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 (1985). 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.
Abstract. The present paper is the continuation of our study of absolute and convective instabilities in open shear layers (Terra-Homem & Erdélyi 2003). In this paper the effects of a magnetic field are included and a series of fully non-linear ideal polytropic 2D MHD numerical simulations is carried out. The amount of mean flow required to sweep away the perturbation before it grows and destroys the whole flow is calculated for various configurations of the magnetic field. The analytical results obtained by Fejér (1964) for a velocity discontinuity were recovered with a very good accuracy. The study focused on uniform, discontinuous and sheared magnetic fields. We found that the value of mean flow needed for a perturbation to become convectively unstable (critical mean flow) decreased with decreasing value of the plasma β. We also found that the low β value side, of a discontinuous and sheared magnetic field, is predominant in the behaviour of the instability. Finally we show the thickness of the magnetic shear layer has no effect on the value of critical mean flow.
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