数学建模基于matlab三维海浪模型仿真含Matlab源码 1159期

Posted 2021-08-29 紫极神光

一、简介

基于matlab三维海浪模型仿真：海洋工程领域中的浮式结构物设计,需要精确计算海浪载荷,保证满足稳定性和安全性.该文利用MATLAB对Longuet-Higgins长峰波海浪模型和三维不规则短峰波随机海浪模型进行了仿真研究.结果表明,利用海浪谱来模拟三维随机海浪能够得到比较精确的海浪波面图和波高值,进一步根据流体的势流理论就可以分析计算出该结构物受到的海浪载荷,为校验结构物的结构强度提供了必要的基础。

二、源代码

clear all;
close all;

nhFig = 0; % Figure Number;
SeaRegLx = 40e+3; % Sea region length, unit: m
SeaRegLy = 40e+3; % Sea region length, unit: m
% 根据频域采样定理，在确定采样周期即波束的足迹宽度之后，
% 可以利用时域采样的采样点数目(通过空间频谱的宽度即根据时域采样定理计算出采样点数)，实现频域采样.
% 对于海洋波谱而言，波谱宽度是非常宽的，因此其波谱宽度一般是指包括了大部分能量(或者说主要的能量部分)的不完全谱宽度
% 所以这里事先根据波谱函数计算主要能量部分对应的谱宽度
xSampleStep = 50; % unit: m
ySampleStep = 50;
xNs = round( SeaRegLx / xSampleStep );
yNs = round( SeaRegLy / ySampleStep );

x = linspace( -SeaRegLx / 2, SeaRegLx / 2, xNs );
y = linspace( -SeaRegLy/ 2, SeaRegLy / 2, yNs );

% 海浪谱仿真
g = 9.8; % gravity acceleration
% swell wave spectrum parameter
SwellWaveLength = 1000; % 涌浪波长
KswellWavePeak = 2 * pi / SwellWaveLength;
SwellAngled=0;
SwellAngle = SwellAngled/ 180 * pi; % 涌浪与观测向夹角
KxswellWavePeak = KswellWavePeak * cos( SwellAngle );
KyswellWavePeak = KswellWavePeak * sin( SwellAngle );
SigmaKx = 2.5e-3; % 涌浪谱宽度
SigmaKy = 2.5e-3;
SigmaHSwell = 2; %涌浪波高
% wind wave spectrum parameter
WindAngle = 45 / 180 * pi; % 风向与观测向夹角
U10 = 12; % 10米高处海面风速 % 5m/s, 10m/s, 15m/s 的风浪谱宽度分别为 1.5, 0.4, 0.15.对应的最大空间采样间隔为2m, 10m, 20m
KwindPeak = g / ( 1.2 * U10 )^2;
% sea wave spectrum parameter
NxSeaWave = xNs; % 频域采样点数，方便傅立叶变换
NySeaWave = yNs; 
KxSeaWave = 2 * pi / SeaRegLx * ( -xNs / 2 : 1 : xNs / 2 - 1 );
KySeaWave = 2 * pi / SeaRegLy * ( -yNs / 2 : 1 : yNs / 2 - 1 );
KxSeaWaveTicks = KxSeaWave;
KySeaWaveTicks = KySeaWave;
KxSeaWave = ( KxSeaWave == 0 ) * ( max( KxSeaWave ) * 1e-16 ) + KxSeaWave; % avoid divided by 0
KySeaWave = ( KySeaWave == 0 ) * ( max( KySeaWave ) * 1e-16 ) + KySeaWave; % avoid divided by 0

% swell wave spectrum
SpectrumSwell = zeros( NySeaWave, NxSeaWave );
Temp1 = ones( NySeaWave, 1 ) * ( KxSeaWave - KxswellWavePeak ) / SigmaKx;
Temp2 = ( KySeaWave - KyswellWavePeak )' / SigmaKy * ones( 1, NxSeaWave );
SpectrumSwell = SigmaHSwell^2 / 2 / pi / SigmaKx / SigmaKy * exp( -0.5 * ( Temp1.^2 + Temp2.^2 ) );
clear Temp1;
clear Temp2;
figure;
colormap(gray(256));
image( KxSeaWave, KySeaWave, 256 - 255 / ( max( max( abs( SpectrumSwell ) ) ) - min( min ( abs( SpectrumSwell ) ) ) ) * ( abs( SpectrumSwell ) - min( min ( abs( SpectrumSwell ) ) ) ) );
axis('xy');
xlabel( 'kx:X方向波数');
ylabel( 'ky:Y方向波数');
title( '涌浪谱');

KxSeaWaveMatrix = ones( NySeaWave, 1 ) * KxSeaWave;
KySeaWaveMatrix = KySeaWave' * ones( 1, NxSeaWave );
KSeaWaveTemp1 = ( sqrt( KxSeaWaveMatrix.^2 + KySeaWaveMatrix.^2 ) );
Fwk1 = exp( - 1.22 * ( sqrt( KSeaWaveTemp1 ./ KwindPeak ) -1 ).^2  );
HKKpx1 = 1.24 * ( ( KSeaWaveTemp1 / KwindPeak < 0.31 ) & ( KSeaWaveTemp1 / KwindPeak >= 0 ) );
HKKpx2 = 2.61 * ( ( KSeaWaveTemp1 / KwindPeak ).^0.65 ) .* ( ( KSeaWaveTemp1 / KwindPeak < 0.9 ) & ( KSeaWaveTemp1 / KwindPeak >= 0.31 ) );
HKKpx3 = 2.28 * ( ( KSeaWaveTemp1 / KwindPeak ).^( -0.65 ) ) .* ( KSeaWaveTemp1 / KwindPeak >= 0.9 );
HKKp1 = HKKpx1 + HKKpx2 + HKKpx3;
Temp1x = 1.62 * 1e-3 * U10 / ( g^0.5 ) ./ ( KSeaWaveTemp1 ).^3.5;
Temp2x = exp( -( KwindPeak ./ KSeaWaveTemp1 ).^2 ) .* ( 1.7 .^ Fwk1 );
Temp3x = ( HKKp1 .* ( sech( ( HKKp1 .* ( atan( ( KySeaWaveMatrix ./ KxSeaWaveMatrix ) ) - WindAngle ) ) ) ).^2 );
% SpectrumWind1 = ( Temp1x .* Temp2x .* Temp3x )';
fid=fopen('sea_top_wl1000_wh50m.dat','w')
fprintf(fid,'%10.5f\\n',real(wh));
status=fclose(fid);

fid=fopen('sea_top_wl1000_wh50m.dat','r');
sea_dem=fscanf(fid,'%g',[800,800]);
fclose(fid);
%image( x, y, 256 - 255 / ( max( max( real( sea_dem ) ) ) - min( min ( real( sea_dem ) ) ) ) * ( real( sea_dem ) - min( min ( real( sea_dem ) ) ) ) );
% 
 mesh(sea_dem)
 colorbar
% view(0,90)
%colormap(gray)
% This function computes the non-coherent integration improvment
% factor using the empirical formula defind in Eq. (2.48)
fact1 = 1.0 + log10( 1.0 / pfa) / 46.6;
fact2 = 6.79 * (1.0 + 0.235 * pd);
fact3 = 1.0 - 0.14 * log10(np) + 0.0183 * (log10(np))^2;
impr_of_np = fact1 * fact2 * fact3 * log10(np);
return

% SpectrumWind = SpectrumWind1';
SpectrumWind = Temp1x .* Temp2x .* Temp3x;
clear KSeaWaveTemp1 Fwk1 HKKpx1 HKKpx2 HKKpx3 HKKp1 Temp1x Temp2x Temp3x;

三、运行结果

四、备注

版本：2014a