三维海浪模型仿真：基于Matlab的数学建模实践

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clear all;close all;nhFig = 0; % Figure Number;SeaRegLx = 40e+3; % Sea region length, unit: mSeaRegLy = 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: mySampleStep = 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 parameterSwellWaveLength = 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 parameterWindAngle = 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, 20mKwindPeak = g / ( 1.2 * U10 )^2;% sea wave spectrum parameterNxSeaWave = 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 0KySeaWave = ( KySeaWave == 0 ) * ( max( KySeaWave ) * 1e-16 ) + KySeaWave; % avoid divided by 0% swell wave spectrumSpectrumSwell = 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;1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.51.52.53.54.55.56.57.58.59.60.61.62.63.64.65.66.67.68.69.70.71.72.73.74.75.76.77.78.79.80.81.82.83.84.85.86.87.88.89.90.91.92.93.94.95.