The stability of oscillatory internal waves

Abstract

The stability of a periodic internal wave has been investigated experimentally and theoretically. From the analysis it is found that if a primary wave, with wave-number k0 and frequency ω0, is perturbed by two infinitesimal wave-like disturbances with wave-numbers k1 and k1 + k0 and frequencies ω1 and ω1 + ω0, exponential growth of these disturbances will take place under certain conditions. The analysis also indicates which resonantly interacting disturbances can induce an instability and, when viscous dissipation is accounted for, predicts the minimum amplitude for which a wave is unstable. Experimental results demonstrate that this type of instability can cause the breakdown of a first mode internal wave propagating in a fluid composed of two layers of uniform density separated by a thin region in which the density varies continuously.