等分频率法模拟随机波列（线性波叠加原理）

线性叠加法

海浪可看做一系列不同周期不同初相位的线性波叠加而成的：
$\eta(t)=\sum\limits_{i=1}^{M}a_i\cos(k_ix-\omega_it+\epsilon_i)$,
$a_i$为第$i$个组成波的振幅，$k_i和\omega_i$为第$i$个组成波的波数和圆频率。$\epsilon_i$为$(0,2\pi)$之间的随机数，代表随机相位。假设靶谱的能量大多分布在区间$[\omega_L\quad\omega_H]$,其他部分可忽略不计。将该区间平分为M个子区间，其间距为$\Delta\omega_i=\omega_i-\omega_{i-1}$，取
$\hat{\omega_i}=(\omega_{i-1}+\omega_i)/2,a_i=\sqrt{2S_{\eta\eta}(\hat{\omega_i})\Delta\omega_i}$,
则将代表M个区间波能的M个线性波叠加起来，可得到海浪波面：
$\eta(t)=\sum\limits_{i=1}^{M}\sqrt{2S_{\eta\eta}(\hat{\omega_i})\Delta\omega_i}\cos(\tilde{\omega_i}t+\epsilon_i)$,
式中$\tilde{\omega_i}$为第i个组成波的代表频率。

程序

% Randam wave simulation
% Designed by: JN-Cui
% Modified on 12/09/2019
%% DEFINITIONS
% alpha - energy scale factor; gama - spectral peak elevation factor;
% omega_m - spectral peak circular frequency; f_m - spectral peak frequency;
% U - wind speed at 10 m above sea surface; H_s - significant wave height;
% g - gravity acceleration;
%% FOR AVERAGE JONSWAP SPECTRAL
% gama=3.3; k=83.7; sigma_a=0.07; sigma_b=0.09;
% alpha=0.076*(X_bar)^(-0.22);
% X_bar=10^(-1)~20^(5); omega_m=22(g/U)*(X_bar)^(-0.33);
% f_m=3.5(g/U)(X_bar)^(-0.33);
%% FUNCTION

function [W_s,R_c,Slope,t,x,Omega,S,ffff,mag,T_m]=random_wave_v1_0(H_s,T_s,dm,dt,T,dx,X)
[S,Omega,omega_p,T_m]=Improved_Jonswap_spectral(H_s,T_s,dm);
d=2000;
g=9.8;
N=200;
M=T/dt;
e=rand(1,N)*2*pi;
w=0:max(Omega)/(N-1):max(Omega);
ww(N)=max(w);
LT1=length(w);
LT2=M;
LT3=M;
for i=1:N-1
    ww(i)=unifrnd(w(i),w(i+1));
end
ww(N)=w(N);
Wait=waitbar(0,'程序计算中，请稍后', 'CreateCancelBtn','setappdata(gcbf,''canceling'',1)');
setappdata(Wait,'canceling',0);
SS_o=zeros(1,length(w));
f=zeros(1,length(w));
T_w=zeros(1,length(w));
K=zeros(1,length(w));
k=zeros(1,length(w));
a=zeros(1,length(w));
L=zeros(1,length(w));
% for i=1:length(w)
for i=1:N
    waitbar(i/(LT1+LT2+LT3));
    if getappdata(Wait,'canceling')
        break
    end
    SS_o(i)=S_Improved_Jonswap_spectral(ww(i),H_s,T_s,dm);
    f(i)=ww(i)/2/pi;
    T_w(i)=1/f(i);
    K(i)=g*T_w(i)^2/(2*pi);
    fun=@(L1) L1/tanh(2*pi/L1*d)-K(i);
    L(i)=Division(fun,0.0001,0,K(i));
    k(i)=(2*pi/L(i));
    a(i)=sqrt(2*SS_o(i)*(w(2)-w(1)));
end
% Time steps
t=zeros(1,M);
for i=1:M
    t(i)=(i-1)*dt;
end
eta=zeros(N,1);
NN=floor(X/dx)+1;
x=0:dx:X;
Eta=zeros(M,NN-1);
for j=1:M
    waitbar((j+LT1)/(LT1+LT2+LT3));
    if getappdata(Wait,'canceling')
        break
    end
    for ii=1:NN
        Eta(j,ii)=sum(a.*cos(k.*x(ii)-ww.*t(j)+e));
    end
end
%%
% Wave Surface
W_s=Eta;
delete(Wait);
end

来源：CSDN

作者：Jr.Cui

链接：https://blog.csdn.net/Nick_Cui/article/details/103464248