Absolute and convective instabilities in open shear layers

I. Hydrodynamic equilibrium

Space and Atmosphere Research Centre, Dept. of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK e-mail: m.homem@sheffield.ac.uk

Corresponding author: R. Erdélyi, robertus@sheffield.ac.uk

Received: 20 December 2002
Accepted: 21 March 2003

Abstract

In the present paper we study the absolute and convective nature of instabilities in open shear flows by carrying out fully non-linear adiabatic 2-D hydrodynamic numerical simulations. The purpose is to identify what influences an instability to become from absolutely to convectively unstable or vice-versa. First we study the case of incompressible fluid approximation and compare our results with the analytic solution of Huerre & Monkewitz ([CITE]). Next we derive the effect of compressibility and of viscosity on the transition from absolute to convective instability of an open shear flow. We found, numerically, the value of the mean flow for which perturbations change from absolutely to convectively unstable. We fully recover the results of the approximate analytic solution. We found that an inviscid incompressible fluid is the most unstable configuration. We also found that compressibility and viscosity decrease the value of the mean flow for which the transition from absolute to convective instability occurs, and that viscosity has a stronger influence than compressibility.