An approximate solution for the steady linear internal wave field generated by a localized, horizontally moving source in a thermocline is derived using ray and WKB (Wentzel–Kramers–Brillouin) theory. The waves are assumed to be steady in a reference frame moving with the source velocity. This solution is shown to agree in the limit of propagating waves with an existing solution that is expressed in terms of an eigenfunction expansion. The WKB method is shown to reproduce all the factors in the eigenfunction solution, not just the eigenfunctions themselves. It also reveals the physical significance of the terms in the eigenfunction solution. Furthermore, the WKB solution suggests an alternate way to compute the wave field numerically that is computationally more efficient.

使用射线和 WKB (Wentzel-Kramers-Brillouin) 理论推导出了温跃层中由局部水平移动源产生的稳定线性内波场的近似解。假设波在随源速度移动的参考系中是稳定的。该解在传播波的极限上与用本征函数展开式表示的现有解一致。WKB 方法被证明可以重现特征函数解中的所有因素，而不仅仅是特征函数本身。它还揭示了本征函数解中各项的物理意义。此外，WKB 解决方案提出了一种在数值上计算波场的替代方法，该方法在计算上更有效。