使用波数谱绘制海浪波幅畸变的校正

摘要

针对快速傅里叶逆变换形式 Gerstner 波绘制海浪出现波幅畸变的问题, 提出使用波数谱绘制海浪波幅畸变的校正方法. 首先重新推导了包含基元波振幅的快速傅里叶逆变换形式 Gerstner 波; 然后用右侧 Riemann 求和对波数谱的定积分进行离散, 离散积分域的边界值由快速傅里叶逆变换对波数向量的采样方式决定, 得到基元波振幅的近似解; 最后将该近似解代入上述推导所得的形式中, 得到傅里叶系数中包含波数谱和离散积分域面积的快速傅里叶逆变换形式 Gerstner 波. 实验结果表明, 采用该方法可以准确地计算海浪势能和基元波振幅, 绘制结果波形稳定,有效地解决了波幅畸变的问题.%Because the rendered ocean wave of the inverse fast Fourier transform (IFFT) Gerstner wave is malformed, we raise a method using the wave number spectrum to correct the amplitude malformation. First, the IFFT Gerstner wave including the elementary wave amplitude is re-deduced. Then, we employ the right Riemann sum to discretize the definite integral of the wave number spectrum. The boundary value of the discrete integral domain depends on the sample mode for the wave number vector in IFFT. An approximate solution of the elementary wave amplitude is gotten. Finally, substituting the solution into the re-deduced expression, we get another IFFT Gerstner wave. Its Fourier coefficient contains the wave number spectrum and the area of the discrete integral domain. The experimental results show the method of the paper can pre-cisely calculate the wave potential and the amplitude, keep the shape of the rendered wave stable, and cor-rect the malformation.