The effect of confinement on the stability of two-dimensional shear flows

Abstract

It has been shown recently that the instability of a two-dimensional wake increases when it is confined in the transverse direction by two flat plates. Confinement causes the transition from convective to absolute instability to occur at lower values of shear. This paper examines this effect comprehensively and concludes that it is due to the constructive interaction of modes with zero group velocity in the wake (or jet) and in the surrounding flow. Maximum instability occurs when the wavenumber of the fundamental mode in the wake (or jet) matches that of the fundamental mode in the surrounding flow. Other regions of high instability occur when the harmonics of one mode interact with the fundamental of the other. This effect is examined at density ratios from 0.001 to 1000. At each density ratio, the confinement which causes maximum absolute instability can be predicted. This study also shows that it is vital to examine the wavenumber of absolutely unstable modes in order to avoid over-predicting the absolute instability. In some situations this wavenumber is vanishingly small and the mode must be discounted on physical grounds.