‘Explosive’ resonant wave interactions in a three-layer fluid flow

Abstract

Cairns (1979) has recently shown how the concept of negative wave energy used in plasma physics can be exploited to obtain insights into the linear and nonlinear instability of certain parallel flows. We here analyse the linear stability and nonlinear three-wave resonance in a three-layer flow with step-wise velocity and density profiles. The results are in complete agreement with Cairns’ qualitative predictions. In particular, the existence is confirmed of an ‘explosive’ instability in which all three waves of a resonant triad grow simultaneously while total wave energy is conserved. Such nonlinear instabilities, previously undetected in fluid flows, may well be important in the ocean and atmosphere.