CN101308519B - Sea evolution scene emulation method of multiple shortwave nonlinearly modulated by longwave - Google Patents

Abstract

The invention relates to an evolution scene simulation method for waves after multiple short waves are nonlinearly modulated by long waves. The method comprises the following steps: according to the deep-sea dynamic boundary conditions, a perturbation method is used to a solve the sea surface space-time evolution analytical solution when a short 0 is nonlinearly modulated by a long wave 0; the obtained analytical solution is taken as a long wave 1, and a second short wave 1 is nonlinearly modulated by the long wave 1; after the short waves are nonlinearly modulated, the waves are regarded as waves with variable amplitude, variable frequency and variable wavelength; the short waves are modulated by the long waves, and the long wave parameters are affected by the short waves, so that the long waves become <non-linear long waves> with the amplitude, frequency and other parameters varying with space and time. Therefore, the problem that boundary conditions are not be used to solve the analytical solution of the nonlinear modulation between a long wave and more than two short waves is solved.

Description

A plurality of shortwaves are subjected to the wave evolution scenario simulation method of long wave non-linear modulation

Technical field

The invention belongs to the ocean dynamics field of engineering technology, be specifically related to the wave evolution scenario simulation method that a kind of a plurality of shortwave is subjected to the long wave non-linear modulation.

Background technology

Deep-sea wave temporal-spatial evolution numerical simulation is an important use research work in the ocean dynamics field of engineering technology, is deep-sea oil platform, the indispensable part in shipbuilding technology field.So far, sea wave simulation Technical Board in deep-sea is limited to linear wave model.

Pierson and Moskowitz[1] at first by observation, famous PM ocean wave spectrum is proposed to full grown stormy waves and parameter thereof.Hasselman etc. have proposed JONSWAP spectrum [2] to northeast part of China wave and parameter observation.Recently, J.H.G.M.Alves etc. [3] revises the PM spectrum.These ocean wave spectrum models become and carry out sea wave simulation basis, deep-sea in the ocean dynamics field of engineering technology.

At present, people to deep-sea wave temporal-spatial evolution analogy method are: based on above-mentioned ocean wave spectrum (PM spectrum, JONSWAP spectrum), adopt pseudo-spectrum fourier method that ocean wave spectrum is carried out Fourier transform, obtain sea evolution function by numerous different wave amplitudes, wavelength, the monochromatic wave linear superposition of frequency.For example, F.Berizzi etc. [4] propose fractal sea model in 1999, and the method for employing is the monochromatic wave linear superposition with a large amount of different FRACTAL DIMENSION, characterize between the wave model on sea and definite sea at random.Because the deep-sea wave is not linear, long wave has modulating action (Longuet-Higgins etc. [5]) to parameters such as shortwave wavelength, wave amplitudes, the analogy method of linear wave stack can not accurately be simulated true sea situation, though E.Lo, C.C.Mei etc. [6] propose a kind of pseudo-spectrum fourier method non-linear Schrodinger's EVOLUTION EQUATION are carried out numerical simulation, but Schrodinger's EVOLUTION EQUATION mainly is to consider what complete nonlinear solitary wave developed, in fact, the deep-sea wave is a model of being modulated the linearity and the Nonlinear Superposition of a plurality of shortwaves by a long wave.Existing theory can not obtain the analytic solution that a plurality of shortwaves are subjected to the long wave modulation, thereby causes existing wave model can not characterize the non-linear modulation effect of long wave to a plurality of shortwaves.

List of references

[1] W.J.Pierson?and?L.Moskowitz，A?proposed?spectrum?formfor?fully?developed?wind?seas?based?on?the?similarity?theory?ofS.A，Kitaigorodskii，J.Geophys.Res.，Vol.69，p：5181-5190，1964.

[2]G.J.Komen，L.Cavaleri，M.Donelan，K.Hasselman，S.Hasselman?and?P.A.E.M.Janssen?Dynamics?and?modelling?of?oceanwaves，Cambridge?University?Press，1994.

[3]J.H.G.M.Alves，M.L?Banner?and?Ian?R?Young，Revisitingthe?Pierson-Moskowitz?asymptotic?limits?for?fully?developed?windwaves.Journal?of?Physical?Oceanography.Vol.33，Iss.7；p：1301-1323，2003。

[4]F.Berizzi，E.D.Mese?and?G.Pinelli，One-dimensionalfractal?model?of?the?sea?surface，IEE?Proc.Radar，Sonar?Navig.，Vol.146，No.1，pp：55-64，1999.

[5]M.S.Longuet-Higgins?and?R.W.Stewart，Changes?in?theform?of?short?gravity?waves?on?long?waves?and?tidal?currents.Journal?of?fluid?Mechanics，Vol.8，p：565-583，1960.

[6]E.Lo，C.C.Mei，A?numerical?study?of?water-wavemodulation?based?on?a?higher-order?nonlinear

equation，J.Fluid?Mech.Vol.150，p：395?416，1985.

Summary of the invention

The wave evolution scenario simulation method that provides a kind of a plurality of shortwave to be subjected to the long wave non-linear modulation is provided the object of the invention.

The non-linear wave evolution scenario simulation method that the present invention proposes is based on the analogy method that shortwave is subjected to the wave evolution scene of long wave non-linear modulation.Longuet-Higgins etc. are according to unlimited degree of depth ocean dynamics boundary condition and perturbation method, derive the non-linear parsing expression formula of wave temporal-spatial evolution that a shortwave is subjected to a long wave modulation, from resolving the angle of mathematics, have no idea to shift onto out the wave temporal-spatial evolution analytical expression that two and above shortwave are subjected to long wave modulation situation.The present invention is directed to this problem, proposed a kind of method that a plurality of shortwaves are subjected to the wave evolution scene of long wave non-linear modulation of simulating.

To achieve these goals, the method applied in the present invention is:

First step: adopt perturbation method, according to deep-sea dynamics boundary condition, find the solution a shortwave and (be called for short: (be called for short: the sea temporal-spatial evolution analytic solution of non-linear modulation long wave 0) by a long wave;

Second step: (be called for short: long wave 1), second shortwave (is called for short: shortwave 1) be subjected to this long wave non-linear modulation to regard the analytic solution that obtain as a long wave;

Third step: at the analytic solution that can not find the solution its non-linear modulation, the one, regard in time long wave 1 as with space luffing, frequency conversion, change wave number " nonlinear long wave 1 ", the 2nd, the long wave of the corresponding wave amplitude of certain spatial point of different concrete certain time point, frequency all satisfies deep-sea dynamics boundary condition, with long wave 1 regard as these long waves respectively during non-linear modulation shortwaves 1 in the stack (being called discrete analytic solution) of the analytic solution of corresponding time point and spatial point;

The 4th step: " the discrete analytic solution " that adopting uses the same method finds the solution the 3rd, 4, a 5...... shortwave is subjected to front " nonlinear long wave 2,3,4...... " modulation;

The 5th step: compose according to PM, obtain parameters such as the long and short wave-wave width of cloth under the different wind speed and corresponding frequency thereof and wavelength as input, by being that operator carries out numerical simulation, can simulate the wave evolution scene that different sea situations, a plurality of shortwaves in deep-sea are subjected to the long wave non-linear modulation with " discrete analytic solution ".

Among the present invention, proposed the wave after the length ripple non-linear modulation is regarded as the thought of luffing, frequency conversion, change wavelength wave.Shortwave is modulated by long wave, and the long wave parameter is subjected to the influence of shortwave to become " nonlinear long wave " conversely, and parameters such as its amplitude, frequency are space-variantization and changing at any time, and this is the precondition of core technology of the present invention.

The present invention proposes the core technology of " nonlinear long wave " discretize.Deep-sea dynamics boundary condition also only is suitable for fixedly, and the sine wave of different parameters interacts, so luffing, frequency conversion, become " nonlinear long wave " of wavelength and the non-linear modulation situation of other shortwave, can not utilize boundary condition to obtain its analytic solution, and concrete corresponding wave amplitude of certain spatial point of certain time point, frequency and wavelength are fixed, with " nonlinear long wave " discretize, being about to " nonlinear long wave " regards as in corresponding time point and spatial point, corresponding fixedly wave amplitude, the stack of the analytic solution when the isoparametric different long waves of frequency are distinguished the non-linear modulation shortwave has so just solved the difficulty that can not utilize boundary condition to obtain a long wave and two above shortwave non-linear modulation analytic solution.

Description of drawings

Fig. 1 modulates " nonlinear long wave " frequency space evolution diagram of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Fig. 2 modulates " nonlinear long wave " frequency temporal evolution figure of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Fig. 3 modulates " nonlinear long wave " initial phase spatial evolution figure of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Fig. 4 modulates " nonlinear long wave " initial phase temporal evolution figure of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Fig. 5 modulates " nonlinear long wave " amplitude space evolution diagram of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Fig. 6 modulates " nonlinear long wave " amplitude temporal evolution figure of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Fig. 7 modulates the spatial evolution figure of 2,3,4,5,6 shortwaves respectively for long wave of the present invention.

Long wave of Fig. 8 is modulated respectively among the temporal evolution figure figure of 2,3,4,5,6 shortwaves: 19.5 meters high wind speed: U=[20 7.5 7 6.5 65.5 5 that generate 7 ripple correspondences]; Calculate the amplitude of 7 ripples according to the PM spectrum: a=[4.27 0.6 0.52 0.450.38 0.32 0.27]; Calculate 7 wave frequencies according to the PM spectrum: f=[0.07 0.180.2 0.21 0.23 0.25 0.27]; The wavelength of 7 ripples: Lamda=[318.31 48.1438.99 35.37 29.48 24.96 21.40]; The angular frequency of 7 ripple correspondences: w=[0.441.13 1.26 1.32 1.45 1.57 1.70]; 7 ripple wave number k=[0.020.13 0.16 0.18 0.21 0.25 0.29 separately]; The initial phase of 7 ripples is made as: thet=[0 185 124 35 105 20 141].

Embodiment

The present invention is described in further detail below in conjunction with accompanying drawing.

The present invention proposes the wave evolution scenario simulation method that a plurality of shortwaves are subjected to the long wave non-linear modulation, mainly comprises three steps:

1. at concrete length wave system system, solve " the discrete analytic solution " of system, obtain the evolution operator;

2. according to the PM spectrum model,, obtain under the different wind speed sea situations parameter informations such as corresponding wave wave amplitude, wavelength and frequency by numerical evaluation;

3. the phylogeny operator that utilizes step 1 to obtain, the system parameter message that obtains with step 2 is input, a plurality of shortwaves of simulation output are subjected to the wave evolution scene of long wave non-linear modulation.

Wherein the first step is that the evolution operator of system obtains, and the concrete obtain manner of evolution operator of 2 shortwaves of 1 long wave modulation is:

According to document [5], the deep-sea sea wave power is learned boundary condition and is satisfied:

$u=\&dtri;\mathrm{\&phi;}---\left(1a\right)$

${\&dtri;}^2\mathrm{\&phi;}=0---\left(1b\right)$

$\frac{p}{\mathrm{\&rho;}}+\mathrm{gz}+\frac{1}{2}{u}^2+\frac{\&PartialD;\mathrm{\&phi;}}{\&PartialD;t}=0---\left(1c\right)$

U wherein, φ, p, ρ, ζ represent speed, velocity potential, pressure, density and surface elevation respectively.When long wave to the shortwave perturbation, relevant parameter is:

u＝u ⁽⁰⁾+εu ⁽¹⁾+… (2a)

φ＝φ ⁽⁰⁾+εφ ⁽¹⁾+… (2b)

ζ＝ζ ⁽⁰⁾+εζ ⁽¹⁾+… (2c)

$\frac{p}{\mathrm{\&rho;}}+\mathrm{gz}=p^{\left(0\right)}+\mathrm{\&epsiv;}{p}^{\left(1\right)}+...---\left(2d\right)$

Modulate two shortwave systems for a long wave, represent each parameter of long wave with subscript 1, shortwave 2,3 is represented each parameter of two shortwaves respectively.

At first consider the modulating action of 1 (long wave) to 2 (shortwaves 1), can obtain each perturbation quantity according to boundary condition formula (1) and perturbation method, wherein wave height ζ is:

${\mathrm{\&zeta;}}_{12}=(a_1\sin {\mathrm{\&psi;}}_1-\frac{1}{2}\mathrm{\&epsiv;}{a}_1^2{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2008100479843E00022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&psi;}}_1)+(a_2\sin {\mathrm{\&psi;}}_2-\frac{1}{2}\mathrm{\&epsiv;}{a}_2^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\sin 2{\mathrm{\&psi;}}_2)---\left(3\right)$

$-\mathrm{\&epsiv;}{a}_1{a}_2({\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\cos {\mathrm{\&psi;}}_1\cos {\mathrm{\&psi;}}_2-{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2008100479843E00022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\sin {\mathrm{\&psi;}}_1\sin {\mathrm{\&psi;}}_2)+...$

K wherein ₁X-σ ₁T+ θ ₁=ψ ₁, k ₂X-σ ₂T+ θ ₂=ψ ₂, k ₂＞＞k ₁, a represents wave amplitude, and k represents wave number, and σ represents angular frequency, ε=k ₁a ₁For the long wave kurtosis is perturbation.By ζ ₁₂, each parameter that can obtain long wave 1 is subjected to the influence of shortwave 2, is expressed as:

a ₁₂＝a ₁(1+εa ₂k ₁sinψ ₂) (4a)

k ₁₂＝k ₁(1+εa ₂k ₁sinψ ₂) (4b)

${\mathrm{\&sigma;}}_{12}=\sqrt{g{k}_{12}}---\left(4c\right)$

Secondly, on the basis of 1 pair 2 modulating action, consider modulating action again to shortwave 3.With ζ ₁₂Regard " nonlinear long wave " of luffing, change wave number and frequency conversion as, the wave height ζ after it acts on shortwave 3 ₁₂₃Expression.Because can not be according to ζ ₁₂Expression formula, utilize boundary condition and perturbation method to obtain the analytic solution of 12 pairs 3 non-linear modulation of nonlinear long wave, therefore the present invention proposes " nonlinear long wave " discretize thought, promptly for the ripple of certain spatial point under certain time point, corresponding to the corresponding fixedly sine wave of wave amplitude, wave number and frequency, i.e. space i point j certain wave height ζ of the moment _{(12, i, j)}Can be expressed as again:

ζ _(12，i，j)＝a _(12，i，j)sinψ _(l2，i，j) (5)

ψ wherein _{(12, i, j)}=k _{(12, i, j)}x _i-σ _{(12, i, j)}t _j+ θ _{(12, i, j)}, θ _{(12, i, j)}Can by

Obtain.

With ζ _{(12, i, j)}Continuation is ζ ₁₂=a ₁₂Sin ψ ₁₂, regard it sinusoidal wave ζ of different events of different wave amplitudes, wave number and frequency as ₁₂Respectively with the result of shortwave 3 modulation, ζ ₁₂₊₃Then be that (i, discretize result j) is formed by stacking different corresponding point positions.ζ like this ₁₂Modulation to shortwave 3 just can be obtained by boundary condition and perturbation method, thereby solves " the discrete analytic solution " of system, obtains the evolution operator.

The operator of native system is, corresponding point (i, j) locate wave height and be:

${\mathrm{\&zeta;}}_{(12+3,i,j)}={\mathrm{\&zeta;}}_{12+3}^{\left(0\right)}{|}_{x=x_i,t=t_j}+\mathrm{\&epsiv;}{\mathrm{\&zeta;}}_{(12+3,i,j)}^{\left(1\right)}---\left(6\right)$

${\mathrm{\&zeta;}}_{12+3}^{\left(0\right)}=(a_1\sin {\mathrm{\&psi;}}_1-\frac{1}{2}\mathrm{\&epsiv;}{a}_1^2{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2008100479843E00022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&psi;}}_1)+(a_2\sin {\mathrm{\&psi;}}_2-\frac{1}{2}\mathrm{\&epsiv;}{a}_2^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&psi;}}_2)---\left(7\right)$

$-\mathrm{\&epsiv;}{a}_1{a}_2({\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\cos {\mathrm{\&psi;}}_1\cos {\mathrm{\&psi;}}_2-{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2008100479843E00022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\sin {\mathrm{\&psi;}}_1\sin {\mathrm{\&psi;}}_2)+{\mathrm{\&zeta;}}_3$

${\mathrm{\&zeta;}}_{(12+3,i,j)}^{\left(1\right)}=-\frac{1}{2}{a}_3^2{k}_3\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&psi;}}_3-\frac{1}{2}{a}_{12}^2{k}_{12}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&psi;}}_{12}---\left(8\right)$

$-a_{12}{a}_3(k_3\cos {\mathrm{\&psi;}}_{12}\cos {\mathrm{\&psi;}}_3-k_{12}\sin {\mathrm{\&psi;}}_{12}\sin {\mathrm{\&psi;}}_3){|}_{x=x_i,t=t_j}$

ζ wherein ₃=a ₃Sin ψ ₃, ψ ₃=k ₃X-σ ₃T+ θ ₃

N of 1 long wave modulation (n=3,4,5...) the concrete obtain manner of evolution operator of shortwave is:

Use ζ _{12 ... n-1}The wave height of n-2 shortwave before the modulation of expression long wave is with ζ _{12 ... n-1}Regard luffing as, become " nonlinear long wave " of wave number and frequency conversion, its wave height ζ after to shortwave n effect _{12 ... n-1}Expression., can obtain " nonlinear long wave " (21 ... n-1) each parameter is subjected to the influence of shortwave n, is expressed as:

$a_{12...n}=a_{12...n-1}(1+{\mathrm{\&epsiv;}}_{12...n-1}{a}_n{k}_{12...n-1}\sin {\mathrm{\&psi;}}_n){|}_{x=x_i,t=t_j}---\left(9a\right)$

$k_{12...n}=k_{12...n-1}(1+{\mathrm{\&epsiv;}}_{12...n-1}{a}_n{k}_{12...n-1}\sin {\mathrm{\&psi;}}_n){|}_{x=x_i,t=t_j}---\left(9b\right)$

${\mathrm{\&sigma;}}_{12...n}=\sqrt{g{k}_{12...n}}{|}_{x=x_i,t=t_j}---\left(9c\right)$

For the ripple of certain spatial point under certain time point, corresponding to the corresponding fixedly sine wave of wave amplitude, wave number and frequency, i.e. space i point j certain wave height ζ of the moment _{(12 ... n-1, i, j)}Can be expressed as again:

ζ _{(12…n-1，i，j)}＝a _{(12…n-1，i，j)}sinψ _{(12…n-1，i，j)} (10)

ψ wherein _{(12 ... n-1, i, j)}=k _{(12 ... n-1, i, j)}x _i-σ _{(12 ... n-1, i, j)}t _j+ θ _{(12 ... n-1, i, j)}, θ _{(12 ... n-1, i, j)}Can by

Obtain.

With ζ _{(12 ... n-1, i, j)}Continuation is

Regard it sinusoidal wave ζ of different events of different wave amplitudes, wave number and frequency as _{12 ... n-1}Respectively with the result of shortwave n modulation, ζ _{12 ... n}Then be that (i, discretize result j) is formed by stacking different corresponding point positions.ζ like this _{12 ... n-1}Modulation to shortwave n just can be obtained by boundary condition and perturbation method, thereby solves " the discrete analytic solution " of system, obtains the evolution operator.

N of 1 long wave modulation (n=3,4,5...) the evolution operator of shortwave is, corresponding point (i, j) locate wave height and be:

${\mathrm{\&zeta;}}_{(12\&CenterDot;\&CenterDot;\&CenterDot;n,i,j)}{|}_{x=x_i,t=t_j}={\mathrm{\&zeta;}}_{12\&CenterDot;\&CenterDot;\&CenterDot;n}^{\left(0\right)}{|}_{x=x_i,t=t_j}+{\mathrm{\&epsiv;}}_{12\&CenterDot;\&CenterDot;\&CenterDot;n}{\mathrm{\&zeta;}}_{(12\&CenterDot;\&CenterDot;\&CenterDot;n,i,j)}^{\left(1\right)}{|}_{x=x_i,t=t_j}---\left(11\right)$

${\mathrm{\&zeta;}}_{12...n}^{\left(0\right)}{|}_{x=x_i,t=t_j}={\mathrm{\&zeta;}}_{12...n-1}{|}_{x=x_i,t=t_j}+{\mathrm{\&zeta;}}_n{|}_{x=x_i,t=t_j}---\left(12\right)$

${\mathrm{\&zeta;}}_{(12...n,i,j)}^{\left(1\right)}{|}_{x=x_i,t=t_j}=-\frac{1}{2}{a}_n^2{\mathrm{<figure-callout\; id="2"\; label="k\; n\; sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_n\sin 2{\mathrm{\&psi;}}_n{|}_{x=x_i,t=t_j}-\frac{1}{2}{a}_{12...n-1}^2{\mathrm{<figure-callout\; id="21"\; label="k"\; filenames="H2008100479843E00022.png"\; state="\{\{state\}\}">k</figure-callout>}}_{21...n-1}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100479843E00021.png,H2008100479843E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&psi;}}_{12...n-1}{|}_{x=x_i,t=t_j}$ (13)

$-a_{12...n-1}{a}_n(k_n\cos {\mathrm{\&psi;}}_{12...n-1}\cos {\mathrm{\&psi;}}_n-k_{12...n-1}\sin {\mathrm{\&psi;}}_{12...n-1}\sin {\mathrm{\&psi;}}_n){|}_{x=x_i,t=t_j}$

Wherein

ζ _n=a _nSin ψ _n, ψ _n=k _nX-σ _nT+ θ _n

After obtaining the phylogeny operator, according to the PM spectrum model, by numerical evaluation, obtain under the different wind speed sea situations, parameter informations such as corresponding wave wave amplitude, wavelength and frequency are imported as system, and a plurality of shortwaves of simulation output are subjected to the wave evolution scene of long wave non-linear modulation.

The content that this instructions is not described in detail belongs to this area professional and technical personnel's known prior art.

Claims (1)

1. a plurality of shortwaves are subjected to the wave evolution scenario simulation method of long wave non-linear modulation, and the method that is adopted is:

First step: adopt perturbation method, according to deep-sea dynamics boundary condition, find the solution the sea temporal-spatial evolution analytic solution that a shortwave 0 is subjected to long wave 0 non-linear modulation;

Second step: regard the analytic solution that obtain as a long wave 1, the second shortwave 1 and be subjected to this long wave non-linear modulation;

Third step: at the analytic solution that can not find the solution its non-linear modulation, the one, regard in time long wave 1 as with space luffing, frequency conversion, change wave number nonlinear long wave 1, the 2nd, the long wave of the corresponding wave amplitude of certain spatial point of different concrete certain time point, frequency all satisfies deep-sea dynamics boundary condition, with long wave 1 regard as these long waves respectively during non-linear modulation shortwaves 1 in the stack of the analytic solution of corresponding time point and spatial point;

The 4th step: adopting uses the same method finds the solution the stack that n shortwave is subjected to n-1 the nonlinear long wave modulation in front, wherein, and n 〉=3;

The 5th step: obtain the evolution operator according to above step, compose according to PM, obtain the long and short wave-wave width of cloth under the different wind speed and corresponding frequency and wavelength parameter carried out numerical simulation as input, simulate the wave evolution scene that different sea situations, a plurality of shortwaves in deep-sea are subjected to the long wave non-linear modulation.

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