CN109799065B - Method for generating continuous focusing wave based on second-order wave generation theory - Google Patents
Method for generating continuous focusing wave based on second-order wave generation theory Download PDFInfo
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Abstract
The invention provides a method for generating continuous focusing waves based on a second-order wave generation theory, which comprises the following steps: selecting a proper focusing position and time of a focusing wave target, determining the wave amplitude and initial phase of each wave component of the focusing wave, calculating the motion displacement of a wave maker and making waves in a water tank by using a second-order wave making theory according to the theoretical wave making parameters of the wave components, observing the wave surface time course at the focusing point and carrying out correlation analysis on the wave surface time course and the target wave surface; if the waveform does not meet the requirements, reasonably correcting the wave-making input parameters according to the target amplitude and phase, substituting the corrected wave-making parameters into a wave-making machine displacement calculation equation to calculate the displacement of the wave-making machine and make waves in the water tank, observing the wave surface at the focus point and comparing with the ideal wave surface, and if the waveform does not meet the requirements, iterating again. By applying the wave making method provided by the invention, continuous focusing waves with good wave forms and specific periods can be obtained within less iterative wave making times, and the efficiency of a wave groove hydrodynamic test is improved.
Description
Technical Field
The invention relates to a test technology of a hydrodynamic wave water tank test in offshore and oceanographic engineering, in particular to a method for generating a continuous focusing wave based on a second-order wave-making theory.
Background
Sea-going infrastructures such as offshore wind turbines, offshore oil platforms, land-sea junctions, etc. have begun to and are becoming an important foundation for the development of offshore economic zones. The infrastructure structures are in complex marine environments and face a series of environmental disasters such as wind, wave, ocean current, earthquake, corrosion and the like. Extreme waves belong to marine environmental disasters that pose a serious threat to marine building safety (Whittaker et al 2016; Chien et al 2002). The research result of catastrophe shows that the frequency of occurrence of future marine disasters such as strong typhoon, extreme waves, tsunami and the like is not obviously increased under the background of global climate change, but the intensity of single-time disasters can be obviously increased. If strong typhoon 'sky pigeon' in 2017 causes great social and economic loss to China at Zhu triangular region, and extreme waves caused by the sky pigeon cause damage to engineering structures such as breakwater, revetment and the like in offshore region. Therefore, the deep recognition of the effect of the extreme waves on the engineering structure has important significance for improving the safety of the marine and offshore engineering structures. The wave water power model test is used as a powerful means for researching the wave-structure action problem of the ocean engineering structure, and plays a role in propulsion in the ocean engineering development process.
At present, the method of focusing waves is generally used for simulating extreme waves in a laboratory, and the focusing waves can be regarded as regular waves with multiple frequencies, wherein wave crests appear in a uniform place at the same time, so that the wave crests are superposed to form waves with larger wave amplitude. In 1990, two scholars, Rapp and Melville, use a wave focusing method to generate large-amplitude waves in a water tank and observe the phenomenon that the focused waves are broken under the deep water condition; cox and Ortega observed the slamming pressure of the focused waves on the horizontal dock plate in 2002; Hunt-Raby et al (2011) studied the wave overtopping phenomenon of focused waves on bank; the focus principle of the focused wave is also researched by subject groups of national academists (Maet al.2010), Yangjian people (Deng et al.2016) and the wave-structure effect is observed by using the focused wave. Although the generation of large amplitude waves by the wave focusing method has been known for almost thirty years, the focusing waves used so far still have the phenomenon of focus moment and focus point shift down (Fern end et. 2014).
In order to improve the test efficiency, the applicant previously proposed a practical method of generating a continuous focusing wave in a water bath, but this method also has a phenomenon in which the focusing time and the focusing point move down.
Disclosure of Invention
Aiming at the problem that the focus point of continuous focusing waves generated in a water tank moves downwards, the invention aims to provide a wave making method for generating continuous focusing waves with ideal waveforms in the water tank based on a high-order wave making theory, which can repeatedly and stably generate a plurality of focusing waves with ideal waveforms in a short time, reduce iteration times, improve test efficiency, provide actual wave tank tests as input waves and improve wave simulation precision.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for generating continuous focusing wave based on second order wave-making theory comprises the following steps: firstly, selecting a proper focusing position and time of a focusing wave target, determining the wave amplitude and initial phase of each wave component of the focusing wave, calculating the motion displacement of a wave generator by using a second-order wave-making theory according to the theoretical wave-making parameters of the wave components, making waves in a water tank, observing the wave surface time course at the focusing point and carrying out correlation analysis on the wave surface time course and the target wave surface; if the waveform does not meet the requirements, reasonably correcting the wave making input parameters according to the target amplitude and phase, substituting the corrected wave making parameters into a wave making machine displacement calculation equation to calculate the displacement of the wave making machine and make waves in the water tank, observing the wave surface at the focus point and comparing the wave surface with the ideal wave surface, and if the waveform does not meet the requirements, iterating again until the requirements are met.
The wave-making parameters required by the focusing wave generating good wave shape can be rapidly obtained by applying the second-order wave-making theory in the iterative correction process, the wave-making parameters are substituted into the corresponding unique calculation equation of the continuous focusing wave generator, the wave-making machine displacement required by the continuous focusing wave can be obtained, and the displacement is loaded into a wave-making machine control program, so that the ideal continuous focusing wave with wave shape can be obtained at the focusing point; by using the method, the displacement signal of the push plate wave maker, which can be used for generating continuous focusing waves with good waveforms in the wave water tank, can be obtained after a few iterative correction times.
The invention also has the following technical characteristics
1. The specific method of the required wave generator displacement data is as follows:
perturbation expansion is carried out on the wave surface η by taking the wave steepness H/L as a small parameter, and the wave steepness is accurately expressed to the second order:
η＝η(1)+2η(2)(1)
in the formula:
-small parameters, steepness of wave;
η(1)-a first order wave surface;
η(2)-a second order wave surface;
linear wave-making theory only considers the first-order component η(1)The displacement of the push plate based on the linear wave-making theory is X(1)(ii) a Wave maker push plate linear displacement X(1)Calculated from the following formula:
in the formula:
Nf-composition ofThe total number of harmonics;
i-a virtual unit;
fn-the nth wave frequency component;
t is time;
Xan-frequency f of component wavesnThe first order wavemaking plate complex amplitude of (1);
c.c. -conjugate complex numbers of antecedent expressions, in order to convert complex expressions into real expressions;
the corresponding first order wavefront is:
in the formula:
kjwave number, including real wave number k0And the number of imaginary waves kj(j is more than or equal to 1), which are respectively a real root and an imaginary root of a dispersion equation and correspond to a propagation mode and a non-propagation mode in a first-order wave surface;
x-spatial position;
cjn-a first order transfer function derived directly from the linear wave theory;
the dispersion equation is:
ωn 2＝gkjntanh(kjnh) (4)
in the formula:
ωn-component wave angular frequency, ωn＝2πfn；
h-water depth;
frequency f of component wavenComplex amplitude a of the propagating mode ofnComplex amplitude X of motion of wave making plateanThe following relationships exist:
An＝cn0Xan(5)
wherein the complex amplitude AnInvolving the frequency f of the component wavenAmplitude a of the wave component ofnAnd an initial phase phinInformation, determined by:
the generation of continuous focusing wave with good waveform in the water tank generally requires several attempts to make wave and collect wave surface correction amplitude anAnd an initial phase phinThe process of (2); when the initial trial wave manufacturing is carried out, the position x of the focus point is determined according to the theorybAnd a focusing time tbDetermining an initial phase phin：
φn＝-k0nxb+2πfntb(7)
In the formula:
xb-a target focus position;
tb-target focus point moment;
because of the constrained harmonic generated by the interaction of the first-order wave components and the free pseudo harmonic generated by the mismatching of the first-order propagation mode velocity potential of the wave making plate away from the average position at the boundary of the wave making plate, when the wave making plate moves according to the first-order displacement, the wave surface generated in the wave water tank actually contains the two high-order harmonic components which are respectively recorded as η(21)And η(22)I.e. η being present in the water bath at the same time(1)+η(21)+η(22)；
η(21)Due to the interaction of first order wave components, which cannot be corrected by manual means, η(22)Due to the mismatch of the wave-making plate boundary, by adding an extra wave-making plate displacement X(2)Corrected and second-order displacement X by adding wave-making plate(2)Generating free harmonics η(23)To cancel free pseudo-harmonics η(22)So as to obtain a wave surface of η in the water tank(1)+η(21)；
The generation of focused waves using the second order wave generation theory requires a specific frequency (f) for each pair of wavesn,fm) Analyzing the components to obtain the corresponding second-order wave making plate displacement Xnm (2)The expression is as follows:
in the formula:
F±-a second order transfer function;
representing that the sum frequency term is unchanged and the difference frequency term takes the conjugate complex number of the sum frequency term for the complex expression;
the expression of the second-order transfer function is:
in the formula:
Kp ±-generalized dispersion equation (ω)n±ωm)2＝gKp ±tanh(Kp ±h) The real root (p ═ 0) and the virtual root solution (p ≧ 1);
therefore, only the first-order displacement X of the push plate needs to be calculated for generating the continuous focusing wave by utilizing the linear wave-making theory(1)Equation (2), the generation of continuous focusing wave by using the second-order wave-making theory requires the calculation of the first-order displacement X(1)And a second order displacement X(2)±And a displacement X2nd：
The generation of a continuous focused wave in the water bath only requires the setting of a plurality of focusing moments (t)b1,tb2,tb3,tb4… …) respectively substituted into the formula (10) to obtain the second-order wave-making push plate displacement X2nd 1，X2nd 2，X2nd 3，X2nd 4… …, and then adding and summing:
X＝X2nd 1+X2nd 2+X2nd 3+X2nd 4+… (11)
when the test water tank is provided with the push plate wave generator in the formula (9)
M2(kjn,K0 ±)＝0 (12)
Wherein:
if the push plate wave generator is positioned at the position where x is 0m in the water tank, setting the expected wave focusing time tbThe focusing point is x ═ xbSelecting proper wave spectrum according to the user's requirement to determine the amplitude a of each wave frequency componentn 1。
Calculating to obtain the initial phase phi of each wave frequency component required by the first wave generation according to the formula (7)n 1：
φi 1＝-kixb+ωitb
Will be at the initial phase phin 1And amplitude an 1Substituting the formula (10) and the formula (11) to calculate the push plate displacement X of the first wave generation1Starting the wave generator to generate wave and collecting the time course η of wave surface1；
The wave surface time course η obtained by the acquisition1Performing correlation analysis with the theoretical wave surface, evaluating the waveform, and if the waveform does not meet the requirement, performing η on the wave surface time course1Performing fast Fourier transformation to obtain the first wave-making actual measurement initial phase phin 1,measuredAnd amplitude an 1,measuredWill input phin 1，an 1And actually measures phin 1,measured，an 1,measuredSubstituting into a formula:
φi,new＝φi,old+(φi,target-φi,measured) (15)
obtaining the input initial phase phi of the second wave generationn 2And amplitude an 2；
The obtained initial phase phii 2And amplitude ai 2And (5) substituting the formula (10) and the formula (11), and repeating the process until the wave surface measured at the focusing point meets the requirement, thereby obtaining the wave maker push plate displacement required for generating the wave direction good continuous focusing wave in the water tank.
2. When a rocking plate type wave generator is equipped in the test water tank, in the formula (9), E±And M2(kjn,K0 ±) The two parameters are determined by equations (17) and (18), respectively:
the invention has the following beneficial effects and advantages: by applying the wave making method provided by the invention, the continuous focusing wave with good waveform can be obtained in a short time through less iteration steps, the test efficiency of the focusing wave with good waveform is improved, the simulation precision, the repeatability and the stability of the input wave of the wave-structure action hydrodynamic test are improved, the focusing wave repeated test becomes a feasible scheme, and the test efficiency is improved.
Drawings
FIG. 1 is a diagram of an ideal wave surface generated in a water tank by a linear wave generation method, wherein the peak frequency f is the wave surface of the first step iteration 1p0.6Hz, target maximum amplitude Amax11.0 cm; the correlation coefficient of the actually measured wave surface and the theoretical wave surface is 0.9530;
FIG. 2 is a 3 rd step iteration wave surface of ideal wave surface generated in a water tank by a linear wave making method, and the peak frequency fp0.6Hz, target maximum amplitude Amax11.0 cm; measured in factThe correlation coefficient of the wave surface and the theoretical wave surface is 0.9562;
FIG. 3 is the 6 th step of iterative wave surface of ideal wave surface generated in the water tank by the linear wave-making method, the peak frequency fp0.6Hz, target maximum amplitude Amax11.0 cm; the correlation coefficient of the actually measured wave surface and the theoretical wave surface is 0.9607;
FIG. 4 shows the first step of iterative wavefront, peak frequency f, of an ideal wavefront generated in a water tank by a second-order wave generation methodp0.6Hz, target maximum amplitude Amax11.0 cm; the correlation coefficient of the actually measured wave surface and the theoretical wave surface is 0.9726;
FIG. 5 is a diagram of an ideal wave surface generated in a water tank by a second-order wave generation method, the peak frequency f, the 2 nd step of an iterative wave surfacep0.6Hz, target maximum amplitude Amax11.0 cm; the correlation coefficient of the actually measured wave surface and the theoretical wave surface is 0.9758;
FIG. 6 is a diagram of an ideal wave surface generated in a water tank by a second-order wave generation method, the peak frequency f of the ideal wave surface and the step 3 iteration wave surfacep0.6Hz, target maximum amplitude Amax11.0 cm; the correlation coefficient of the actually measured wave surface and the theoretical wave surface is 0.9764;
Detailed Description
The following further describes the specific derivation processes and embodiments of the present invention, and for the sake of brevity, the derivation processes are expressed in plural forms:
example 1
Perturbation expansion is carried out on the wave surface η by taking the wave steepness H/L as a small parameter, and the wave steepness is accurately expressed to the second order:
η＝η(1)+2η(2)(19)
in the formula:
-small parameters, steepness of wave;
η(1)-a first order wave surface;
η(2)-a second order wave surface;
linear wave-making theory only considers the first-order component η(1)The displacement of the push plate based on the linear wave-making theory is X(1). Wave maker push plate linear displacement X(1)Can be calculated from the following formula:
in the formula:
Nf-forming a total number of harmonics;
i-a virtual unit;
fn-the nth wave frequency component;
t is time;
Xan-frequency f of component wavesnThe first order wavemaking plate complex amplitude of (1);
c.c. -conjugate complex numbers of antecedent expressions, in order to convert complex expressions into real expressions;
corresponding to a first order wave surface of
In the formula:
kjwave number, including real wave number k0And the number of imaginary waves kj(j is more than or equal to 1), which are respectively a real root and an imaginary root of a dispersion equation and correspond to a propagation mode and a non-propagation mode in a first-order wave surface;
x-spatial position;
cjnthe first-order transfer function can be directly derived and solved by a linear wave theory;
the dispersion equation is:
ωn 2＝gkjntanh(kjnh) (22)
in the formula:
ωn-component wave angular frequency, ωn＝2πfn；
h-water depth.
Frequency f of component wavenComplex amplitude a of the propagating mode (i.e. micro-amplitude wave in the popular sense)nComplex amplitude X of motion of wave making plateanThe following relationships exist:
An＝cn0Xan(23)
wherein the complex amplitude AnInvolving the frequency f of the component wavenAmplitude a of the wave component ofnAnd an initial phase phinInformation, can be determined by:
the generation of continuous focusing wave with good waveform in the water tank generally requires several attempts to make wave and collect wave surface correction amplitude anAnd an initial phase phinThe process of (1). When the wave is manufactured for the first time, the theoretical focusing point position x can be usedbAnd a focusing time tbDetermining an initial phase phin：
φn＝-k0nxb+2πfntb(25)
In the formula:
xb-a target focus position;
tb-target focal point instant.
Because of the constrained harmonic generated by the interaction of the first-order wave components and the free pseudo harmonic generated by the mismatching of the first-order propagation mode velocity potential of the wave making plate away from the average position at the boundary of the wave making plate, when the wave making plate moves according to the first-order displacement, the wave surface generated in the wave water tank actually contains the two high-order harmonic components which are respectively recorded as η(21)And η(22)I.e. η being present in the water bath at the same time(1)+η(21)+η(22)。
η(21)Due to the interaction of first order wave components, which cannot be corrected by manual means, η(22)Is generated due to the mismatch of the wave making plate boundary, and can be obtained by adding extra wave making plate displacement X(2)Corrected and second-order displacement X by adding wave-making plate(2)Generating free harmonics η(23)To cancel free pseudo-harmonics η(22)So as to obtain a wave surface of η in the water tank(1)+η(21)。
The generation of focused waves using the second order wave generation theory requires a specific frequency (f) for each pair of wavesn,fm) Analyzing the components to obtain the corresponding second-order wave making plate displacement Xnm (2)The expression is as follows:
in the formula:
F±-a second order transfer function;
and represents that the sum frequency term is unchanged and the difference frequency term takes the conjugate complex number of the sum frequency term for the complex expression.
The second-order transfer function is the most important achievement of a second-order wave generation theory, and the expression of the second-order transfer function is as follows:
in the formula:
Kp ±-generalized dispersion equation (ω)n±ωm)2＝gKp ±tanh(Kp ±h) The real root (p ═ 0) and the virtual root solution (p ≧ 1);
E±and M2(kjn,K0 ±) Two parameters are related to the type of wave generator, see detailed examples 2-3.
Therefore, only the first-order displacement X of the push plate needs to be calculated for generating the continuous focusing wave by utilizing the linear wave-making theory(1)Equation (20), the generation of continuous focusing wave by using the second-order wave-making theory requires the calculation of the first-order displacement X(1)And a second order displacement X(2)±And a displacement X2nd：
The continuous focusing wave generated in the water tank only needs to be provided with moreA time of focus (t)b1,tb2,tb3,tb4… …) respectively substituted into the formula (28) to obtain the second-order wave-making push plate displacement X2nd 1，X2nd 2，X2nd 3，X2nd 4… …, and then adding and summing:
X＝X2nd 1+X2nd 2+X2nd 3+X2nd 4+… (29)
when continuous focusing waves are generated in a laboratory, when a linear wave-making theory is adopted, 5-8 times are generally needed to obtain ideal focusing waves, and the iterative wave-making times required for obtaining good focusing waves are reduced to 2-3 times by applying the second-order focusing wave-making method disclosed by the invention, so that the hydrodynamic force test efficiency is improved.
Example 2
If the test water tank is provided with the push plate wave generator, the formula (27) shows
M2(kjn,K0 ±)＝0 (30)
Wherein:
if the push plate wave generator is positioned at the position where x is 0m in the water tank, setting the expected wave focusing time tbThe focusing point is x ═ xbSelecting proper wave spectrum according to the user's requirement to determine the amplitude a of each wave frequency componentn 1。
Calculating to obtain the initial phase phi of each wave frequency component required by the first wave generation according to a formula (25)n 1：
φi 1＝-kixb+ωitb
Will be at the initial phase phin 1And amplitude an 1Substituting the formula (28) and the formula (29) to calculate the push plate displacement X of the first wave generation1Starting the wave generator to generate wave and collecting the time course η of wave surface1。
The wave surface time course η obtained by the acquisition1Performing correlation analysis with the theoretical wave surface, evaluating the waveform, and if the waveform does not meet the requirement, performing η on the wave surface time course1Performing fast Fourier transformation to obtain the first wave-making actual measurement initial phase phin 1,measuredAnd amplitude an 1,measuredWill input phin 1，an 1And actually measures phin 1,measured，an 1,measuredSubstituting into a formula:
φi,new＝φi,old+(φi,target-φi,measured) (33)
obtaining the input initial phase phi of the second wave generationn 2And amplitude an 2。
The obtained initial phase phii 2And amplitude ai 2And (6) substituting the formula (28) and the formula (29), and repeating the process until the wave surface measured at the focusing point meets the requirement, thereby obtaining the displacement of the wave maker push plate required for generating the wave direction good continuous focusing wave in the water tank.
Example 3
The rocking plate type wave generator hinged to the bottom of a water pool is generally used for generating focused waves in a deep water environment. If the continuous focusing wave in the deep water environment needs to be simulated, the basic steps of the method are the same as those of the specific embodiment 2, except that in the formula (27), E±And M2(kjn,K0 ±) The two parameters are determined by equations (17) and (18), respectively:
Claims (2)
1. a method for generating continuous focusing wave based on second order wave-making theory is characterized in that the method comprises the following steps: selecting a proper focusing position and time of a focusing wave target, determining the wave amplitude and initial phase of each wave component of the focusing wave, calculating the motion displacement of a wave maker and making waves in a water tank by using a second-order wave making theory according to the theoretical wave making parameters of the wave components, observing the wave surface time course at the focusing point and carrying out correlation analysis on the wave surface time course and the target wave surface; if the waveform does not meet the requirements, reasonably correcting the wave-making input parameters according to the target amplitude and phase, substituting the corrected wave-making parameters into a wave-making machine displacement calculation equation to calculate the displacement of the wave-making machine and make waves in a water tank, observing the wave surface at the focus point and comparing the wave surface with the ideal wave surface, and if the waveform does not meet the requirements, iterating again until the requirements are met;
the specific method of the required wave generator displacement data is as follows:
perturbation expansion is carried out on the wave surface η by taking the wave steepness H/L as a small parameter, and the wave steepness is accurately expressed to the second order:
η＝η(1)+2η(2)(1)
in the formula:
-small parameters, steepness of wave;
η(1)-a first order wave surface;
η(2)-a second order wave surface;
linear wave-making theory only considers the first-order component η(1)The displacement of the push plate based on the linear wave-making theory is X(1)(ii) a Wave maker push plate linear displacement X(1)Calculated from the following formula:
in the formula:
Nf-forming a total number of harmonics;
i-a virtual unit;
fn-the nth wave frequency component;
t is time;
Xan-frequency f of component wavesnThe first order wavemaking plate complex amplitude of (1);
c.c. -conjugate complex numbers of antecedent expressions, in order to convert complex expressions into real expressions;
the corresponding first order wavefront is:
in the formula:
kjwave number, including real wave number k0And the number of imaginary waves kj(j is more than or equal to 1), which are respectively a real root and an imaginary root of a dispersion equation and correspond to a propagation mode and a non-propagation mode in a first-order wave surface;
x-spatial position;
cjn-a first order transfer function derived directly from the linear wave theory;
the dispersion equation is:
ωn 2＝gkjntanh(kjnh) (4)
in the formula:
ωn-component wave angular frequency, ωn＝2πfn；
h-water depth;
frequency f of component wavenComplex amplitude a of the propagating mode ofnComplex amplitude X of motion of wave making plateanThe following relationships exist:
An＝cn0Xan(5)
wherein the complex amplitude AnInvolving the frequency f of the component wavenAmplitude a of the wave component ofnAnd an initial phase phinInformation, determined by:
the generation of continuous focusing wave with good waveform in the water tank generally requires several attempts to make wave and collect wave surface correction amplitude anAnd an initial phase phinThe process of (2); when the initial trial wave manufacturing is carried out, the position x of the focus point is determined according to the theorybAnd a focusing time tbDetermining an initial phase phin：
φn＝-k0nxb+2πfntb(7)
In the formula:
xb-a target focus position;
tb-target focus point moment;
because of the constrained harmonic generated by the interaction of the first-order wave components and the free pseudo harmonic generated by the mismatching of the first-order propagation mode velocity potential of the wave making plate away from the average position at the boundary of the wave making plate, when the wave making plate moves according to the first-order displacement, the wave surface generated in the wave water tank actually comprises two high-order harmonic components which are respectively recorded as η(21)And η(22)I.e. η being present in the water bath at the same time(1)+η(21)+η(22)；
η(21)Due to the interaction of first order wave components, which cannot be corrected by manual means, η(22)Due to the mismatch of the wave-making plate boundary, by adding an extra wave-making plate displacement X(2)Corrected and second-order displacement X by adding wave-making plate(2)Generating free harmonics η(23)To cancel free pseudo-harmonics η(22)So as to obtain a wave surface of η in the water tank(1)+η(21)；
The generation of focused waves using the second order wave generation theory requires a specific frequency (f) for each pair of wavesn,fm) Analyzing the components to obtain the corresponding second-order wave making plate displacement Xnm (2)The expression is as follows:
in the formula:
F±-a second order transfer function;
representing that the sum frequency term is unchanged and the difference frequency term takes the conjugate complex number of the sum frequency term for the complex expression;
the expression of the second-order transfer function is:
in the formula:
Kp ±-generalized dispersion equation (ω)n±ωm)2＝gKp ±tanh(Kp ±h) The real root (p ═ 0) and the virtual root solution (p ≧ 1);
therefore, only the first-order displacement X of the push plate needs to be calculated for generating the continuous focusing wave by utilizing the linear wave-making theory(1)Equation (2), the generation of continuous focusing wave by using the second-order wave-making theory requires the calculation of the first-order displacement X(1)And a second order displacement X(2)±And a displacement X2nd：
The generation of a continuous focused wave in the water bath only requires the setting of a plurality of focusing moments (t)b1,tb2,tb3,tb4… …) respectively substituted into the formula (10) to obtain the second-order wave-making push plate displacement X2nd 1，X2nd 2，X2nd 3，X2nd 4… …, and then adding and summing:
X＝X2nd 1+X2nd 2+X2nd 3+X2nd 4+… (11)
when the test water tank is provided with the push plate wave generator in the formula (9)
M2(kjn,K0 ±)＝0 (12)
Wherein:
if the push plate wave generator is positioned at the position where x is 0m in the water tank, setting the expected wave focusing time tbThe focusing point is x ═ xbSelecting proper wave spectrum according to the user's requirement to determine the amplitude a of each wave frequency componentn 1。
Calculating to obtain the initial phase phi of each wave frequency component required by the first wave generation according to the formula (7)n 1：
Will be at the initial phase phin 1And amplitude an 1Substituting the formula (10) and the formula (11) to calculate the push plate displacement X of the first wave generation1Starting the wave generator to generate wave and collecting the time course η of wave surface1；
The wave surface time course η obtained by the acquisition1Performing correlation analysis with the theoretical wave surface, evaluating the waveform, and if the waveform does not meet the requirement, performing η on the wave surface time course1Performing fast Fourier transformation to obtain the first wave-making actual measurement initial phase phin 1,measuredAnd amplitude an 1,measuredWill input phin 1，an 1And actually measures phin 1,measured，an 1,measuredSubstituting into a formula:
φi,new＝φi,old+(φi,target-φi,measured) (15)
obtaining the input initial phase phi of the second wave generationn 2And amplitude an 2；
The obtained initial phase phii 2And amplitude ai 2And (5) substituting the formula (10) and the formula (11), and repeating the process until the wave surface measured at the focusing point meets the requirement, thereby obtaining the wave maker push plate displacement required for generating the wave direction good continuous focusing wave in the water tank.
2. The method for generating continuous focusing waves based on the second-order wave generation theory as claimed in claim 1, wherein when a rocking plate type wave generator is equipped in the test water tank, formula (9), E±And M2(kjn,K0 ±) The two parameters are determined by equations (17) and (18), respectively:
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