An analytical method for wave diffraction coefficient of open double jetties

Abstract

The present invention relates to a method for analyzing the wave diffraction coefficient for an open double jetty. The method comprises the following steps: Step S1, establishing an open double jetty model in a Cartesian coordinate system; Step S2, obtaining the Helmholtz equation for the complex function in the velocity potential function based on the velocity potential function and linearized free surface boundary conditions; using the Schwarz-Christoffel conformal transformation and the Green's function method to perform a boundary value solution on the Helmholtz equation to obtain a wave diffraction coefficient model for the open double jetty; and Step S3, numerically solving the wave diffraction coefficient model using the method to obtain an analytical value of the wave diffraction coefficient. Compared with the prior art, the method of the present invention fills a gap in the theory of wave diffraction for open double jetties and has the advantage of high analytical prediction accuracy.

Description

Technical Field

[0001] The invention relates to the field of coastal engineering hydrodynamics, and in particular to a wave diffraction coefficient analysis method for an open double breakwater. Background Art

[0002] When constructing a port, breakwaters are necessary to create a sheltered area to protect the harbor from waves and provide a stable and safe area for ships to anchor and operate. Breakwaters also prevent or reduce the intrusion of sediment into the harbor and prevent strong coastal currents or drifting ice from invading the harbor. This makes breakwaters a crucial component of harbor engineering. When calculating wave elements within the harbor, wave diffraction is the primary consideration, and therefore a classic problem.

[0003] Existing research on wave diffraction in breakwaters has largely been limited to simple breakwater configurations, such as single breakwaters, collinear double breakwaters, and island breakwaters. However, in practical engineering, breakwater configurations can be broadened to encompass a wide variety of configurations. Currently, research on breakwaters with symmetrical and asymmetrical open double breakwaters is limited. Therefore, an analytical method for calculating the wave diffraction coefficient for open double breakwaters is urgently needed to effectively simulate wave diffraction. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a wave diffraction coefficient analysis method for open double jetties, which can effectively simulate the wave diffraction problem of open double jetties.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The present invention proposes a wave diffraction coefficient analysis method for an open double jetty, the method comprising the following steps:

[0007] Step S1, establishing an open double jetty model in a Cartesian coordinate system;

[0008] Step S2: Based on the velocity potential function and the linearized free surface boundary condition, the Helmholtz equation for the complex function in the velocity potential function is obtained; the Schwarz-Christoffel conformal transformation and the Green's function method are used to perform boundary value solutions on the Helmholtz equation to obtain a wave diffraction coefficient model for the open double jetty;

[0009] Step S3: Use The wave diffraction coefficient model is numerically solved by this method to obtain the analytical value of the wave diffraction coefficient.

[0010] Preferably, the open double breakwater model in the Cartesian coordinate system in step S1 is a symmetrical open breakwater model, specifically:

[0011] Arrange two semi-infinite breakwaters symmetrically in the Cartesian coordinate system Oxyz, with the x and y axes on the horizontal plane and the z axis pointing vertically upward. The intersection of the extension lines of the two breakwaters on the horizontal plane is the origin of the coordinate system O. The distance from the fixed ends of the two breakwaters to the origin O is l, and the distance between the fixed ends of the two breakwaters is the gate width d. s , the wave propagates along the direction with an angle α with the positive direction of the x-axis.

[0012] Preferably, in step S2, based on the velocity potential function and the linearized free surface boundary condition, the Helmholtz equation for the complex function in the velocity potential function is obtained, specifically:

[0013] Assuming that the fluid is incompressible and irrotational, there exists a velocity potential function that satisfies the Laplace equation. After linearizing the free surface boundary conditions, the boundary value problem of the velocity potential function φ(x, y, z, t) is obtained, which is expressed as:

[0014]

[0015]

[0016]

[0017]

[0018] Where x, y, and z are the coordinates in the Cartesian coordinate system, and h s is the uniform water depth, η is the free surface displacement, g is the acceleration due to gravity, and t is the time;

[0019] From equations (1) and (2), the mathematical expression of the velocity potential function φ(x, y, z, t) is obtained as follows:

[0020] φ(x,y,z,t)=A cosh k(z+h s )f(x,Y)e iσt (5)

[0021] Where k is the wave number, is the wavelength, σ is the angular frequency, and f(x, y) is a complex function;

[0022] Substituting equation (5) into equation (1), we obtain the Helmholtz equation for f(x, y):

[0023]

[0024] Substituting equation (5) into equations (3) and (4) yields the dispersion relation:

[0025] σ 2 =gktanh(kh s ) (7)

[0026] The boundary conditions for the flow are:

[0027]

[0028] Where, is the normal vector, and Γ is the perimeter of the jetty at the water surface.

[0029] Preferably, the Schwarz-Christoffel conformal transformation in step S2 is specifically as follows: using the Schwarz-Christoffel conformal transformation formula, the physical domain of the Z plane is conformally transformed to the mathematical domain of the upper half plane of W2, and then applying w2=e w Map the upper half plane of W2 into an infinite strip of width π.

[0030] Preferably, the diffraction coefficient model of the symmetrical open double embankment is:

[0031]

[0032] External domain wave height:

[0033] ξ=a1e 2(1-β)u ,u≥0 (10)

[0034] a1=lβk 11)

[0035]

[0036]

[0037]

[0038] Inner domain wave height:

[0039]

[0040] a2=l(1-β)k (16)

[0041]

[0042]

[0043]

[0044] Where f′ out and f′ innThey are respectively the outer wave height and inner wave height when long wave incident on the breakwater, that is, when the width of the gate is less than the incident wavelength and the wavelength is smaller than the set value, f out and f inn are the external and internal wave heights under other conditions respectively; x and y are the coordinates in the Cartesian coordinate system, u and v are the coordinates after the Schwarz-Christoffel conformal transformation and W2 = e W Mapped coordinates; ε, C n is the intermediate constant, a1 and a2 are intermediate parameter variables introduced; for ε n , when n=0, ε0=2, when n≥1, ε n =1; k is the wave number, is the wavelength; J γ (x) is the Bessel function of the first kind, is the second kind of Hankel function, γ is the order;

[0045] In the case of long waves incident on the breakwater, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0046]

[0047] f′ out =f′ inn

[0048] Otherwise, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0049]

[0050] f out =f inn

[0051] Preferably, the open double breakwater model in the Cartesian coordinate system in step S1 is an asymmetric open breakwater, specifically:

[0052] Arrange two semi-infinite breakwaters symmetrically in the Cartesian coordinate system Oxyz. The first breakwater is placed on the x-axis, and the fixed end of the first breakwater is at the origin O. The second breakwater is arranged at an angle βπ to the positive half axis of the x-axis. The distance between the fixed end of the first breakwater and the fixed end of the second breakwater is l, and the width of the mouth is l. The uniform water depth h is s , the wave propagates along the direction with an angle α with the positive direction of the x-axis.

[0053] Preferably, in step S2, based on the velocity potential function and the linearized free surface boundary condition, the Helmholtz equation for the complex function in the velocity potential function is obtained, specifically:

[0054] Assuming that the fluid is incompressible and irrotational, there exists a velocity potential function that satisfies the Laplace equation. After linearizing the free surface boundary conditions, the boundary value problem of the velocity potential function φ(x, y, z, t) is obtained, which is expressed as:

[0055]

[0056]

[0057]

[0058]

[0059] Where x, y, and z are the coordinates in the Cartesian coordinate system, and h s is the uniform water depth, η is the free surface displacement, g is the acceleration due to gravity, and t is the time;

[0060] From equations (20) and (21), the mathematical expression of the velocity potential function φ(x, y, z, t) is obtained as follows:

[0061] φ(x,y,z,t)=A cosh k(z+h s )f(x,y)e iσt (twenty four)

[0062] Where k is the wave number, is the wavelength, σ is the angular frequency, and f(x, y) is a complex function;

[0063] Substituting Equation (24) into Equation (20), we obtain the Helmholtz equation for f(x, y):

[0064]

[0065] Substituting Equation (24) into Equations (22) and (23) yields the dispersion relation:

[0066] σ 2 =gktanh(kh s ) (26)

[0067] The boundary conditions for the flow are:

[0068]

[0069] Where, is the normal vector, and Γ is the perimeter of the jetty at the water surface.

[0070] Preferably, the diffraction coefficient model of the asymmetric open double pier is as follows:

[0071]

[0072]

[0073]

[0074] ξ=s1e βu (31)

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Where f′ out and f′ inn They are respectively the outer wave height and inner wave height when long wave incident on the breakwater, that is, when the width of the gate is less than the incident wavelength and the wavelength is smaller than the set value, f out and f inn are the external and internal wave heights under other conditions respectively; x and y are the coordinates in the Cartesian coordinate system, u and v are the coordinates after the Schwarz-Christoffel conformal transformation and W2 = e W Mapped coordinates; ε, C n is the intermediate constant, a1 and a2 are intermediate parameter variables introduced; for ε n , when n=0, ε0=2, when n≥1, ε n =1; k is the wave number, is the wavelength; J γ (x) is the Bessel function of the first kind, is the second kind of Hankel function, γ is the order;

[0085] In the case of long waves incident on the breakwater, the unknown coefficient Dn and E n It is calculated from the following continuous conditions:

[0086]

[0087] f out =f inn

[0088] Otherwise, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0089]

[0090] f out =f inn

[0091] Preferably, the step S3 adopts The wave diffraction coefficient model is numerically solved by this method to obtain the analytical value of the wave diffraction coefficient, which is specifically:

[0092] The specific process of solving the double integral equation representing wave height in the wave diffraction coefficient model is as follows:

[0093] The integration interval [a′, b′] is divided into steps Divide into m equal parts, and divide the interval [c′, d′] into steps of Divide it into n equal parts, with coordinate x i =a′+i*q(i=0,1,…,m),y j =c′+j*p(j=0, 1, ..., n), then the discrete form of the integral equation representing the wave height is:

[0094]

[0095] Where the interval [a′, b′] represents the range of the variable s, [c′, d′] represents the range of the variable t, f(x, y) is the unknown function, A(x, y) is the known function, and G(x, y, s, t) is the kernel function.

[0096] The double integral in equation (41) is discretized using the trapezoidal formula:

[0097]

[0098] The discretized integral equation is transformed into a system of linear equations, and the approximate solution of the integral equation is obtained by solving this system of linear equations.

[0099] Preferably, the step S3 further comprises truncating the infinite integral term contained in the integral equation, that is, selecting a finite value to approximate the upper limit of the infinite integral.

[0100] Compared with the prior art, the present invention has the following advantages:

[0101] 1) The present invention proposes a wave diffraction analytical method for open double jetties. Based on the Schwarz-Christoffel conformal transformation and the Green's function method, the boundary value problem of the Helmholtz equation is solved. The diffraction coefficient model for different open double jetties is obtained by applying this method. The wave diffraction distribution of the open double jetty configuration is obtained by numerical solution.

[0102] 2) The present invention establishes a diffraction coefficient model for two different open double-pier configurations, taking into account more comprehensive scenarios and having high applicability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 It is a symmetrical open double jetty (the width of the gate is DB);

[0104] Figure 2 It is an asymmetric open double jetty (the width of the gate is OD);

[0105] Figure 3 It is a conformal mapping from the physical domain to the mathematical domain of the symmetrical open double jetty;

[0106] Figure 4 It is a conformal mapping from the physical domain to the mathematical domain of asymmetric open double jetty;

[0107] Figure 5 The width of the mouth is δ = 1.0, Comparison of the diffraction coefficient of waves behind the breakwater at different incident angles; Figure 5 a is the diffraction coefficient of the wave behind the breakwater when the incident angle α = 0°, Figure 5 b is the diffraction coefficient of waves behind the breakwater when the incident angle α = 45°;

[0108] Figure 6 The wave diffraction coefficients are compared after the breakwaters are arranged at different angles, with the wave incident angle α = 270° and the gate width δ = 1.0. Figure 6 a is The wave diffraction coefficient behind the breakwater is Figure 6 b is The wave diffraction coefficient behind the breakwater is:

[0109] Figure 7 The wave diffraction coefficients are compared when the wave incident angle is α = 90° and the gate width is δ = 1.0, and the breakwaters are arranged at different angles. Figure 7 a is The wave diffraction coefficient behind the breakwater is Figure 7 b is The wave diffraction coefficient behind the breakwater is Figure 7 c is The wave diffraction coefficient behind the breakwater is:

[0110] Figure 8 The wave diffraction coefficients are compared when the wave incident angle is α = 90° and the gate width is δ = 1.0, and the breakwaters are arranged at different angles. Figure 8 a is the wave diffraction coefficient behind the breakwater when δ = 0.944, Figure 8 b is the wave diffraction coefficient behind the breakwater when δ = 1.845;

[0111] Figure 9 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0112] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0113] Example 1

[0114] This embodiment is aimed at an asymmetric open breakwater and provides a wave diffraction coefficient analysis method for an open double breakwater. The method includes the following steps:

[0115] Step S1: Establish a symmetrical open breakwater model in a Cartesian coordinate system, specifically:

[0116] like Figure 1 As shown, two semi-infinite breakwaters are symmetrically arranged in the Cartesian coordinate system Oxyz, with the x and y axes located on the horizontal plane and the z axis pointing vertically upward. The intersection of the extension lines of the two breakwaters on the horizontal plane is the origin of the coordinate system O. The distance from the fixed ends of the two breakwaters to the origin O is l, and the distance between the fixed ends of the two breakwaters is the gate width d. Among them, the uniform water depth h s , the wave propagates along the direction with an angle α with the positive direction of the x-axis.

[0117] Step S2: Based on the velocity potential function and the linearized free surface boundary conditions, the Helmholtz equation for the complex function in the velocity potential function is obtained; the Schwarz-Christoffel conformal transformation and the Green's function method are used to solve the Helmholtz equation for the boundary value, and the wave diffraction coefficient model of the open double jetty is obtained, which is specifically:

[0118] Assuming that the fluid is incompressible and irrotational, there exists a velocity potential function that satisfies the Laplace equation. After linearizing the free surface boundary conditions, the boundary value problem of the velocity potential function φ(x, y, z, t) is obtained, which is expressed as:

[0119]

[0120]

[0121]

[0122]

[0123] Where x, y, and z are the coordinates in the Cartesian coordinate system, and h s is the uniform water depth, η is the free surface displacement, g is the acceleration due to gravity, and t is the time;

[0124] From equations (1) and (2), the mathematical expression of the velocity potential function φ(x, y, z, t) is obtained as follows:

[0125] φ(x,y,z,t)=A cosh k(z+h s )f(x,y)e iσt (5)

[0126] Where k is the wave number, is the wavelength, σ is the angular frequency, and f(x, y) is a complex function;

[0127] Substituting equation (5) into equation (1), we obtain the Helmholtz equation for f(x, y):

[0128]

[0129] Substituting equation (5) into equations (3) and (4) yields the dispersion relation:

[0130] σ 2 =gktah(kh s ) (7)

[0131] The boundary conditions for the flow are:

[0132]

[0133] Where, is the normal vector, and Γ is the perimeter of the jetty at the water surface.

[0134] In order to solve the boundary value problem of formula (6), the Schwarz-Christoffel conformal transformation formula is used to convert Figure 1 The physical domain of the Z plane shown is transformed conformally to Figure 3 The mathematical domain of the upper half plane of W2 shown in a, and then applying w2=e W Will Figure 3 The upper half plane mapping of W2 shown in a is Figure 3 b shows an infinitely long strip with a width of π; the Schwarz-Christoffel conformal transformation formula is:

[0135]

[0136] Table 1 below shows the angle-conservative transformation Figure 1 and Figure 3 The correspondence between the points.

[0137] Table 1

[0138] Point (Z) <![CDATA[α j ]]> <![CDATA[Point b j (W2)]]> Point (W) D -π -d (0，iπ) C -π +1 (0，0) A 3π-βπ 0 (-∞，0)；(-∞，iπ) B βπ+π ∞ (+∞，0)；(+∞，iπ)

[0139] The diffraction coefficient model of the symmetrical open double jetty is:

[0140]

[0141] External domain wave height:

[0142] ξ=a1e 2(1-β)u ,u≥0 (10)

[0143] a1=lβk (11)

[0144]

[0145]

[0146]

[0147] Inner domain wave height:

[0148]

[0149] a2=l(1-β)k (16)

[0150]

[0151]

[0152]

[0153] Where f′ out and f′ inn They are respectively the outer wave height and inner wave height when long wave incident on the breakwater, that is, when the width of the gate is less than the incident wavelength and the wavelength is smaller than the set value, f out and f innare the external and internal wave heights under other conditions respectively; x and y are the coordinates in the Cartesian coordinate system, u and v are the coordinates after the Schwarz-Christoffel conformal transformation and W2 = e W Mapped coordinates; ε, C n is the intermediate constant, a1 and a2 are intermediate parameter variables introduced; for ε n , when n=0, ε0=2, when n≥1, ε n =1; k is the wave number, is the wavelength; J γ (x) is the Bessel function of the first kind, is the second kind of Hankel function, γ is the order;

[0154] In the case of long waves incident on the breakwater, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0155]

[0156] f′ out =f′ inn

[0157] Otherwise, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0158]

[0159] f out =f inn

[0160] Step S3: Use The wave diffraction coefficient model is numerically solved by this method to obtain the analytical value of the wave diffraction coefficient. Specifically, the double integral equation representing the wave height in the wave diffraction coefficient model is solved as follows:

[0161] The integration interval [a′, b′] is divided into steps Divide into m equal parts, and divide the interval [c′, d′] into steps of Divide it into n equal parts, with coordinate x i =a′+i*q(i=0,1,…,m),y j =c′+j*p(j=0, 1, ..., n), then the discrete form of the integral equation representing the wave height is:

[0162]

[0163] Where the interval [a′, b′] represents the range of the variable s, [c′, d′] represents the range of the variable t, f(x, y) is the unknown function, A(x, y) is the known function, and G(x, y, s, t) is the kernel function.

[0164] The double integral in equation (41) is discretized using the trapezoidal formula:

[0165]

[0166] The discretized integral equation is transformed into a system of linear equations, and the approximate solution of the integral equation is obtained by solving this linear equation. The infinite integral term contained in the integral equation is truncated, that is, a finite value is selected to approximate the upper limit of the infinite integral.

[0167] This embodiment analyzes the wave diffraction coefficients of different breakwater configurations, including:

[0168] Note: In this embodiment, the width of the gate is dimensionless with wavelength λ, i.e.

[0169] 1) The wave diffraction coefficient behind the breakwater at different incident angles is numerically solved. The specific parameters are shown in Table 2. The calculation results are shown in the attached figure. Figure 5 , Attachment Figure 6 As shown, the solid line is the analytical solution of the present invention, the dotted line is the analytical solution of Penny and Price, and the solid circles are the analytical solutions of Sobey and Johnson.

[0170] Table 2

[0171]

[0172]

[0173] 2) The width of the regular wave entrance is δ = 1.0. The wave diffraction coefficient behind the symmetrical open breakwater at different β values ​​is shown in the attached figure. Figure 7 The specific calculation parameters are shown in Table 3.

[0174] Table 3

[0175]

[0176] Example 2

[0177] This embodiment is aimed at asymmetric open breakwaters and provides a wave diffraction coefficient analysis method for open double breakwaters. The method includes the following steps:

[0178] Step S1: Establish an asymmetric open breakwater model in a Cartesian coordinate system, specifically:

[0179] Arrange two semi-infinite breakwaters symmetrically in the Cartesian coordinate system Oxyz. The first breakwater is placed on the x-axis, and the fixed end of the first breakwater is at the origin O. The second breakwater is arranged at an angle βπ to the positive half axis of the x-axis. The distance between the fixed end of the first breakwater and the fixed end of the second breakwater is l, and the width of the mouth is l. The uniform water depth h is s , the wave propagates along the direction with an angle α with the positive direction of the x-axis.

[0180] Step S2: Based on the velocity potential function and the linearized free surface boundary conditions, the Helmholtz equation for the complex function in the velocity potential function is obtained; the Schwarz-Christoffel conformal transformation and the Green's function method are used to solve the Helmholtz equation for the boundary value, and the wave diffraction coefficient model of the open double jetty is obtained, which is specifically:

[0181] Based on the velocity potential function and the linearized free surface boundary conditions, the Helmholtz equation for the complex function in the velocity potential function is obtained, specifically:

[0182] Assuming that the fluid is incompressible and irrotational, there exists a velocity potential function that satisfies the Laplace equation. After linearizing the free surface boundary conditions, the boundary value problem of the velocity potential function φ(x, y, z, t) is obtained, which is expressed as:

[0183]

[0184]

[0185]

[0186]

[0187] Where x, y, and z are the coordinates in the Cartesian coordinate system, and h s is the uniform water depth, η is the free surface displacement, g is the acceleration due to gravity, and t is the time;

[0188] From equations (20) and (21), the mathematical expression of the velocity potential function φ(x, y, z, t) is obtained as follows:

[0189] φ(x,y,z,t)=A cosh k(z+h s )f(x,y)e iσt (26)

[0190] Where k is the wave number, is the wavelength, σ is the angular frequency, and f(x, y) is a complex function;

[0191] Substituting Equation (24) into Equation (20), we obtain the Helmholtz equation for f(x, y):

[0192]

[0193] Substituting Equation (24) into Equations (22) and (23) yields the dispersion relation:

[0194] σ 2 =gktanh(kh s ) (28)

[0195] The boundary conditions for the flow are:

[0196]

[0197] Where, is the normal vector, and Γ is the perimeter of the jetty at the water surface.

[0198] In order to solve the boundary value problem of Equation (27), the Schwarz-Christoffel conformal transformation formula is used to convert Figure 2 The physical domain of the Z plane shown is transformed conformally to Figure 3 The mathematical domain of the upper half plane of W2 shown in a, and then applying W2=e W Will Figure 3 The upper half plane mapping of W2 shown in a is Figure 3 b shows an infinitely long bar with a width of π.

[0199] The diffraction coefficient model of the asymmetric open double jetty is as follows:

[0200]

[0201]

[0202]

[0203] ξ=s1e βu (33)

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213] Where f′ out and f′ inn They are respectively the outer wave height and inner wave height when long wave incident on the breakwater, that is, when the width of the gate is less than the incident wavelength and the wavelength is smaller than the set value, f out and f inn are the external and internal wave heights under other conditions respectively; x and y are the coordinates in the Cartesian coordinate system, u and v are the coordinates after the Schwarz-Christoffel conformal transformation and W2 = e W Mapped coordinates; ε, C n is the intermediate constant, a1 and a2 are intermediate parameter variables introduced; for ε n , when n=0, ε0=2, when n≥1, ε n =1; k is the wave number, is the wavelength; J γ (x) is the Bessel function of the first kind, is the second kind of Hankel function, γ is the order;

[0214] In the case of long waves incident on the breakwater, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0215]

[0216] f' out =f' inn

[0217] Otherwise, the unknown coefficient D n and E n It is calculated from the following continuous conditions:

[0218]

[0219] f out =f inn

[0220] Step S3: Use The wave diffraction coefficient model is numerically solved by this method to obtain the analytical value of the wave diffraction coefficient.

[0221] The other settings in this embodiment are the same as those in embodiment 1.

[0222] Wave incident angle α=90°, arrangement angle The wave diffraction coefficient behind the breakwater with different opening widths is shown in the attached figure. Figure 4 The specific calculation parameters are shown in Table 4. Note: In this embodiment, the gate width is dimensionless with wavelength λ, that is,

[0223] Table 4

[0224]

[0225] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for analyzing the wave diffraction coefficient of an open double jetty, characterized in that: The method comprises the following steps: Step S1, establishing an open double jetty model in a Cartesian coordinate system; Step S2: Based on the velocity potential function and the linearized free surface boundary condition, the Helmholtz equation for the complex function in the velocity potential function is obtained; the Schwarz-Christoffel conformal transformation and the Green's function method are used to perform boundary value solutions on the Helmholtz equation to obtain a wave diffraction coefficient model for the open double jetty; Step S3, using the Nyström method to numerically solve the wave diffraction coefficient model to obtain an analytical value of the wave diffraction coefficient; The diffraction coefficient model of the asymmetric open double jetty is as follows: （28） （29） （30） （31） （32） （33） （34） （35） （36） （37） （38） （29） （40） Where, and They are respectively the outer wave height and inner wave height when long waves incident on the breakwater, that is, when the width of the gate relative to the incident wavelength is less than the set value, and are the outer domain wave height and inner domain wave height in other cases respectively; are the coordinates in the Cartesian coordinate system, is the Schwarz-Christoffel conformal transformation and Mapped coordinates; is the intermediate constant, is the intermediate parameter variable introduced; for , when n=0, , hour, ; is the wave number, , is the wavelength; is the Bessel function of the first kind, is the second kind Hankel function, is the order; In the case of long waves incident on the breakwater, the unknown coefficient and It is calculated from the following continuous conditions: Otherwise, the unknown coefficients and It is calculated from the following continuous conditions: 。 2. The wave diffraction coefficient analysis method for an open double jetty according to claim 1, characterized in that: The open double breakwater model in the Cartesian coordinate system in step S1 is a symmetrical open breakwater model, specifically: Arrange the two semi-infinite breakwaters symmetrically in the Cartesian coordinate system Oxyz middle, The axis is in the horizontal plane, The axis is vertically upward, and the intersection of the extension lines of the two breakwaters on the horizontal plane is the origin of the coordinate system O. The distance from the fixed ends of the two breakwaters to the origin O is l The distance between the fixed ends of the two breakwaters is the width of the gate. d Among them, the uniform water depth , waves along with The angle between the positive axis and the The direction of the incident propagation.

3. The wave diffraction coefficient analysis method for an open double jetty according to claim 2, characterized in that: In step S2, based on the velocity potential function and the linearized free surface boundary condition, the Helmholtz equation for the complex function in the velocity potential function is obtained, specifically: Assuming that the fluid is incompressible and irrotational, there exists a velocity potential function that satisfies the Laplace equation. After linearizing the free surface boundary conditions, the velocity potential function is obtained. The boundary value problem is expressed as: （1） （2） （3） （4） Where, are the coordinates in the Cartesian coordinate system, For uniform water depth, is the free surface displacement, is the acceleration due to gravity, For time; From equations (1)-(2), we get the velocity potential function The mathematical expression is: （5） Where, is the wave number, , is the wavelength, is the angular frequency, is a complex function; Substituting formula (5) into formula (1), we can get The Helmholtz equation: （6） Substituting Equation (5) into Equations (3) and (4) yields the dispersion relation: （7） The boundary conditions for the flow are: （8） Where, is the normal vector, and Γ is the perimeter of the jetty at the water surface.

4. The wave diffraction coefficient analysis method for an open double jetty according to claim 3, characterized in that: The Schwarz-Christoffel conformal transformation in step S2 is specifically as follows: using the Schwarz-Christoffel conformal transformation formula, the physical domain of the Z plane is conformally transformed to the mathematical domain of the upper half plane of W2, and then applying Map the upper half plane of W2 to a width of Infinite strips of .

5. The wave diffraction coefficient analysis method for an open double jetty according to claim 4, characterized in that: The diffraction coefficient model of the symmetrical open double jetty is: （9） External domain wave height: （10） （11） （12） （13） （14） Inner domain wave height: （15） （16） （17） （18） （19） Where, and They are respectively the outer wave height and inner wave height when long waves incident on the breakwater, that is, when the width of the gate relative to the incident wavelength is less than the set value, and are the outer domain wave height and inner domain wave height in other cases respectively; are the coordinates in the Cartesian coordinate system, is the Schwarz-Christoffel conformal transformation and Mapped coordinates; is the intermediate constant, is the intermediate parameter variable introduced; for , when n=0, , hour, ; is the wave number, , is the wavelength; is the Bessel function of the first kind, is the second kind Hankel function, is the order; In the case of long waves incident on the breakwater, the unknown coefficient and It is calculated from the following continuous conditions: Otherwise, the unknown coefficients and It is calculated from the following continuous conditions: 。 6. The wave diffraction coefficient analysis method for an open double jetty according to claim 1, characterized in that: The open double breakwater model in the Cartesian coordinate system in step S1 is an asymmetric open breakwater, specifically: Arrange the two semi-infinite breakwaters symmetrically in the Cartesian coordinate system Oxyz The first breakwater is located in axis, and the fixed end of the first breakwater is at the origin O, and the second breakwater is at the origin O. The positive half axis is The angle is inclined, and the distance between the fixed end of the first breakwater and the fixed end of the second breakwater is l Among them, the uniform water depth , waves along with The angle between the positive axis and the The direction of the incident propagation.

7. A wave diffraction coefficient analysis method for an open double jetty according to claim 6, characterized in that: In step S2, based on the velocity potential function and the linearized free surface boundary condition, the Helmholtz equation for the complex function in the velocity potential function is obtained, specifically: Assuming that the fluid is incompressible and irrotational, there exists a velocity potential function that satisfies the Laplace equation. After linearizing the free surface boundary conditions, the velocity potential function is obtained. The boundary value problem is expressed as: （20） （21） （22） （23） Where, are the coordinates in the Cartesian coordinate system, For uniform water depth, is the free surface displacement, is the acceleration due to gravity, For time; From equations (20)-(21), we get the velocity potential function The mathematical expression is: （24） Where, is the wave number, , is the wavelength, is the angular frequency, is a complex function; Substituting formula (24) into formula (20), we can get The Helmholtz equation: （25） Substituting Equation (24) into Equations (22) and (23) yields the dispersion relation: （26） The boundary conditions for the flow are: （27） Where, is the normal vector, and Γ is the perimeter of the jetty at the water surface.

8. The wave diffraction coefficient analysis method for an open double jetty according to claim 1, characterized in that: In step S3, the Nyström method is used to numerically solve the wave diffraction coefficient model to obtain the analytical value of the wave diffraction coefficient, which is specifically: The specific process of solving the double integral equation representing wave height in the wave diffraction coefficient model is as follows: The integration interval By step length Divide into m equal parts, the interval By step length Divide it into n equal parts, with coordinates , , then the discrete form of the integral equation representing the wave height is: （41） In the formula, the interval represents the scope of the variable s, represents the range of the variable t, is an unknown function, is a known function, is the kernel function; The double integral in equation (41) is discretized using the trapezoidal formula: （42） The discretized integral equation is transformed into a system of linear equations, and the approximate solution of the integral equation is obtained by solving this system of linear equations.

9. The wave diffraction coefficient analysis method for an open double jetty according to claim 8, characterized in that: The step S3 also includes truncating the infinite integral term contained in the integral equation, that is, selecting a finite value to approximate the upper limit of the infinite integral.

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