University Of Tasmania

File(s) under permanent embargo

Accurate methods for computing inviscid and viscous Kelvin-Helmholtz instability

journal contribution
posted on 2023-05-17, 05:28 authored by Chen, MJ, Lawrence ForbesLawrence Forbes
The Kelvin–Helmholtz instability is modelled for inviscid and viscous fluids. Here, two bounded fluid layers flow parallel to each other with the interface between them growing in an unstable fashion when subjected to a small perturbation. In the various configurations of this problem, and the related problem of the vortex sheet, there are several phenomena associated with the evolution of the interface; notably the formation of a finite time curvature singularity and the ‘roll-up’ of the interface. Two contrasting computational schemes will be presented. A spectral method is used to follow the evolution of the interface in the inviscid version of the problem. This allows the interface shape to be computed up to the time that a curvature singularity forms, with several computational difficulties overcome to reach that point. A weakly compressible viscous version of the problem is studied using finite difference techniques and a vorticity-streamfunction formulation. The two versions have comparable, but not identical, initial conditions and so the results exhibit some differences in timing. By including a small amount of viscosity the interface may be followed to the point that it rolls up into a classic ‘cat’s-eye’ shape. Particular attention was given to computing a consistent initial condition and solving the continuity equation both accurately and efficiently.


Publication title

Journal of Computational Physics










School of Natural Sciences


Elsevier Inc

Place of publication

United States

Rights statement

The definitive version is available at

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences