We derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a two-dimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the axis of the waveguide: those that are almost trapped in the thin layer, and thus model surface waves, and those that penetrate deep in the waveguide, and thus model body waves. The remaining modes are evanescent waves. We introduce a mathematical theory of mode coupling induced by scattering in the thin layer, and derive a radiative transfer equation which quantifies the mean mode power exchange. We study the solution of this equation in the asymptotic limit of infinite width of the waveguide. The main result is a quantification of the rate of convergence of the mean mode powers toward equipartition.

我们推导了一个辐射传递方程，该方程解释了从表面波到体波以及相反方向的耦合。该模型是具有反射边界的二维波导中的声波方程。波导在顶表面附近有一个薄的，随机不规则的异质层，在其下面有一个厚的均匀层。沿波导轴传播的模式有两种：一种几乎陷在薄层中，从而对表面波建模；一种在波导中深处渗透，从而对体波建模。其余模式是are逝波。我们介绍了由薄层中的散射引起的模式耦合的数学理论，并推导了量化平均模式功率交换的辐射传递方程。我们在波导的无限宽度的渐近极限中研究该方程的解。主要结果是量化了平均模功率向均分的收敛速度。