Acoustics Division, Naval Research Laboratory, Washington, DC 20375, USA.
J Acoust Soc Am. 2010 Jul;128(1):39-49. doi: 10.1121/1.3445783.
This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.
本文介绍了一种在一维粗糙海面下的声学域到具有平顶的域的保角变换。这种非微扰变换可以包括数百个波长的表面变化。所得的二维平顶域允许直接应用任何现有的亥姆霍兹或波动方程的声学传播模型，使用变换后的声速。这种变换-模型组合适用于表面粒子速度远低于声速的情况，因此可以忽略边界运动。一旦计算出声场，双射（一一映射）映射允许根据原始坐标进行场插值。伯格斯特龙方法用于反黎曼映射，通过迭代求解一个表面匹配项的积分方程来确定变换。利用亥姆霍兹方程的特定抛物方程模型进行的粗糙海面前向散射测试案例验证了该方法。
