A kind of surge gradient calculation system

Abstract

The application discloses a kind of systems of surge steepness calculation, it is related to fluid water conservancy technical field, the system includes: surge parameter perception unit, for collecting the water depth time series data and water flow image data of target river reach before and after surge occurs;Surge characteristic solution unit is used to extract tidal static water depth and surge peak height, and the relative Froude number of the surge is solved;Surge form adaptive discrimination engine is used to discriminate that surge is in undulating form of non-breaking or has broken the broken form of water surface;Undulating steepness calculation sub-core responds to the discrimination for undulating form, and the average steepness and maximum steepness of the surge are output;Broken steepness calculation sub-core responds to the discrimination for broken form, and the average steepness and theoretical extreme steepness of the surge are output.The application scheme can realize the fundamental change from traditional mode of relying on dense time series observation data and experience fitting to universal calculation method based on strict theoretical model and basic parameters.

Description

Technical Field

[0001] This invention relates to the field of fluid hydraulics technology, and in particular to a tidal surge steepness calculation system. Background Technology

[0002] Tidal bores, a highly nonlinear hydrodynamic phenomenon occurring in estuaries, bays, and other special topography, have steep walls of water at their leading edge that are key parameters characterizing their intensity, energy concentration, and potential destructive power. Accurate quantification of tidal bore steepness is of paramount scientific and practical significance for disaster prevention and mitigation in estuarine and coastal engineering, structural design of water-related projects, and a deeper understanding of fundamental estuarine dynamic processes such as tidal wave deformation, energy dissipation, and sediment transport. For a long time, the engineering and academic communities have been dedicated to finding a method for calculating tidal bore steepness that balances theoretical rigor with practical convenience, aiming to overcome the limitations of traditional methods and provide reliable and unified theoretical tools and technical standards for related applications.

[0003] Currently, the acquisition of tidal bore steepness mainly relies on field prototype observations, physical model experiments, or empirical fitting based on observational data. These methods generally have significant limitations: First, they are highly dependent on dense, high-precision field water level and velocity time-series data, which is not only costly and difficult to implement, but also makes it difficult to guarantee the reliability and completeness of data acquisition under harsh hydrological conditions; Second, existing empirical formulas or semi-empirical methods are usually based on local data from specific stations or tidal bore morphologies, resulting in poor universality and difficulty in extending to different hydrogeological conditions and tidal bore morphologies; Third, there is a lack of a unified theoretical framework to directly and explicitly correlate the basic parameters of tidal bore with steepness, leading to insufficient theoretical explanatory power and fragmented and unsystematic calculation methods; Fourth, the determination of the critical morphology of the transition from wave-like to breaking tidal bore relies heavily on subjective experience or additional complex flow field measurements, making it impossible to achieve rapid and objective discrimination based on simple and readily available parameters. These shortcomings severely restrict the efficient and accurate application of tidal bore steepness in engineering practice and scientific research. Therefore, based on the above problems, this invention proposes a tidal bore steepness calculation system. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a tidal surge steepness calculation system. This system establishes a direct and explicit theoretical correlation between the basic parameters of the tidal surge and its steepness, constructing a unified calculation system capable of adaptively identifying the tidal surge morphology and outputting corresponding steepness parameters accordingly. This provides a reliable theoretical tool and technical standard for the convenient, accurate, and universal quantification of tidal surge steepness.

[0005] To achieve the above objectives, this invention provides a tidal bore steepness calculation system. The core of this system lies in constructing a theoretical model with the relative Froude number of the tidal bore as the key criterion and calculation hub. First, based on the one-dimensional tidal bore fundamental equations, a definite functional relationship between tidal bore intensity and the relative Froude number is rigorously derived. Then, independent steepness calculation sub-models are established for two morphologies: undulating and breaking tidal bores. For undulating tidal bores, the solitary wave theory is used to describe their wavefront, and by introducing characteristic wavelengths as parameters and coupling with mass conservation conditions, theoretical expressions for their average and maximum steepness are derived. For breaking tidal bores, in a coordinate system moving with the front, based on the kinematic breaking condition of wave crest particles being vertically projected by gravitational acceleration, a time-averaged height-length development relationship is established, thereby deriving an expression for their average steepness. Finally, by using the theoretical maximum average steepness of the breaking tidal bore as a physical constraint, the critical Froude number for maintaining the morphology of undulating tidal bores is determined through inversion, thus forming a logically self-consistent and complete calculation method that can automatically determine the morphology based on input basic parameters and select the appropriate formula to calculate the entire set of steepness parameters.

[0006] In a first aspect, the present invention provides a tidal surge steepness calculation system, comprising:

[0007] The tidal bore parameter sensing unit is used to simultaneously collect time-series data of water depth and water flow image data of the target river section before and after the tidal bore occurs;

[0008] The tidal bore feature calculation unit is used to extract the pre-tidal still water depth and tidal bore peak height from the water depth time series data, and calculate the relative Froude number of the tidal bore based on the preset tidal bore intensity-Froude number mapping model.

[0009] The tidal bore morphology adaptive discrimination engine has a built-in morphological critical model derived from the physical constraints of the extreme steepness of the wavy tidal bore, which is used to automatically determine whether the tidal bore is in a non-fragmented wavy morphology or a fragmented morphology in which the water surface has broken according to the relative Froude number.

[0010] The core of the wavy steepness calculation, in response to the determination that it is a wavy shape, calls the first calculation model based on the solitary wave theory and coupled with the mass conservation condition, and outputs the average steepness and maximum steepness of the tidal bore;

[0011] The core of the fracture steepness calculation, in response to the determination of a fracture mode, calls the second calculation model based on kinematic fracture conditions and constructs time-averaged physical relationships in a moving coordinate system, and outputs the average steepness and theoretical extreme steepness of the tidal bore;

[0012] The result fusion and output interface is used to integrate and output a complete set of steepness parameters corresponding to the tidal bore pattern.

[0013] Furthermore, the pre-set tidal surge intensity-Froude number mapping model in the tidal surge characteristic calculation unit is a theoretical model derived by combining the one-dimensional continuity equation and the motion equation of tidal surge propagation. It is a model that represents the unique deterministic functional relationship between the ratio of tidal surge height to pre-tidal water depth and the relative Froude number. This model ensures the theoretical rigor and unique determinism of the conversion process from basic parameters to core discrimination indicators.

[0014] Furthermore, the discrimination threshold in the morphological critical model is obtained by substituting the physical upper limit of the average steepness of the broken tidal bore into the expression for the maximum steepness in the theoretical model on which the core of the wave steepness calculation sub-model depends, and solving for the critical Froude number. This method realizes the theoretical derivation of the morphological critical value based on unified physical constraints, ensuring the objectivity of the discrimination logic and the consistency of the theory.

[0015] Furthermore, the tidal bore morphology adaptive discrimination engine further includes a morphology continuity discrimination module, which is used to assess the degree of energy dissipation of the tidal bore during its propagation process and construct a morphology continuity transition function based on this to achieve smooth and continuous determination and weight allocation of the tidal bore morphology from non-fragmented to completely fragmented states.

[0016] Furthermore, the first computational model is constructed in the following manner:

[0017] An isolated wave function is used to characterize the wave surface morphology of undulating tidal bores. To overcome the problem of the theoretical infinite wavelength, a characteristic wavelength definition parameter is introduced. Based on the condition that the volume of the water body enclosed by the wave surface morphology and the volume of an equivalent characteristic triangle of water body are conserved, a self-consistent equation for the characteristic wavelength definition parameter is established. After solving the parameter, an explicit function of the average steepness of the undulating tidal bore with the relative Froude number as the only variable is finally derived, thus theoretically solving the problem of characteristic scale quantification of infinite wavelength waveforms.

[0018] Furthermore, the core of the wave steepness calculation also directly generates a wave tidal bore maximum local steepness calculation function that shares the same variable basis as the average steepness function by performing a first derivative operation on the isolated wave function.

[0019] Furthermore, the second computational model is constructed in the following manner:

[0020] In a moving coordinate system that moves with the tidal front, the wave crest breaking particles are assumed to move vertically with gravitational acceleration. Based on this kinematic condition, the time-averaged relationships of tidal height growth time, front horizontal displacement, and propagation velocity in the moving coordinate system are established. Combining the tidal intensity-Froude number mapping model, intermediate variables are eliminated, and finally, an explicit function of the average steepness of the breaking tidal wave with a monotonic interval and the relative Froude number as the only variable is derived. This achieves a simplified but physically meaningful time-averaged description of complex breaking flows.

[0021] Furthermore, the core of the fracture steepness calculation also includes an extreme value analysis module, which is used to perform differentiation analysis on the explicit function of the average steepness of the fracture tidal bore, determine whether there is an extreme point in the domain of the function, and output the corresponding theoretical maximum average steepness value and its occurrence conditions, thereby revealing the theoretical law of the change of the average steepness of the fracture tidal bore.

[0022] Furthermore, the tidal bore parameter sensing unit includes a distributed water level sensor array and a high-speed image acquisition module;

[0023] The tidal bore feature calculation unit also includes an image analysis module that automatically identifies and corrects the height of the tidal bore peak from the water flow image data using an edge detection algorithm.

[0024] Furthermore, the system also includes a pre-tidal water depth dynamic simulation module, which is used to perform time-varying simulation and real-time correction of the pre-tidal still water depth of the target river section based on the water level time series data of at least one reference position upstream of the target river section, combined with the river topography and tidal wave propagation law, so as to obtain a dynamic water depth value that matches the arrival time of the tidal bore.

[0025] Furthermore, the system also integrates a three-dimensional front reconstruction and verification module that fuses multiple data sources. This module reconstructs a three-dimensional spatial surface model of the tidal front in a unified spatiotemporal coordinate system by synchronously fusing visual image sequences and vertical array pressure sensing data. Based on this model, it performs high-precision feature parameter extraction and spatial morphology verification of the core output results of dual-modal steepness calculation, forming an enhanced closed loop that includes measurement, calculation, and three-dimensional visualization verification.

[0026] In a second aspect, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned system.

[0027] This invention provides a tidal bore steepness calculation system. The system first establishes a deterministic mapping relationship between the fundamental tidal bore parameters and the relative Froude number, starting from the one-dimensional tidal bore equations. Then, for two fundamentally different tidal bore forms—wave-like and breaking—separate steepness calculation sub-models are constructed: for wave-like tidal bores, the solitary wave theory is used to characterize the wavefront, and by introducing characteristic wavelength parameters and combining the principle of mass conservation, explicit theoretical functions for average and maximum steepness are derived; for breaking tidal bores, a time-averaged height-length development relationship is established in a coordinate system moving with the front, based on the kinematic conditions of wave crest particle escape, thus deriving its average steepness function. Finally, by using the theoretical steepness extremum of the breaking tidal bore as a physical constraint, the critical Froude number distinguishing the two forms is determined in reverse, thus forming a theoretical calculation system capable of adaptively identifying tidal bore forms and calculating corresponding steepness parameters based on input fundamental parameters.

[0028] This system establishes a direct and explicit theoretical link between tidal surge steepness and readily available basic parameters, significantly reducing reliance on complex and expensive field monitoring and improving the convenience and economy of calculations. Secondly, through built-in morphological discrimination logic based on physical constraints and a bimodal calculation model, the system can automatically and objectively adapt to the steepness calculation of undulating and breaking tidal surges under different hydrogeographic conditions, overcoming the limitations of traditional methods in terms of poor universality and strong subjective dependence. Finally, the system outputs a complete set of parameters covering both average and maximum steepness, providing a more unified, complete, and theoretically sound key dynamic input for tidal surge disaster risk assessment, determination of water-related engineering loads, and research on estuarine dynamic processes, effectively improving the scientific rigor, reliability, and decision-making efficiency of related fields.

[0029] Beneficial effects

[0030] By implementing the tidal surge steepness calculation system provided by the present invention, the following technical effects are achieved:

[0031] (1) By establishing a deterministic theoretical mapping between the basic parameters of tidal bore and the relative Froude number, and using this as the core variable to construct explicit steepness functions for wavy and broken tidal bores respectively, the previously scattered and experience-dependent methods are unified under a rigorous theoretical system, fundamentally solving the problems of poor universality of calculation methods and weak theoretical basis.

[0032] (2) By taking the theoretical steepness extreme value of the broken tidal bore as a physical constraint, the theoretical boundary Froude number between wave-like and broken morphology is derived in reverse, so that the morphology discrimination is freed from the dependence on subjective experience or additional complex observations, and an objective automatic discrimination with clear physical meaning can be completed based on only a few basic parameters.

[0033] (3) By introducing energy dissipation assessment and continuous function, the computational abrupt change near the critical Froude number of the traditional binary discriminant model is eliminated, so that the tidal surge steepness presents a physically real smooth transition with the change of hydraulic conditions, which significantly improves the output stability and computational accuracy of the model in the morphological transformation sensitive area.

[0034] (4) By real-time simulation and correction of the dynamic value of the pre-tidal water depth, the systematic input error caused by ignoring the tidal wave propagation time delay and the "pre-flood" effect is effectively compensated, thereby significantly improving the accuracy of the relative Froude number calculation from the source and enhancing the model's environmental adaptability under long river channels or varied terrain conditions.

[0035] (5) By fusing multi-source data to reconstruct the three-dimensional front, not only is spatial representativeness beyond single-point measurement provided for feature parameter extraction, but more importantly, a high-precision three-dimensional spatial verification benchmark is created for the prediction results of the theoretical model, thereby greatly improving the verifiability and reliability of the entire technical solution. Attached Figure Description

[0036] To make the above-described tidal surge steepness calculation system of the present invention more clear and understandable, the accompanying drawings used in the specific embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0037] Figure 1 This is a flowchart illustrating the implementation process of this application;

[0038] Figure 2 A schematic diagram illustrating the characteristic parameters involved in calculating the average wave steepness of a wavy tidal bore.

[0039] Figure 3 A schematic diagram illustrating the characteristic parameters involved in calculating the average wave steepness of a broken tidal bore.

[0040] Figure 4 This chart compares the average steepness of different tidal bore formations with field observation and experimental data. Detailed Implementation

[0041] Example 1:

[0042] This embodiment provides a unified steepness calculation method based on the relative Froude number of tidal bores. Its core lies in directly and explicitly linking readily obtainable basic hydrological parameters with the dynamic characteristics of tidal bores through theoretical modeling. In practice, the stable water depth before the target tidal bore and the maximum vertical rise of the tidal bore peak relative to the still water surface are first obtained through field observation or experimental measurement. Subsequently, based on the continuity and motion equations of one-dimensional tidal bore propagation, a deterministic mathematical relationship between tidal bore intensity and the relative Froude number is established. This relative Froude number becomes the core pivot and criterion for all subsequent calculations.

[0043] To calculate the tidal bore steepness under different physical morphologies, the system constructs theoretical sub-models for undulating tidal bores and breaking tidal bores. For undulating tidal bores, the solitary wave theory is used to describe their wave surface morphology. To address the problem that the wavelength of the solitary wave theory is infinitely large and cannot be directly used to calculate characteristic lengths, the system introduces a characteristic wavelength definition parameter, which characterizes the ratio of the relative wave height at a point on the wave surface to the wave height at the wave crest. By setting a mass conservation condition that the total volume of the wave surface water is equal to the volume of an equivalent characteristic triangle water body used to define the average steepness, a specific optimal solution for this characteristic wavelength definition parameter can be obtained. Substituting this solution into the morphological equation and combining it with the previously established tidal bore intensity-Froude number relationship, an explicit theoretical formula for calculating the average steepness of undulating tidal bores, using only the relative Froude number as the independent variable, is finally derived. Simultaneously, by differentiating the solitary wave morphological equation, the formula for calculating the maximum local steepness of undulating tidal bores can also be obtained, which is also expressed as a function of the relative Froude number.

[0044] For breaking tidal bores, different physical models are required for steepness calculation. The system is derived based on the kinematic breaking condition: when the horizontal velocity of water particles at the wave crest exceeds the velocity of the wave crest itself, the particles will escape from the wave surface, leading to breaking. In a moving coordinate system that follows the movement of the tidal bore front, it is assumed that the escaped water particles move with gravitational acceleration in the vertical direction. Based on this assumption, a time-averaged physical relationship can be established between the time required for tidal bore height growth, the horizontal distance the front moves in the moving coordinate system during this time, and the tidal bore propagation velocity in the moving coordinate system. Combining this relationship with the tidal bore intensity-Froude number relationship eliminates intermediate variables, deriving another explicit theoretical formula for calculating the average steepness of breaking tidal bores with only the relative Froude number as the independent variable. Analyzing this formula, the possible extreme values ​​of the average steepness of breaking tidal bores and their corresponding Froude number conditions can also be theoretically obtained.

[0045] To achieve automatic differentiation between the two morphologies and selection of calculation paths, the system proposes a morphology boundary determination criterion based on physical constraints. The principle is as follows: when a tidal bore evolves from a wavy to a breaking tidal bore, there is a physical upper limit to its wave surface steepness. Substituting the theoretical extreme value of the average steepness of the breaking tidal bore as a constraint into the calculation formula for the maximum steepness of the wavy tidal bore, a critical Froude number can be obtained by solving the inequality. When the actual calculated relative Froude number is less than or equal to this critical value, the tidal bore is determined to be in a wavy morphology, and the average steepness formula for wavy tidal bores is used for calculation; when the relative Froude number is greater than this critical value, the tidal bore is determined to be in a breaking morphology, and the average steepness formula for breaking tidal bores is used for calculation. This method was calibrated and verified through systematic flume physical model tests and field observation data from multiple typical estuaries. The results show that, compared with traditional empirical methods that rely on fitting dense time-series data, the formula provided by this invention can more consistently and accurately reflect the variation law of tidal surge steepness under different hydraulic conditions, providing a more reliable theoretical tool for disaster prevention, mitigation, early warning, and load analysis of water-related projects.

[0046] Example 2:

[0047] Based on the aforementioned embodiments, the specific implementation steps of the tidal bore steepness calculation method are explained, such as... Figure 1 As shown.

[0048] Step 1: Obtain relevant parameters. By obtaining the pre-tidal water depth and tidal height of a certain incident tidal bore through on-site observation or experimental measurement, the corresponding relationship between tidal bore intensity and relative Froude number is obtained, as shown in equations (1) and (2):

[0049] (1)

[0050] (2)

[0051] In the formula, For the tidal bore relative to the Froude number; The height of the tidal bore; The water depth before high tide; The intensity of the tidal bore.

[0052] Step 2: Calculate the wave surface morphology of the wavy tidal bore. The wave surface morphology of the wavy tidal bore is calculated using the isolated wave surface equation, as shown in equations (3) and (4):

[0053] (3)

[0054] (4)

[0055] In the formula, The wavefront height; It is a hyperbolic secant function; Wave number; This represents the horizontal distance traveled by the undulating tidal bore.

[0056] Step 3: Calculate the characteristic wavelength of the wavy tidal bore, taking into account the distance between the isolated wave crest and the wave peak. The point is infinitely close to the still water level, meaning it has an infinite wavelength; therefore, an index is introduced. The characteristic wavelength is defined as shown in equation (5):

[0057] (5)

[0058] In the formula, Distance from the peak The relative wave height ratio at that location.

[0059] For characteristic wavelength It can be obtained from the inverse function of equation (5), as shown in equation (6):

[0060] (6)

[0061] Based on the law of conservation of mass, assuming that the volume of water enclosed by the wave surface is consistent with the volume of the triangle used to calculate the average steepness of the tidal bore, then a system is established. The conservation equation is in the form of the following equation, as shown in equation (7):

[0062] (7)

[0063] The formula sets the area ratio to 1, which essentially introduces an equivalent geometric modeling concept based on volume conservation. Although the theoretical wavelength of an isolated wave is infinite, the water volume is mainly concentrated near the wave crest. To reasonably define a characteristic wavelength reflecting the overall tilt, an equivalent geometric shape needs to be constructed that characterizes the spatial distribution of the main water body and facilitates the calculation of the average slope. Here, this characteristic shape is designed as a triangle, and its area is agreed to be equal to the area of ​​the water body enclosed by the actual wave surface within the characteristic interval. This agreement follows the principle of mass conservation, ensuring that the geometric simplification process can still reasonably reflect the water volume distribution characteristics of the real wave surface, thus giving the defined "characteristic wavelength" a clear physical meaning. Based on this equality condition, a uniquely determined characteristic ratio constant can be obtained.

[0064] Preferably, when hour, .

[0065] Step 4: Calculate the average steepness of the undulating tidal bore. The characteristic parameters involved are as follows: Figure 2 As shown, a method for calculating the average steepness of wavy tidal bores is established, as shown in equation (8):

[0066] (8)

[0067] In the formula, The average steepness of the undulating tidal bore.

[0068] The result obtained by iterative calculation of equation (7) Substituting into equation (8) and combining with equation (2), we obtain the formula for calculating the average steepness of the wave-shaped tidal bore, with the relative Froude number as the index, as shown in equation (9):

[0069] (9)

[0070] Step 5: Calculate the maximum steepness of the undulating tidal bore. Differentiate equation (3) and combine it with equation (2) to obtain the calculation formula for the maximum steepness of the undulating tidal bore, as shown in equation (10):

[0071] (10)

[0072] In the formula, This represents the maximum local steepness of the undulating tidal bore.

[0073] Step Six: Calculate the average steepness of the breaking tide, involving characteristic parameters such as... Figure 3 As shown, based on the kinematic conditions for tidal bore formation, the horizontal velocity of fluid particles at the wave crest is... Greater than the peak movement speed ,Right now At this point, fluid particles escape from the wave crest, the free surface breaks up, and a tidal bore forms on the fore-slope. During the propagation of the tidal bore, complex flow phenomena such as the rolling, breaking, and re-entry of the free surface occur. Intense turbulence significantly distorts the free surface, and the high-frequency oscillations cause particularly dramatic instantaneous changes in the tidal bore's steepness. However, traveling with the front at a relative velocity... In a moving coordinate system, the average steepness of a breaking tide under a certain time-averaged condition can be obtained. This is based on the fact that when fluid particles escape from the wave surface at the crest of a breaking tide, the second time derivative of their displacement in the vertical direction is the acceleration due to gravity. Further based on the initial conditions At time (tidal bore height is 0) and At time (the moment corresponding to the height of the tidal bore), the time-averaged changes of each parameter are taken to establish the physical relationship between the vertical two-dimensional time and space quantities of the breaking tidal bore, as shown in equation (11):

[0074] (11)

[0075] In the formula, It is the acceleration due to gravity; The horizontal characteristic length of the breaking tidal bore in the moving coordinate system; The propagation speed of the tidal bore under moving coordinates; For the tidal bore height to increase to The required time is calculated using equation (12).

[0076] (12)

[0077] A method for calculating the average steepness of a breaking tidal bore is established, as shown in equation (13):

[0078] (13)

[0079] In the formula, The average steepness of the broken tidal bore.

[0080] Substituting equation (2) into equation (13), we obtain the formula for calculating the average steepness of the breaking tidal bore, which uses the relative Froude number of the tidal bore as an indicator, as shown in equation (14):

[0081] (14)

[0082] Step 7: Calculate the extreme value of the average steepness of the breaking tide. During the propagation of the breaking tide, for T=[0, ] Taking the average variation of parameters and ignoring the factor of turbulence intensity, extreme value analysis is performed on equation (14) to obtain the extreme value of the average steepness of the breaking tidal bore. This extreme value depends on the relative Froude number of the tidal bore. Preferably, when The breaking tidal bore has an average steepness extreme value, as shown in equation (15):

[0083] (15)

[0084] In the formula, This represents the theoretical extreme value of the average steepness of the broken tidal bore.

[0085] Step 8: Determine the calculation domain of the average steepness of the tidal bore. When the tidal bore changes from wavy to breaking, its wave surface gradually becomes steeper. When the critical threshold is reached, the wave surface will show rolling waves, and the fluid particles at the wave crest will lose the support of the free liquid surface and escape from the wave surface. Assuming that the maximum steepness value of the wavy and breaking tidal bore will converge to the physical upper limit of breaking, the extreme value of the breaking tidal bore, 0.4142, is substituted into equation (14) to obtain the constraint condition of the wavy tidal bore, as shown in equation (16):

[0086] (16)

[0087] Solving equation (16), we obtain equation (17):

[0088] (17)

[0089] In the formula, It is the critical Froude number for maintaining the shape of a wave-like tidal surge.

[0090] Step 9: Calculation of the average steepness of tidal bores of different forms. Establish the calculation formula and applicable range of the average steepness of tidal bores of different forms, as shown in formula (18):

[0091] (18)

[0092] Comparison of average steepness of different tidal bore formations with field observation and experimental data Figure 4 As shown. The tidal bore experiment was conducted in a tidal bore tank that was 50m long, 1.2m wide, and 0.6m high. The tank generated tidal bores with different Froude numbers using the Bore 2010 tidal bore monitoring and control system, and the average steepness of different tidal bore morphologies was identified using image recognition. According to the statistics of field observation data, the Froude numbers of the tidal bores ranged from 1.0 to 3.0, and more than 100 sets of scheme experiments were carried out. Based on the field observation data and experimental data, the steepness of different tidal bore morphologies was calibrated and verified, and a method for calculating the average steepness of different tidal bore morphologies with the relative Froude number of the tidal bore as an indicator and its applicable scope were proposed, namely, formula (18). Using this formula, the average steepness of different tidal bore morphologies can be calculated using known basic parameters such as the pre-tidal water depth and tidal bore height.

[0093] Example 3:

[0094] In existing methods, the steepness calculation of undulating and breaking tidal bores uses two independent formulas, with an abrupt switch at a critical Froude number. This contradicts the actual physical characteristic of tidal bore morphology gradually transitioning with energy dissipation, leading to discontinuities and biases in the calculation results near the critical point. Tidal bore morphology is not abrupt but evolves continuously with increasing wave crest energy dissipation. Therefore, this embodiment introduces a dimensionless energy dissipation factor, which is related to the relative Froude number and tidal bore intensity, to quantify the impact of turbulent kinetic energy dissipation at the wave crest on wave surface stability. By constructing a morphological continuity function based on the energy dissipation factor, replacing the original "either / or" discrimination and calculation mode, a smooth and continuous calculation of tidal bore steepness from undulating to breaking morphology is achieved, which is more consistent with physical reality.

[0095] First, we define the energy dissipation factor. Its principle is that the turbulence intensity of water particles at the wave crest is proportional to the square of the water velocity, which in turn is related to the Froude number. Simultaneously, energy dissipation is also affected by the height of the tidal bore itself. Therefore, we construct the following empirical formula:

[0096]

[0097] In the formula, It is the energy dissipation factor; This is an empirical index used to adjust the weight of the Froude number's contribution to energy dissipation, preferably 1.2; This is an empirical index used to adjust the contribution weight of tidal surge intensity to energy dissipation, preferably 0.8.

[0098] Construct a smooth Transition functions as morphologically continuous functions Its value range is [0,1], and it is used for the calculation results of the mixed wave and breaking model:

[0099]

[0100] In the formula, It is a morphologically continuous function; Parameters used to control the steepness of the transition curve; The threshold value for the characteristic energy dissipation factor characterizing the center point of morphological transformation. When much smaller hour, The system tends to follow a wave-like model; when Much larger hour, The system tends to follow a fragmentation model; in nearby, Smooth transition.

[0101] Instead of using a fixed Froude number for discrimination, calculations are performed using the mean steepness function of undulating tidal bore and the mean steepness function of broken tidal bore, respectively.

[0102] The final continuous steepness value is calculated using the following formula:

[0103]

[0104] In the formula, It represents the continuous average steepness.

[0105] In this way, the steepness calculation results will change smoothly with the relative Froude number and tidal surge intensity, eliminating the numerical jumps at the traditional critical point.

[0106] Compared with traditional fixed critical value switching models, this method significantly improves computational accuracy near the critical Froude number. By comparing field observation data from 10 sets of data located in the critical region of a river estuary, the traditional method achieved an average computational error of 18.5% on both sides of the critical point, while the average error was reduced to 6.3% using this continuous transition model. This is mainly due to the introduction of the physical concept of energy dissipation and the use of continuous functions to simulate the actual morphological transition process, making the calculation results, especially in the critical transition zone sensitive to engineering design, more accurate and reliable, providing higher-quality data input for structural safety assessment.

[0107] This method is essentially a mathematical smoothing technique for engineering calculations, designed to alleviate the discontinuity in steepness calculation results caused by abrupt morphological changes near critical points in traditional binary discriminant models. It aims to improve the numerical stability and practicality of the model output in sensitive engineering design regions. It is important to clarify that this approach does not constitute a mandatory assumption or denial of the weakly discontinuous physical nature of tidal bores. Rather, it serves as an optional enhancing mathematical module, providing an auxiliary tool for obtaining continuous and smooth calculation results in morphological transition zones without affecting the core physical discriminant model. Therefore, the implementation and application of this continuous transition module does not alter the core theoretical foundation and discriminant logic of the system. Specifically, the original segmented calculation mode based on explicit critical values ​​can be selected or retained according to actual needs.

[0108] Example 4:

[0109] In existing methods, the pre-tidal depth is usually considered as a static value at a point before the arrival of the tidal bore. However, in actual estuarine environments, since tides are a dynamic process, the water depth before the arrival of the tidal bore front has already changed due to the propagation of preceding tidal waves, especially in long channels or complex terrain, where this "dynamic depth" effect is significant. Directly using the static pre-tidal depth value introduces systematic errors, leading to inaccurate calculations of the Froude number and subsequent steepness. Therefore, when calculating tidal bore characteristics, an effective dynamic depth should be used, which is not only a function of location but also a function of the tidal bore propagation time. By establishing a simplified one-dimensional shallow water equation propagation model, and using the water level observation sequence before the arrival of the tidal bore, the true pre-tidal depth at the calculation point can be extrapolated and corrected in real time.

[0110] At least one water level reference station is set up in the upstream river channel of the calculation point, and it is ensured that continuous high-frequency water level time series data of the water level reference station before and after the tidal bore can be obtained.

[0111] Assuming the propagation of the tidal wave between the calculation point and the water level reference station follows the linear long-wave theory, the wave speed is... In the formula, The average water depth. The time it takes for the tidal bore to travel from the water level reference station to the calculation point. , For distance.

[0112] The core idea of ​​calculating the effective dynamic water depth at the point of calculation at the arrival of the tidal bore is to calculate the point. The water level at a given moment is equal to the water level reference station at an earlier moment. The water level, minus the correction for the water surface gradient along the course, is used to establish the following correction formula:

[0113]

[0114] In the formula, This is the effective dynamic water depth at the calculation point; For water level reference station time Water level value; The elevation of the riverbed at the calculation point; This is a slope correction term based on the average bottom slope and distance of the river channel.

[0115] A more refined model could be considered. It is also considered as a quantity that changes with water depth and is calculated iteratively.

[0116] The calculated The static pre-tidal depth is replaced and substituted along with the tidal bore height in the calculation of the dynamic Froude number.

[0117] Subsequent morphological discrimination and steepness calculation are both based on dynamic Froude numbers.

[0118] Compared with methods using a single static water depth value, this dynamic correction method significantly improves the spatiotemporal accuracy of Froude number and steepness calculations. A comparative verification was conducted on a 30-kilometer stretch of a river estuary. On spring tides with large tidal ranges, the average deviation between the Froude number calculated by the traditional static water depth method and the value inverted based on a high-precision hydrodynamic model in the middle section of the river was 12.7%. After applying this dynamic correction method, this deviation decreased to 4.1%. This demonstrates that this method, by introducing propagation time delay and slope correction, effectively captures the true dynamics of the pre-tidal water depth, thus making the input parameters of the entire tidal steepness calculation chain more accurate. It is particularly suitable for long river channels, estuarine environments with significant slopes or strong tidal asymmetry, improving the universality and reliability of engineering applications.

[0119] Example 5:

[0120] The current method of obtaining tidal bore height and determining its morphology mainly relies on single-point water level gauges or two-dimensional images, which suffers from limitations in dimensionality and insufficient local representativeness. Tidal bore fronts are actually three-dimensional curved surfaces with varying local steepness. This embodiment proposes a multi-source data fusion system for three-dimensional reconstruction and cross-validation of tidal bore fronts. This system simultaneously acquires and fuses visual sequences from a side-viewing high-speed camera and data from a high-frequency pressure sensor array deployed at different heights on the water-bearing structure. Using computer vision technology, the contour line of the tidal bore front is extracted from the image sequence, and combined with instantaneous water level information retrieved from the pressure data, the spatial surface of the tidal bore front at a specific moment is reconstructed in three-dimensional space. Comparing and validating this reconstructed surface with a two-dimensional profile calculated by a theoretical model not only improves the measurement accuracy of single-point parameters but also evaluates the overall representational ability of the theoretical model for three-dimensional spatial morphology.

[0121] The system's construction and operation steps are as follows:

[0122] Deployment at the target cross-section: a) Vision system: Install one or more synchronously calibrated high-speed cameras on one side or above the river channel to ensure that the field of view covers the target cross-section and a certain range upstream and downstream; b) Pressure sensor array: On the vertical piles at the cross-section, deploy a series of high-frequency response pressure sensors at certain intervals along the vertical direction to synchronously measure changes in water pressure.

[0123] All sensors are triggered by a unified time base signal for synchronous high-speed data acquisition. The video data undergoes preprocessing such as distortion correction and coordinate system calibration to convert image pixel coordinates into real-world coordinates.

[0124] Using algorithms such as video frame difference and edge detection, the water-vapor interface line of the tidal front is automatically identified and extracted from each frame of synchronized image;

[0125] Based on the readings of each pressure sensor, the static pressure portion is subtracted, and the sensor elevation is considered to calculate the water level time series at each sensor location in real time. At the instant the front passes, a set of discrete water level points along the vertical direction of the pile can be obtained, that is, the vertical cross-section of the front at that pile location;

[0126] The visual contour lines at the same moment are fused with the water point locations derived from pressure inversion in a unified three-dimensional spatial coordinate system. A three-dimensional spatial surface model of the tidal front at that moment is generated using spatial interpolation or surface fitting algorithms.

[0127] From the reconstructed 3D front model, a 2D profile can be extracted at any location, yielding the actual height and spatial morphology of the profile. This measured morphology is then superimposed and compared with the wavefront morphology predicted by the theoretical model. By calculating the morphological agreement between the two, the effectiveness of the theoretical model can be spatially verified. Simultaneously, the extracted actual height is used to correct the original input parameters, achieving a verification loop and improving the accuracy and reliability of the entire system.

Claims

1. A tidal surge steepness calculation system, characterized in that, include: The tidal bore parameter sensing unit is used to simultaneously collect time-series data of water depth and water flow image data of the target river section before and after the tidal bore occurs; The tidal bore feature calculation unit is used to extract the pre-tidal still water depth and tidal bore peak height from the water depth time series data, and calculate the relative Froude number of the tidal bore based on the preset tidal bore intensity-Froude number mapping model. The tidal bore morphology adaptive discrimination engine has a built-in morphological critical model derived from the physical constraints of the extreme steepness of the wavy tidal bore, which is used to automatically determine whether the tidal bore is in a non-fragmented wavy morphology or a fragmented morphology in which the water surface has broken according to the relative Froude number. The core of the wavy steepness calculation sub-system, in response to the determination of a wavy morphology, calls a first calculation model based on solitary wave theory coupled with mass conservation conditions, and outputs the average and maximum steepness of the tidal bore. The first calculation model is constructed in the following way: using solitary wave functions to characterize the wave surface morphology of the wavy tidal bore; to overcome the problem of the infinite theoretical wavelength, a characteristic wavelength definition parameter is introduced; based on the condition that the volume of the water body enclosed by the wave surface morphology and the volume of an equivalent characteristic triangle of water body are conserved, a self-consistent equation for the characteristic wavelength definition parameter is established; after solving the parameter, an explicit function of the average steepness of the wavy tidal bore with the relative Froude number as the only variable is finally derived. The core of the fracture steepness calculation, in response to the determination of a fracture mode, calls the second calculation model based on kinematic fracture conditions and constructs time-averaged physical relationships in a moving coordinate system, and outputs the average steepness and theoretical extreme steepness of the tidal bore; The result fusion and output interface is used to integrate and output a complete set of steepness parameters corresponding to the tidal bore pattern.

2. The system according to claim 1, characterized in that: The pre-set tidal surge intensity-Froude number mapping model in the tidal surge characteristic calculation unit is a theoretical model derived by combining the one-dimensional continuity equation and the motion equation of tidal surge propagation. It is a model that represents the unique deterministic functional relationship between the ratio of tidal surge height to pre-tidal water depth and the relative Froude number.

3. The system according to claim 1, characterized in that: The discrimination threshold in the morphological critical model is the critical Froude number obtained by substituting the physical upper limit of the average steepness of the breaking tidal bore into the expression for the maximum steepness in the theoretical model upon which the core of the wave steepness calculation depends.

4. The system according to claim 1, characterized in that: The adaptive tidal bore morphology discrimination engine further includes a morphology continuity discrimination module, which is used to assess the degree of energy dissipation of the tidal bore during its propagation process and construct a morphology continuity transition function based on this to achieve smooth and continuous determination and weight allocation of the tidal bore morphology from non-fragmented to completely fragmented states.

5. The system according to claim 1, characterized in that: The core of the wave steepness calculation also directly generates a wave tidal bore maximum local steepness calculation function that shares the same variable basis as the average steepness function by performing a first derivative operation on the isolated wave function.

6. The system according to claim 1, characterized in that, The second computational model is constructed in the following way: In a moving coordinate system that moves with the tidal bore front, the wave crest breaking particles are assumed to move vertically with gravitational acceleration. Based on this kinematic condition, the time-averaged relationships between the tidal bore height growth time, the front horizontal displacement, and the propagation velocity in the moving coordinate system are established. Combining the tidal bore intensity-Froude number mapping model, intermediate variables are eliminated, and finally, an explicit function of the average steepness of the breaking tidal bore with a monotonic interval and the relative Froude number as the only variable is derived.

7. The system according to claim 6, characterized in that: The core of the breakage steepness calculation also includes an extreme value analysis module, which is used to perform derivative analysis on the explicit function of the breakage tidal bore average steepness, determine whether there are extreme points in the domain of the function, and output the corresponding theoretical maximum average steepness value and its occurrence conditions.

8. The system according to claim 1, characterized in that: The system also includes a pre-tidal water depth dynamic simulation module, which is used to perform time-varying simulation and real-time correction of the pre-tidal still water depth of the target river section based on the water level time series data of at least one reference position upstream of the target river section, combined with the river topography and tidal wave propagation law, so as to obtain a dynamic water depth value that matches the arrival time of the tidal bore.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it implements the system according to any one of claims 1-8.

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