On the instability of finite-amplitude inertia-gravity waves

Abstract

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.