随机波浪Jonswap谱 | 易学教程

随机海浪往往具有统计特征，组成频率会呈现出某一频率集中的特征。由此而衍生出的海浪谱多种多样。其中较为著名的一种海浪谱Jonswap被广泛应用在海洋科学、海洋工程领域。
以合田改进的Jonswap谱（1999）为例：
$S(f)=\beta_jH_{1/3}^2T_P^{-4}f^{-5}\exp[-\frac{5}{4}(T_Pf)^{-4}]\gamma^{\exp[-(\frac{f}{f_P}-1)^2/2\sigma^2]}$
其中，
$\beta_j=\frac{0.06238}{0.230+0.0336\gamma-0.185(1.9+\gamma)^{-1}}[1.094-0.01915\ln\gamma]$ ,
$T_P=\frac{T_{H_{1/3}}}{1-0.132(\gamma+0.2)^{-0.559}}$ ,

对于平均Jonswap谱来说：
$\gamma=3.3,\sigma_a=0.07,\sigma_b=0.09,$
$\alpha=0.076\bar{X}^{-0.22},\bar{X}=10^{-1}to10^{5},$
$\omega_m=22(g/\bar{U})\bar{X}^{-0.33}$
或 $f_m=3.5(g/\bar{U})\bar{X}^{-0.33}，$
$\bar{X}=gX/U^2.$
峰型参数 $\sigma=\sigma_a$ (当 $\omega<=\omega_m$ 时)， $\sigma=\sigma_b$ (当 $\omega>\omega_m$ )时。

% Improved Jonswap Spectral
% 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);
%% IMPUT PARAMETERS
% H_s - significant wave height; T_s -  wave period at 1/3 wave height
% dm - calculation interval of omega
%% FUNCTION

function [S,Omega,omega_p,T_p]=Improved_Jonswap_spectral(H_s,T_s,dm)
gama=3.3; sigma_a=0.07;sigma_b=0.09;
beta_j=0.06238/(0.23+0.0336*gama-0.185*(1.9+gama)^(-1))*(1.094-0.01915*log(gama));
T_p=T_s/(1-0.132*(gama+0.2)^(-0.559));
f_p=1/T_p;
omega_p=f_p*2*pi;
i=1;
df=dm/2/pi;
S_o=zeros(1,length(0:dm:1/T_s*2*pi*4));
Omega1=zeros(1,length(0:dm:1/T_s*2*pi*4));
for omega=0:dm:1/T_s*2*pi*4
    if omega<omega_p
        sigma=sigma_a;
        S_o(i)=beta_j*H_s^2*T_p^(-4)*(omega/2/pi)^(-5)*exp(-5/4*((omega_p/omega))^(4))...
            *gama^(exp(-((omega)/omega_p-1)^2/(2*sigma^2)))/(2*pi);
    else
        sigma=sigma_b;
        S_o(i)=beta_j*H_s^2*T_p^(-4)*(omega/2/pi)^(-5)*exp(-5/4*((omega_p/omega))^(4))...
            *gama^(exp(-((omega)/omega_p-1)^2/(2*sigma^2)))/(2*pi);
    end
    Omega1(i)=omega; 
    i=i+1;
end
Omega=Omega1(2:end);
S=S_o(2:end);
end

来源：CSDN

作者：Jr.Cui

链接：https://blog.csdn.net/Nick_Cui/article/details/103463349

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