Direct numerical simulations of variable-density plane jets

Abstract

Two-dimensional incompressible and heterogeneous free jets are studied numerically. They are characterized by two linearly unstable modes: the sinuous mode and the varicose mode. When the density is constant, the sinuous mode dominates, in a sense that it has a maximum growth rate nearly three times greater than that of the varicose mode, both in the temporal and spatial stability frameworks. This suggests that jet evolution at the linear and nonlinear regimes, at least at early stage, would be sinuous with the frequency and wavenumber of the most unstable mode. This is confirmed in the present work. When the jet density is decreased, it is found that the varicose mode growth rate is enhanced and its maximum value can exceed that of the sinuous mode. Furthermore, in the spatial case, only the varicose mode is subject to a convective/absolute instability transition. It is shown, however, that the maximum varicose growth rate exceeds that of the sinuous mode before the transition occurs. Therefore, a natural question is: does the convective/absolute transition dictate its frequency to the nonlinear evolution of the jet, leading to a global oscillating varicose mode, or is it, simply, the frequency of the maximum varicose growth rate that does? The main part of this paper is devoted to answering this question by direct numerical simulation for a wide range of jet-exit to ambient density ratios.