A method for simulating flexible vegetation movement based on different wave nonlinearities

Abstract

The present invention proposes a flexible vegetation motion simulation method based on different wave nonlinearities, including the following steps: S1, establishing and verifying a flexible vegetation dynamic model under wave action; S2, calculating characteristic wave velocity and wave period parameter KC (Keulegan–Carpenter) number; S3, calculating the resistance coefficient of given wave conditions and vegetation parameters in combination with existing formulas; S4, simulating the force motion of flexible vegetation under given incident wave conditions and vegetation parameters; S5, clarifying the influence of wave nonlinearity on the motion of submerged flexible vegetation. The flexible vegetation motion simulation method provided by the present invention uses a flexible vegetation dynamic model and different wave nonlinear theories to improve the accuracy of flexible vegetation force motion simulation, optimize the simulation theory and method, and lay a foundation for studying flexible vegetation wave dissipation.

Description

Technical Field

[0001] The invention relates to a flexible vegetation motion calculation technology based on different wave nonlinearities, belonging to the technical field of coastal protection. Background Art

[0002] Coastal vegetation is an important component of the ecosystem and plays a vital role in attenuating waves, mitigating storm surge hazards, and improving the ability of the coast to resist erosion and sea level rise. Although a large number of studies on wave attenuation by rigid vegetation have made satisfactory progress, the understanding of the wave attenuation mechanism of flexible vegetation is still in its infancy. Given the obvious differences in wave attenuation mechanisms between flexible and rigid vegetation, and the fact that flexible vegetation such as seagrass is widely distributed in coastal areas around the world, the dynamic characteristics and wave attenuation mechanisms of flexible vegetation have become the forefront of coastal engineering research.

[0003] The bending and swaying of flexible vegetation are key processes in the interaction between waves and flexible vegetation. The propagation and attenuation of waves in nearshore waters with flexible vegetation are directly affected by the movement of vegetation. Studying the dynamic characteristics of flexible vegetation is a necessary prerequisite for clarifying the wave attenuation mechanism of flexible vegetation. At present, the research on the movement of flexible vegetation mainly focuses on linear waves rather than nonlinear wave conditions. Based on the research results of rigid vegetation, there are a large number of flexible vegetation and nonlinear waves in coastal areas, so it is necessary to further explore the impact of wave nonlinearity on the movement of flexible vegetation. Under different wave nonlinear conditions, the dynamic changes of flexible vegetation that may occur will inevitably affect the wave attenuation it produces.

[0004] Previous studies were mainly limited to rigid vegetation, and there is still a lack of research on how wave nonlinearity affects the movement of flexible vegetation and the wave attenuation it produces. Although existing studies have numerically studied the impact of wave nonlinearity on vegetation drag and the wave attenuation it produces, the existing numerical models are mainly calculated based on linear wave theory, and few modeling studies are based on nonlinear wave theory. In addition, the impact of different wave theories and characteristic wave velocity calculation methods on flexible vegetation movement and wave attenuation has not been fully quantified. Summary of the invention

[0005] The present invention proposes a flexible vegetation motion simulation method based on different wave nonlinearities, which improves the feasibility and accuracy of flexible vegetation force motion simulation and lays a foundation for the field of flexible vegetation wave attenuation, thereby providing technical support for engineering practices based on coastal natural ecology.

[0006] In order to solve the above technical problems, the present invention adopts the following technical means:

[0007] A flexible vegetation motion simulation method based on different wave nonlinearities comprises the following steps:

[0008] S1, establish and verify the dynamic model of flexible vegetation under wave action;

[0009] S2, calculate the characteristic wave speed and wave period parameter KC (Keulegan–Carpenter number);

[0010] S3, calculate the drag coefficient for given wave conditions and vegetation parameters by combining the existing formula;

[0011] S4, simulating the force motion of flexible vegetation under given incident wave conditions and vegetation parameters;

[0012] S5. Clarify the influence of wave nonlinearity on the movement of submerged flexible vegetation.

[0013] As a further preferred solution, step S1 proposes a dynamic model of submerged flexible vegetation under wave action, establishes a two-dimensional submerged flexible vegetation motion control equation in a Cartesian coordinate system, proposes a numerical solution method for the model control equation based on finite differences, simulates the force and motion of a single submerged flexible vegetation under wave action, and combines the spatial morphological data of vegetation measured in the flexible vegetation flume experiment to debug the model grid and parameter settings;

[0014] The model control equations are shown below:

[0015]

[0016]

[0017] Where θ is the local bending angle of vegetation, s is the distance between vegetation and the origin of coordinates along the vegetation axis, and is the horizontal and vertical acceleration of vegetation, E is the elastic modulus of vegetation, I is the moment of inertia, ρ v is the density of vegetation material, V1 is the drainage volume per unit length of vegetation, F T is the tensile force perpendicular to the cross section, f B 、f D 、f F 、f Ix and f Iz They are net buoyancy, drag, friction, horizontal and vertical inertial forces;

[0018] The calculation formula is as follows:

[0019] f B =(ρ-ρ v )gV1

[0020]

[0021]

[0022]

[0023]

[0024] Where ρ is water density, is gravity acceleration, vegetation width, C D , C f and C m are the drag coefficient, friction coefficient and additional mass coefficient respectively, V2 is the volume related to the additional mass, u w With w w are the horizontal and vertical velocities of the wave water particle, and are the horizontal and vertical accelerations of the wave water particles, and are the horizontal and vertical acceleration of vegetation, respectively;

[0025] The finite difference algorithm is used to numerically solve the above partial differential equation, and then the numerical solution value θ of the bending angle of a single flexible vegetation at each elevation that changes with time can be obtained: i , i is the spatial serial number, and the two-dimensional spatial coordinates of vegetation can be expressed as and The horizontal force on vegetation is Where h is the spatial step size and M is the number of grid points for vegetation space calculation.

[0026] As a further preferred solution, step S2 gives the incident wave conditions, vegetation and other model parameters, including water depth d, wave height H, wave period T, vegetation elastic modulus, vegetation material density, wave theory, and applies linear wave and Stokes second-order wave theory to calculate the characteristic wave velocity U C and wave period parameter KC number, and generate flow fields to drive the simulated flexible vegetation movement;

[0027] The KC number calculation formula is:

[0028]

[0029] The calculation formula of characteristic wave velocity and flow field in the case of linear wave is:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] The calculation formula of characteristic wave velocity and flow field in the case of Stokes second-order wave is:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] Where k is the wave number, ω is the circular frequency, and L is the wavelength.

[0042] As a further preferred solution, step S3 sets different incident wave conditions and vegetation parameter combinations to calculate the Essel number representing the degree of wave nonlinearity. The calculation formula is U r =HL 2 / d 3 Then, the drag coefficient for given wave conditions and vegetation parameters is calculated according to different drag coefficient empirical formulas; the drag coefficient empirical formula is: C D1 =(81 / KC) 0.36 ; C D2 =1.17+12.89 / KC -1.25 ; C D3 =0.683+(12.07 / KC) 2.25 .

[0043] As a further preferred solution, in order to evaluate the impact of wave nonlinearity on the movement of flexible vegetation, step S4 simulates the movement of flexible vegetation under different wave conditions and vegetation parameters based on the established flexible vegetation dynamic model, and organizes and analyzes the characteristic wave speed, resistance coefficient and model calculation results.

[0044] As a further preferred scheme, step S5 clarifies the influence of wave nonlinearity on the movement of submerged flexible vegetation based on the statistical relationship between the simulated maximum horizontal force of a single flexible vegetation, the calculated results of the stem tip swing amplitude and the Essel number; the results show that for given vegetation characteristics, characteristic wave velocity determination method and resistance coefficient formula conditions, the movement of submerged flexible vegetation will be significantly affected by wave nonlinearity; the proposed method can be applied to the simulation of flexible vegetation movement with different wave nonlinearities, and at the same time clarifies the influence of wave nonlinearity.

[0045] After adopting the above technical means, the present invention can obtain the following advantages compared with the prior art:

[0046] The present invention discloses a flexible vegetation motion simulation method based on different wave nonlinearities, establishes a wave-driven flexible vegetation dynamic model, evaluates the rationality and accuracy of the model based on physical model experiments, applies linear and Stokes second-order wave theories to calculate characteristic wave velocities respectively, sets different incident wave conditions, and studies the differences in the motion of a single submerged flexible vegetation under different wave nonlinearities. The present invention helps to understand the impact of wave nonlinearity on the dynamics of flexible vegetation, optimizes the simulation theory and method of flexible vegetation wave attenuation, provides a quantitative understanding of the attenuation of waves by flexible vegetation in coastal areas, and provides a scientific basis for developing new coastal disaster prevention and mitigation engineering methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flowchart of the steps of a flexible vegetation motion simulation method based on different wave nonlinearities of the present invention;

[0048] Figure 2 This is a comparison diagram of the calculation results of the spatial morphology model of vegetation at different times in a wave cycle in an example of a flexible vegetation motion simulation method based on different wave nonlinearities of the present invention and the measured data of the physical model experiment;

[0049] Figure 3 The present invention provides a method for simulating the motion of flexible vegetation based on different wave nonlinearities, and the values ​​of the wave conditions and vegetation parameters are obtained;

[0050] Figure 4 A graph showing the relationship between the maximum horizontal force, the stem tip swing amplitude and the Ursel number under different wave theories and resistance coefficient conditions in an example of a flexible vegetation motion simulation method based on different wave nonlinearities of the present invention;

[0051] Figure 5 The maximum horizontal force and the increase of the stem tip swing amplitude caused by an increase of the Ursel number by 100 in an example of a flexible vegetation motion simulation method based on different wave nonlinearities of the present invention. DETAILED DESCRIPTION

[0052] In order to more clearly understand the technical content of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings:

[0053] like Figure 1 As shown, a flexible vegetation motion simulation method based on different wave nonlinearities includes the following steps:

[0054] S1. A dynamic model of submerged flexible vegetation motion under wave action is proposed, and the two-dimensional submerged flexible vegetation motion control equation in Cartesian coordinate system is established. A numerical solution method for the model control equation based on finite difference is proposed to simulate the force and motion of a single submerged flexible vegetation under wave action. Combined with the spatial morphological data of vegetation measured in the flexible vegetation flume experiment, the model grid and parameter settings are debugged.

[0055] The model control equations are shown below:

[0056]

[0057]

[0058] Where θ is the local bending angle of vegetation, s is the distance between vegetation and the origin of coordinates along the vegetation axis, and is the horizontal and vertical acceleration of vegetation, E is the elastic modulus of vegetation, I is the moment of inertia, ρ v is the density of vegetation material, V1 is the drainage volume per unit length of vegetation, F T is the tensile force perpendicular to the cross section, f B 、f D 、f F 、f Ix and f Iz They are net buoyancy, drag, friction, horizontal and vertical inertia, and the calculation formula is as follows:

[0059] f B =(ρ-ρ v )gV1

[0060]

[0061]

[0062]

[0063]

[0064] Where ρ is water density, is gravity acceleration, vegetation width, C D , C f and C m are the drag coefficient, friction coefficient and additional mass coefficient respectively, V2 is the volume related to the additional mass, u w With w w are the horizontal and vertical velocities of the wave water particle, and are the horizontal and vertical accelerations of the wave water particles, and are the horizontal and vertical acceleration of vegetation, respectively.

[0065] The finite difference algorithm is used to numerically solve the above partial differential equation. Then the numerical solution value θ of the bending angle of a single flexible vegetation at each elevation over time can be obtained. i , i is the spatial serial number. The two-dimensional spatial coordinates of vegetation can be expressed as and The horizontal force on vegetation is Where h is the spatial step size and M is the number of grid points for vegetation space calculation.

[0066] S2, given the incident wave conditions, vegetation and other model parameters, including water depth d, wave height H, wave period T, vegetation elastic modulus, vegetation material density, wave theory, use linear wave and Stokes second-order wave theory to calculate the characteristic wave speed U C and wave period parameter KC number, and generate flow fields to drive the simulated flexible vegetation movement.

[0067] The KC number calculation formula is:

[0068]

[0069] The calculation formula of characteristic wave velocity and flow field in the case of linear wave is:

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] The calculation formula of characteristic wave velocity and flow field in the case of Stokes second-order wave is:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Where k is the wave number, ω is the circular frequency, and L is the wavelength.

[0082] S3, set different incident wave conditions and vegetation parameter combinations, and calculate the Essel number representing the degree of wave nonlinearity. The calculation formula is Ur =HL 2 / d 3 Then, the drag coefficient for given wave conditions and vegetation parameters is calculated according to different drag coefficient empirical formulas. The drag coefficient empirical formula is: C D1 =(81 / KC) 0.36 ; C D2 =1.17+12.89 / KC -1.25 ; C D3 =0.683+(12.07 / KC) 2.25 .

[0083] S4. In order to evaluate the impact of wave nonlinearity on the movement of flexible vegetation, based on the established flexible vegetation dynamic model, the movement of flexible vegetation under different wave conditions and vegetation parameters was simulated, and the characteristic wave speed, resistance coefficient and model calculation results were sorted and analyzed.

[0084] S5, based on the statistical relationship between the maximum horizontal force of a single flexible plant, the calculated results of the stem tip swing amplitude and the Essel number, the influence of wave nonlinearity on the movement of submerged flexible vegetation is clarified. The results show that for given vegetation characteristics, characteristic wave velocity determination method and resistance coefficient formula conditions, the movement of submerged flexible vegetation will be significantly affected by wave nonlinearity. The proposed method can be applied to the simulation of flexible vegetation movement with different wave nonlinearities, and the influence of wave nonlinearity is clarified.

[0085] Example 1

[0086] This example selects experimental data collected from a wave tank physics experiment for research.

[0087] The dynamic model of a single flexible vegetation root under wave action was verified based on the results of the physical model test. The experimental flume was 41.5 meters long, 0.8 meters wide, and 0.9 meters deep, and the experiment used a fixed water depth of 0.65 meters. Figure 2 The calculation results of the spatial morphology model of vegetation at different times in a wave cycle are compared with the measured data of the physical model experiment. The results show that the established dynamic model of flexible vegetation under wave action can better simulate the force process of a single flexible vegetation.

[0088] In order to study the differences in the motion of a single submerged flexible plant under different wave nonlinear conditions, Figure 3 The incident wave conditions and model parameter values ​​are listed, including water depth d, wave height H, wave period T, elastic modulus E, vegetation material density ρ v , characteristic wave speed U C , drag coefficient C Dand wave theory. Linear and Stokes second-order wave theory were applied to calculate the characteristic wave velocity and generate the flow field; the wave period parameter KC number was calculated using the characteristic wave velocity at the top, middle and bottom of the vegetation respectively; and the drag coefficient was calculated using three different calculation formulas. In addition to the above variables, the height and diameter of the vegetation with a circular cross-section were set to be constant at 0.2 m and 4 mm. After assuming that these variables were independent of each other, a total of 28,125 numerical simulation conditions were designed.

[0089] Figure 4 The relationship between the maximum horizontal force, stem tip amplitude and the Ursel number based on the two-wave theory and the three drag coefficient formulas is given. It can be seen from the figure that for a given vegetation characteristic, characteristic wave velocity determination method and drag coefficient formula, the movement of submerged flexible vegetation is significantly affected by wave nonlinearity. The results show that with the increase of the Ursel number, the maximum horizontal force and stem tip swing amplitude of the submerged flexible vegetation increase overall. For a given specific vegetation characteristic, a higher Ursel number may also lead to a smaller maximum horizontal force and stem tip swing amplitude, which may be related to the influence of other single factors (such as wave period). At the same time, with the increase of elastic modulus, the influence of wave nonlinearity on the maximum horizontal force becomes greater. According to STK and C D1 The simulation results show that when the elastic modulus is 0.001GPa, 0.01GPa, 0.1GPa, 1GPa and 10GPa, an increase of 100 in the Ursel number can lead to an increase of 0.04N, 0.06N, 0.13N, 0.2N and 0.21N in the maximum horizontal force, respectively. This is related to the influence of wave nonlinearity on vegetation movement under different elastic modulus conditions. Figure 4 As shown in (df, jl), a smaller elastic modulus helps to increase the effect of wave nonlinearity on the stem tip swing. For vegetation with elastic moduli of 0.001 GPa, 0.01 GPa, 0.1 GPa, 1 GPa and 10 GPa, as the Ursel number increases by 100, the stem tip excursion increases by 0.31 m, 0.24 m, 0.13 m, 0.02 m and 0.002 m respectively. The above results are based on 700 kg / m 3 The density of vegetation material and U CT The same rule can be obtained for other vegetation material density and characteristic wave velocity determination methods. Figure 5 The results are summarized for the changes in the maximum horizontal force and the stem tip swing amplitude caused by an increase in the Ursel number by 100. Therefore, within the parameter range used in this example, wave nonlinearity can significantly affect the motion of submerged flexible vegetation, and this effect should be considered in the determination of the drag coefficient and in wave attenuation studies.

[0090] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in the field without departing from the purpose of the present invention.

Claims

1. A flexible vegetation motion simulation method based on different wave nonlinearities, characterized in that: The following steps are involved: S1, establish and verify the dynamic model of flexible vegetation under wave action; S2, calculate the characteristic wave speed and wave period parameter KC number; S3, calculate the drag coefficient for given wave conditions and vegetation parameters by combining the existing formula; S4, simulating the force motion of flexible vegetation under given incident wave conditions and vegetation parameters; S5, clarify the influence of wave nonlinearity on the movement of submerged flexible vegetation; Among them, the step S1 proposes a kinematic model of submerged flexible vegetation under the action of waves, establishes a two-dimensional submerged flexible vegetation motion control equation in a Cartesian coordinate system, proposes a numerical solution method for the model control equation based on finite differences, simulates the force and movement of a single submerged flexible vegetation under the action of waves, and combines the spatial morphological data of vegetation measured in the flexible vegetation flume experiment to debug the model grid and parameter settings; The model control equations are shown below: Where θ is the local bending angle of vegetation, s is the distance between vegetation and the origin of coordinates along the vegetation axis, and is the horizontal and vertical acceleration of vegetation, E is the elastic modulus of vegetation, I is the moment of inertia, ρ v is the density of vegetation material, V1 is the drainage volume per unit length of vegetation, F T is the tensile force perpendicular to the cross section, f B 、f D 、f F 、f Ix and f Iz They are net buoyancy, drag, friction, horizontal and vertical inertial forces; The calculation formula is as follows: f B =(r-r v )gV1 Where ρ is water density, is gravity acceleration, vegetation width, C D , C f and C m are the drag coefficient, friction coefficient and additional mass coefficient respectively, V2 is the volume related to the additional mass, u w With w w are the horizontal and vertical velocities of the wave water particle, and are the horizontal and vertical accelerations of the wave water particles, and are the horizontal and vertical acceleration of vegetation, respectively; The finite difference algorithm is used to numerically solve the control equation of the above model, and then the numerical solution value θ of the bending angle of a single flexible vegetation at each elevation that changes with time can be obtained: i , i is the spatial serial number, and the two-dimensional spatial coordinates of vegetation are expressed as and The horizontal force on vegetation is Where h is the spatial step size, and M is the number of grid points for vegetation space calculation; The step S2 gives the incident wave conditions, vegetation and other model parameters, including water depth d, wave height H, wave period T, vegetation elastic modulus, vegetation material density, wave theory, and uses linear wave and Stokes second-order wave theory to calculate the characteristic wave velocity U C and wave period parameter KC number, and generate flow fields to drive the simulated flexible vegetation movement; The KC number calculation formula is: The calculation formula of characteristic wave velocity and flow field in the case of linear wave is: The calculation formula of characteristic wave velocity and flow field in the case of Stokes second-order wave is: Where k is the wave number, ω is the circular frequency, and L is the wavelength.

2. The flexible vegetation motion simulation method based on different wave nonlinearities according to claim 1 is characterized in that: The step S3 sets different incident wave conditions and vegetation parameter combinations to calculate the Essel number representing the degree of wave nonlinearity. The calculation formula is U r =HL 2 / d 3 Then, the drag coefficient for given wave conditions and vegetation parameters is calculated according to different drag coefficient empirical formulas; the drag coefficient empirical formula is: C D1 =(81 / KC) 0.36 ; C D2 =1.17+12.89 / KC -1.25 ; C D3 =0.683+(12.07 / KC) 2.25 .

3. The flexible vegetation motion simulation method based on different wave nonlinearities according to claim 1 is characterized in that: In order to evaluate the impact of wave nonlinearity on the movement of flexible vegetation, step S4 simulates the movement of flexible vegetation under different wave conditions and vegetation parameters based on the established flexible vegetation dynamic model, and organizes and analyzes the characteristic wave speed, resistance coefficient and model calculation results.

4. The method for simulating flexible vegetation movement based on different wave nonlinearities according to claim 1, characterized in that: The step S5 clarifies the influence of wave nonlinearity on the movement of submerged flexible vegetation based on the statistical relationship between the simulated maximum horizontal force of a single flexible vegetation, the calculated result of the stem tip swing amplitude and the Ursel number.

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