawater density with S61 The formulas for depth integration and time integration are as follows:

[0049] ;

[0050] in, Net energy exchange rate; For the time period and depth The specific values ​​of energy exchange between mesoscale eddies and near-inertial internal waves within the range;

[0051] S63, Based on net energy exchange The sign of the value determines the direction of energy transfer: when When the value is positive, energy is transferred from the mesoscale eddy to the near-inertial internal wave; when... When the value is negative, energy is transferred from near-inertial internal waves to mesoscale eddies.

[0052] Therefore, the present invention employs the above-mentioned method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves, which has the following beneficial effects:

[0053] 1. A closed-loop analysis system was constructed, encompassing the entire process from selecting the target mesoscale eddy region, preprocessing flow field data, separating the near-inertial flow from the background flow in the frequency domain, calculating Reynolds stress and strain rate parameters, modeling the energy exchange rate, to quantifying the net energy exchange and determining the direction. This system formed a standardized and reproducible eddy-wave energy exchange analysis process, realizing a systematic analysis of the entire chain of energy exchange processes between mesoscale eddies and near-inertial internal waves, and providing a complete and standardized technical path for ocean energy cascade research.

[0054] 2. A fourth-order Butterworth filtering technique, employing baroclinic-barotropic velocity separation and inertial frequency adaptation, achieves high-precision frequency domain separation between near-inertial flow and background flow. The stability of the filter is ensured by using over 30 days of time-series data. Bandpass filtering accurately extracts near-inertial flow components. Bandpass filtering at the cutoff frequency extracts the background flow component, eliminating interference from the barotropic flow field and providing high-fidelity basic flow field data, thus ensuring the reliability of the analysis results from the source.

[0055] 3. By constructing a quantitative coupled energy exchange equation between Reynolds stress and background flow strain rate, and accurately calculating the Reynolds stress component of the near-inertial flow using a moving average of three inertial periods, and combining this with a second-order central difference scheme to solve for the normal and tangential strain rates of the background flow field, the nonlinear coupling of the two is incorporated into the energy exchange rate calculation, reducing the systematic bias in the energy exchange rate calculation and realizing a high-precision quantitative calculation of the vortex-wave energy exchange process.

[0056] 4. Based on the UNESCO EOS-80 seawater state equation, the spatiotemporally dynamic seawater density was calculated. Combined with the energy exchange rate, a double integral of depth and time was completed within the eddy influence range, achieving accurate quantification of net energy exchange across all water depths and time periods. At the same time, a standardized energy transfer direction discrimination mechanism was established through the positive and negative characteristics of the integral results, clarifying the energy transfer path between mesoscale eddies and near-inertial internal waves, providing core quantitative indicators for ocean energy balance analysis.

[0057] 5. It possesses strong multi-source data compatibility and scenario adaptability, and is compatible with various mainstream ocean current field data sources such as satellite altimeter remote sensing data, ocean reanalysis datasets, and ocean field observation data. After standardized preprocessing, all types of data can be incorporated into the analysis process of this method, constructing a generalized eddy-wave energy exchange research technology framework. It can be widely applied to research scenarios such as ocean circulation diagnosis, near-inertial energy propagation and dissipation assessment under different sea areas and observation conditions. At the same time, it can provide high-precision energy input parameters for ocean circulation models, improving the reliability of ocean thermohaline circulation and global climate system simulation.

[0058] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0059] Figure 1 A flowchart illustrating an analysis method for energy exchange between ocean mesoscale eddies and near-inertial internal waves, provided by this invention.

[0060] Figure 2 The scale eddy distribution diagram corresponding to the 7 / 11 time period in an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention;

[0061] Figure 3 The scale eddy distribution map corresponding to the 7 / 14 time period in an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention;

[0062] Figure 4 The scale eddy distribution map corresponding to the 7 / 17 time period in an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention;

[0063] Figure 5 The scale eddy distribution map corresponding to the 7 / 20 time period in an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention;

[0064] Figure 6 The scale eddy distribution map corresponding to time 7 / 23 in an embodiment of the ocean mesoscale eddy and near-inertial internal wave energy exchange analysis method provided by the present invention;

[0065] Figure 7 The scale eddy distribution map corresponding to time 7 / 26 in an embodiment of the ocean mesoscale eddy and near-inertial internal wave energy exchange analysis method provided by the present invention;

[0066] Figure 8 The scale eddy distribution map corresponding to time 7 / 29 in an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention;

[0067] Figure 9 The scale eddy distribution diagram corresponding to the 8 / 1 time period in an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention;

[0068] Figure 10 In an embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention, the depth-time distribution map of energy exchange between mesoscale eddies and near-inertial internal waves at point A1 of the corresponding scale eddy distribution map is shown.

[0069] Figure 11The embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention is a depth-time distribution map of energy exchange between mesoscale eddies and near-inertial internal waves at point A2 of the corresponding scale eddy distribution map.

[0070] Figure 12 The embodiment of the energy exchange analysis method between ocean mesoscale eddies and near-inertial internal waves provided by the present invention is a depth-time distribution map of energy exchange between mesoscale eddies and near-inertial internal waves at point A3 of the corresponding scale eddy distribution map.

[0071] Figure 13 This is a depth-time distribution map of the energy exchange between mesoscale eddies and near-inertial internal waves at point A4 in an embodiment of the energy exchange analysis method between mesoscale eddies and near-inertial internal waves provided by the present invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0073] It should be noted that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of units or components, not necessarily limited to those explicitly listed, but may include other units or components not explicitly listed or inherent to those processes, methods, products, or equipment.

[0074] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0075] Existing technologies for analyzing energy exchange between mesoscale eddies and near-inertial internal waves in the ocean generally lack a quantitative description of the coupling mechanism between the Reynolds stress of near-inertial currents and the strain rate of the background current of mesoscale eddies. They rely solely on simplistic estimations based on kinetic energy differences, which fail to capture the modulation effect of the anisotropy of near-inertial internal wave velocity fluctuations on energy transfer. This leads to a systematic overestimation of the energy exchange intensity in the eddy strain-dominated region and frequent misjudgments of the transfer direction. Furthermore, the lack of a standardized quantitative analysis system for the entire process results in significant deviations in energy exchange calculations and unclear physical mechanisms, severely restricting the parameterization accuracy of energy inputs in ocean circulation models and the development of ocean energy cascade research.

[0076] Based on the above analysis, this invention is designed, see appendix. Figure 1 A method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves includes the following steps:

[0077] S1. Determine the target mesoscale eddy region based on satellite remote sensing and typhoon data, acquire high-resolution three-dimensional flow field data covering the target mesoscale eddy region and complete data preprocessing to obtain standardized three-dimensional flow field data.

[0078] In step S1, based on the spatiotemporal range characteristics of the target mesoscale eddy region, the spatiotemporal range of the high-resolution three-dimensional flow field data is set to be larger than the target mesoscale eddy region. At the same time, the high-resolution three-dimensional flow field data is interpolated to the ocean standard layer in the depth direction to complete the data standardization preprocessing and obtain standardized three-dimensional flow field data containing meridional and zonal velocity information.

[0079] The high-resolution three-dimensional flow field data mentioned in S1 are satellite altimeter remote sensing data, ocean reanalysis datasets, or ocean field observation data.

[0080] S2. Based on the standardized three-dimensional flow field data of S1, frequency domain filtering and separation processing are performed to extract the near-inertial flow component and background flow component through bandpass filters, so as to obtain the near-inertial flow meridional / zonal velocity and the background flow meridional / zonal velocity.

[0081] The specific steps of S2 include:

[0082] S21. Based on the standardized three-dimensional flow field data of S1, extract the original meridional and zonal velocity field data with a duration of no less than thirty days. Perform depth averaging on the original velocity field data to obtain the baroclinic velocity. Subtract the corresponding baroclinic velocity from the original velocity field data to obtain the zonal component of the baroclinic velocity. and meridional components The calculation formula is:

[0083] ;

[0084] ;

[0085] in, , These are the zonal and meridional components of the baroclinic velocity, respectively. , These are the zonal and meridional components of the barotropic velocity, respectively. , These are the zonal and meridional velocity components of the original flow field, respectively.

[0086] S22, Based on the center latitude of the target mesoscale vortex region Calculate its corresponding inertial frequency. The calculation formula is:

[0087] ;

[0088] in, Let be the Earth's rotational angular velocity, and ;

[0089] S23, at the inertial frequency of S22 The core parameter is used to design the passband frequency range as follows: bandwidth is A fourth-order Butterworth bandpass filter was used to cover near-inertial wave characteristics;

[0090] S24, the baroclinic flow velocity of S21 , The input is a fourth-order Butterworth bandpass filter, which filters to obtain the radial component of the near-inertial flow. and latitudinal components ;

[0091] S25, The preset low-pass filter cutoff frequency is: The baroclinic flow velocity , The filter is input again into a fourth-order Butterworth bandpass filter to obtain the background flow radial component. and latitudinal components .

[0092] S3, based on the near-inertial flow meridional / zonal velocity of S2, the Reynolds stress components are obtained by sliding time averaging.

[0093] The specific steps of S3 include:

[0094] S31, Near-inertial flow radial component based on S24 and latitudinal components Calculate the self-multiplication and cross-multiplication values ​​of the flow velocity, respectively. , and ;

[0095] S32, inertial frequency based on S22 Calculate the period of inertia The calculation formula is:

[0096] ;

[0097] And the moving average window covering three near-inertial periods was determined as... ;

[0098] S33, S31's , and According to window length The Reynolds stress components are obtained by performing time-moving average processing. , and .

[0099] S4. Based on the background meridional / zonal velocity of S2, the horizontal strain rate component is obtained through spatial derivative calculation and strain rate derivation.

[0100] The specific steps of S4 include:

[0101] S41, Longitude based on the target mesoscale vortex region and latitude The latitude and longitude grid spacing of the flow field data is converted to metric actual distance using the following formula:

[0102] ; ;

[0103] in This is the difference in longitude. This is the difference in latitude. , Latitude and longitude;

[0104] S42, Transfer the background flow radial component of S25 and latitudinal components And the actual metric distance of S41 and The spatial partial derivatives are calculated using a second-order central difference scheme. The formula is as follows:

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] in, Background flow zonal component First-order partial derivative along the x-direction; Background flow zonal component The first-order partial derivative along the y-direction; Background flow through component First-order partial derivative along the x-direction; Background flow radial component The first-order partial derivative along the y-direction;

[0110] S43, Spatial partial derivatives obtained based on S42 , , , Calculate the normal strain rate components in the horizontal direction. and tangential strain rate components The calculation formula is:

[0111] ;

[0112] .

[0113] S5, based on the Reynolds stress component of S3 and the horizontal strain rate component of S4, are quantitatively calculated by substituting them into the preset energy exchange equation to obtain the energy exchange rate between the mesoscale eddy and the near-inertial flow.

[0114] The specific steps of S5 include:

[0115] S51, the Reynolds stress components from step S33 , , Strain rate components of S43 , As input parameters to the equation, an energy exchange equation is constructed, and the equation formula is as follows:

[0116] ;

[0117] in, Energy exchange rate;

[0118] S52. Substitute the input parameters into the energy exchange equation in S51 and perform point-by-point and time-by-time calculations to obtain the output parameter, energy exchange rate. Energy exchange rate A physical quantity that varies with space, time, and depth.

[0119] S6. Based on the energy exchange rate of S5, the depth and time are integrated by combining the seawater density to obtain the net energy exchange between the mesoscale eddy and the near-inertial internal wave and to determine the direction of energy transfer.

[0120] The specific steps of S6 include:

[0121] S61. Collect seawater temperature, salinity, and pressure data in the target mesoscale eddy region, and input them into the seawater state equation UNESCOEOS-80 to calculate the seawater density as a function of space, time, and depth. ;

[0122] S62. Determine the depth range of influence of the target mesoscale eddy. and time range And based on the energy exchange rate of S52 Seawater density with S61 The formulas for depth integration and time integration are as follows:

[0123] ;

[0124] in, Net energy exchange rate; For the time period and depth The specific values ​​of energy exchange between mesoscale eddies and near-inertial internal waves within the range;

[0125] S63, Based on net energy exchange The sign of the value determines the direction of energy transfer: when When the value is positive, energy is transferred from the mesoscale eddy to the near-inertial internal wave; when... When the value is negative, energy is transferred from near-inertial internal waves to mesoscale eddies.

[0126] Based on a specific embodiment of the above steps, this invention selects two anticyclones in a certain sea area during summer, determines the target mesoscale vortex region based on satellite remote sensing and typhoon data, and roughly estimates that the movement range of these two anticyclones in July is approximately between 14°N and 19°N and between 110°E and 116°E. During this period, the passing of typhoons excites strong near-inertial internal waves, and the energy exchange between the anticyclones and the near-inertial internal waves is calculated.

[0127] Specifically, high-resolution three-dimensional flow field data for July were collected, covering a rectangular region with a spatiotemporal range larger than the estimated area (13°N to 20°N, 109°E to 116°E). Data preprocessing was performed, and the 40 layers of 0.083° × 0.083° high-resolution data provided by the reanalysis data were vertically interpolated to the standard layer. Based on sea surface height anomaly (SLA) data provided by satellite altimeters, a mesoscale eddy time distribution map of this region was plotted, as shown below. Figure 2-9 As shown.

[0128] Subsequently, the original meridional and zonal velocity field data were extracted. The baroclinic velocity was separated by depth averaging and removed from the original flow field to obtain the baroclinic velocity, thus eliminating the interference of the baroclinic flow field on subsequent analysis. Then, based on the latitude of the target area, the inertial frequency was calculated, and a fourth-order Butterworth bandpass filter was designed to filter the baroclinic velocity, accurately separating the meridional and zonal components of the near-inertial flow from the meridional and zonal components of the background flow.

[0129] For the near-inertial velocity obtained by filtering, the self-multiplication and mutual multiplication values ​​of the velocity are first calculated, and then the inertial period is calculated based on the local inertial frequency. A sliding window covering three inertial periods is selected for time moving average, and finally three key Reynolds stress components are obtained. For the separated background flow velocity, the latitude and longitude grid spacing is first converted to the actual distance in meters, and then the four spatial partial derivatives of the background flow velocity are calculated using the second-order central difference scheme. Based on this, the normal strain rate component and the tangential strain rate component in the horizontal direction are obtained. Finally, the Reynolds stress component and the strain rate component are substituted into the energy exchange coupling equation constructed in this invention to complete the point-by-point, time-by-time, and depth-varying energy exchange rate calculation in the target area, realizing a refined solution of the vortex-wave energy exchange process.

[0130] Based on seawater temperature, salinity, and pressure data of the target area, the spatiotemporally dynamic seawater density was calculated using the UNESCO EOS-80 seawater state equation. This density was then combined with the energy exchange rate, and a double integral of depth and time was performed within the depth and time range of the vortex influence to obtain the net energy exchange between the two anticyclones and the near-inertial internal wave. Furthermore, the positive and negative characteristics of the integral results accurately determined the direction of energy transfer between the mesoscale vortex and the near-inertial internal wave. (See also...) Figure 10-13 As shown in the figure, this embodiment also selected four representative points inside and outside the vortex to intuitively present the spatiotemporal distribution law of vortex-wave energy exchange. This not only verifies the adaptability of the method to the analysis of vortex-wave energy exchange under the influence of typhoons, but also proves the operability and promotion value of the method in actual ocean dynamics research.

[0131] In summary, by constructing a standardized analysis method covering the entire process—from selecting the target vortex region, preprocessing flow field data, and achieving high-precision frequency domain separation of near-inertial and background flows, to accurately solving Reynolds stress and strain rate, modeling the energy exchange equations of their nonlinear coupling, and finally quantifying net energy exchange and determining the direction of transfer—this method achieves high-precision, systematic quantitative analysis of the direction and intensity of energy exchange between mesoscale eddies and near-inertial internal waves. It also reveals the physical nature of eddy-wave energy exchange, provides high-precision energy input parameters for ocean circulation models, and improves the reliability of ocean thermohaline circulation and climate system simulations. Furthermore, the method is compatible with multi-source data such as satellite altimeters, ocean reanalysis, and field observations, constructing a general technical framework. This method solves the problems of quantification distortion and unclear mechanism analysis of eddy-wave energy exchange in ocean energy cascade studies, achieving a technological breakthrough from empirical estimation to precise quantitative description in the analysis of energy exchange between ocean mesoscale eddies and near-inertial internal waves. It provides core methodological and theoretical support for related research and applications in the field of ocean dynamics.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves, characterized in that, Includes the following steps: S1. Determine the target mesoscale eddy region based on satellite remote sensing and typhoon data, acquire high-resolution three-dimensional flow field data covering the target mesoscale eddy region and complete data preprocessing to obtain standardized three-dimensional flow field data. S2. Based on the standardized three-dimensional flow field data of S1, frequency domain filtering and separation processing are performed to extract the near-inertial flow component and background flow component through bandpass filters, so as to obtain the near-inertial flow meridional / zonal velocity and the background flow meridional / zonal velocity. S3, based on the near-inertial flow meridional / zonal velocity of S2, the Reynolds stress components are obtained by sliding time averaging. S4. Based on the background meridional / zonal velocity of S2, the horizontal strain rate component is obtained through spatial derivative calculation and strain rate derivation. The specific steps of S4 include: S41, Longitude based on the target mesoscale vortex region and latitude The latitude and longitude grid spacing of the flow field data is converted to metric actual distance using the following formula: ； ； in This is the difference in longitude. This is the difference in latitude. , Latitude and longitude; S42, Transfer background flow through component and latitudinal components And the actual metric distance of S41 and The spatial partial derivatives are calculated using a second-order central difference scheme. The formula is as follows: ； ； ； ； in, Background flow zonal component First-order partial derivative along the x-direction; Background flow zonal component First-order partial derivative along the y-direction; Background flow radial component First-order partial derivative along the x-direction; Background flow radial component First-order partial derivative along the y-direction; S43, Spatial partial derivatives obtained based on S42 , , , Calculate the normal strain rate components in the horizontal direction. and tangential strain rate components The calculation formula is: ； ； S5, based on the Reynolds stress component of S3 and the horizontal strain rate component of S4, are quantitatively calculated by substituting them into the preset energy exchange equation to obtain the energy exchange rate between the mesoscale eddy and the near-inertial flow. The specific steps of S5 include: S51, Reynolds stress components , , Strain rate components of S43 , As input parameters to the equation, an energy exchange equation is constructed, and the equation formula is as follows: ； in, Energy exchange rate; S52. Substitute the input parameters into the energy exchange equation in S51 and perform point-by-point and time-by-time calculations to obtain the output parameter, energy exchange rate. Energy exchange rate A physical quantity that varies with space, time, and depth; S6. Based on the energy exchange rate of S5, the depth and time are integrated by combining the seawater density to obtain the net energy exchange between the mesoscale eddy and the near-inertial internal wave and to determine the direction of energy transfer.

2. The method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves according to claim 1, characterized in that: In step S1, based on the spatiotemporal range characteristics of the target mesoscale eddy region, the spatiotemporal range of the high-resolution three-dimensional flow field data is set to be larger than the target mesoscale eddy region. At the same time, the high-resolution three-dimensional flow field data is interpolated to the ocean standard layer in the depth direction to complete the data standardization preprocessing and obtain standardized three-dimensional flow field data containing meridional and zonal velocity information.

3. The method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves according to claim 2, characterized in that: The high-resolution three-dimensional flow field data mentioned in S1 are satellite altimeter remote sensing data, ocean reanalysis datasets, or ocean field observation data.

4. The method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves according to claim 3, characterized in that: The specific steps of S2 include: S21. Based on the standardized three-dimensional flow field data of S1, extract the original meridional and zonal velocity field data with a duration of no less than thirty days. Perform depth averaging on the original velocity field data to obtain the baroclinic velocity. Subtract the corresponding baroclinic velocity from the original velocity field data to obtain the zonal component of the baroclinic velocity. and meridional components ; S22, Latitude based on the target mesoscale vortex region Calculate its corresponding inertial frequency. The calculation formula is: ； in, This is the Earth's rotational angular velocity; S23, at the inertial frequency of S22 The core parameter is used to design the passband frequency range as follows: bandwidth is A fourth-order Butterworth bandpass filter; S24, the baroclinic flow velocity of S21 , The input is a fourth-order Butterworth bandpass filter, which filters to obtain the radial component of the near-inertial flow. and latitudinal components ; S25, The preset low-pass filter cutoff frequency is: The baroclinic flow velocity , The filter is input again into a fourth-order Butterworth bandpass filter to obtain the background flow radial component. and latitudinal components .

5. The method for analyzing the energy exchange between oceanic mesoscale eddies and near-inertial internal waves according to claim 4, characterized in that: The specific steps of S3 include: S31, Near-inertial flow radial component based on S24 and latitudinal components Calculate the self-multiplication and cross-multiplication values ​​of the flow velocity, respectively. , and ; S32, inertial frequency based on S22 Calculate the period of inertia The calculation formula is: ； And the moving average window covering three near-inertial periods was determined as... ; S33, S31's , and According to window length The Reynolds stress components are obtained by performing time-moving average processing. , and .

6. The method for analyzing the energy exchange between ocean mesoscale eddies and near-inertial internal waves according to claim 5, characterized in that: The specific steps of S6 include: S61. Collect seawater temperature, salinity, and pressure data in the target mesoscale eddy region, and input them into the seawater state equation UNESCOEOS-80 to calculate the seawater density as a function of space, time, and depth. ; S62. Determine the depth range of influence of the target mesoscale eddy. and time range And based on the energy exchange rate of S52 Seawater density with S61 The formulas for depth integration and time integration are as follows: ； in, Net energy exchange rate; For the time period and depth The specific values ​​of energy exchange between mesoscale eddies and near-inertial internal waves within the range; S63, Based on net energy exchange The sign of the value determines the direction of energy transfer: when When the value is positive, energy is transferred from the mesoscale eddy to the near-inertial internal wave; when... When the value is negative, energy is transferred from near-inertial internal waves to mesoscale eddies.

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