The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes

Abstract

The boundary between absolute and convective (linear) instability of two-dimensional inertial jets and wakes is determined as a function of the ratio of jet/wake to ambient density, as well as the ratio of mixing layer thickness to jet/wake width, the velocity ratio, and the Reynolds number. For this, a viscous, heat-conducting ideal gas is taken as the fluid, a zero Mach number, no buoyancy and a parallel basic flow are assumed, and the density variation is achieved by specifying a mean temperature profile similar to the velocity profile. Considering both ‘‘varicose’’ and ‘‘sinuous’’ disturbances, results are obtained for the inviscid top-hat jet/wake bounded by two vortex sheets, the inviscid jet with continuous velocity and density profiles, and the viscous wake. For the latter, both constant and temperature-dependent viscosity are investigated. In all the cases it is found that low density of the high-speed fluid promotes absolute instability, while low density of the low-speed fluid has the opposite effect. By comparison with experiments it is shown that the present results provide useful information about the parameter range in which flow oscillations are self-excited.