The Miles’ theory of wave amplification by wind is extended to the case of finite depth $h$ and a shear flow with (constant) vorticity $\Omega$. Vorticity is characterised through the non-dimensional parameter $\nu =\Omega U_1/g$, where $g$ the gravitational acceleration, $U_1$ a characteristic wind velocity. The notion of ’wave age’ is generalised to account for the effect of vorticity. Several widely used growth rates are derived analytically from the dispersion relation of the wind/water interface, and their dependence on both water depth and vorticity is derived and discussed. Vorticity is seen to shift the maximum wave age, similar to what was previously known to be the effect of water depth. At the same time, a novel effect arises and the growth coefficients, at identical wave age and depth, are shown to experience a net increase or decrease according to the shear gradient in the water flow.

将 Miles 的风波放大理论推广到有限深度的情况 $H$ 和具有（恒定）涡度的剪切流 $\Omega$. 涡度是通过无量纲参数来表征的$\nu =\Omega {你}_1/G$， 在哪里 $G$ 重力加速度， ${你}_1$特征风速。“波龄”的概念被推广以解释涡度的影响。几个广泛使用的增长率从风/水界面的色散关系中解析导出，并导出和讨论了它们对水深和涡度的依赖性。涡度可以改变最大波龄，类似于以前已知的水深影响。同时，出现了一种新效应，并且在相同的波龄和深度下，增长系数会根据水流中的剪切梯度发生净增加或减少。