The Kelvin-Helmholtz Instability: Comparisons of One- and Two-Dimensional Simulations

Abstract

A 1D two-fluid model for horizontal stratified flow is presented and discussed in the context of the Kelvin-Helmholtz instability. The model is well-posed because it includes surface tension. However, well-posedness is not sufficient. It is shown that non-linear stability (i.e., bounded wave growth) is also a necessary condition for convergence.A turbulent viscosity is constituted for the 1D two-fluid model by means of 2D LES using the VOF piece-wise linear approach to track the interface. The 1D model Reynolds stress thus obtained is used to represent missing physics in 1D associated with viscous dissipation due to vorticity. With the added Reynolds stress the 1D numerical model exhibits bounded wave growth and it also converges.