Effects of the free‐stream density ratio on free and forced spatially developing shear layers

The effects of the free‐stream density ratio on the evolution of the incompressible, high Reynolds and Froude number, confined mixing layer are investigated numerically. Two‐dimensional simulations of the spatially developing flow with and without external forcing are obtained using the Lagrangian transport element method. Results indicate that a nonunity density ratio alters the flow characteristics significantly. In the unforced flow, it increases the layer growth as the slow stream becomes denser, biases the speed of both the linear instability waves and the rollup eddies toward that of the denser stream, and modifies entrainment in favor of the dense fluid. These results, which are in agreement with experimental and analytical evidence, are analyzed in terms of the evolution of the vorticity field and, in particular, of the action of the mechanism of baroclinic vorticity generation. It is found that this mechanism creates vorticity of opposite signs across each eddy, which, through simple kinematical arguments, is linked to the alteration of the eddy speed and the modification of the local entrainment patterns. High‐amplitude external forcing modifies the growth behavior of the layer while leaving its entrainment characteristics and the eddy speeds unaffected. In this case the layer growth is no longer monotonically varying with the free‐stream density ratio. Instead, it is a strong function of the momentum ratio, reaching a minimum at a momentum ratio of unity and increasing more significantly for higher values of this parameter. Enhancement of the layer growth via forcing occurs only when the momentum ratio is substantially different from unity. It is found that the forced layer growth characteristics are related to the layer orientation, which is also a function of the momentum ratio. Using this fact and basic principles, a simple analytical model is derived to explain the numerical results. It is suggested that the unforced flow behaves differently due to its initial instability characteristics that are bypassed when forcing is present.