Mode coupling in nonlinear Kelvin--Helmholtz instability

This paper investigates the interaction of a small number of modes in the two-fluid Kelvin--Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e.~short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.