The hydrodynamic instability of monochromatic inertia-gravity waves (IGWs) of finite amplitude, propagating at small angles either to the vertical or horizontal, is studied. In both cases, the corresponding angle serves as a small parameter in the problem, and instability is investigated using the Galerkin method. For IGWs that propagate at a small angle to the vertical, it is shown that stable density stratification is a stabilizing factor, and fluid rotation is destabilizing. The opposite is true for IGWs that propagate at a small angle to the horizontal. Previous analysis of the short wave instability of the monochromatic internal gravity waves of finite amplitude that propagate at small angles to the vertical is generalised to the case of the IGW. As an auxiliary but methodologically useful problem, the stability of a monochromatic inertial wave of finite amplitude in a fluid of uniform density is investigated in the same mathematical formulation.

中文翻译：

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有限振幅惯性重力波的不稳定性

研究了与垂直或水平方向成小角度传播的，振幅有限的单色惯性重力波（IGW）的流体动力学不稳定性。在这两种情况下，相应的角度都只是问题中的一个小参数，并且使用Galerkin方法研究了不稳定性。对于与垂直线成小角度传播的IGW，表明稳定的密度分层是稳定因素，而流体旋转却不稳定。对于与水平面成小角度传播的IGW，情况恰恰相反。以前对以垂直于小角度传播的有限幅度的单色内部重力波的短波不稳定性的分析被推广到了IGW的情况。作为辅助但在方法上有用的问题，