Stability investigations of a laminar wall jet using the complete Navier-Stokes equations

Abstract

The hydrodynamic stability of a plane, two-dimensional, incompressible wall jet subjected to small disturbances is investigated by direct numerical integration of the complete Navier-Stokes equations. The numerical model allows growing or decaying of disturbances in the downstream direction as in physical experiments. In the past, various numerical investigations were published using the linear stability theory for the case of temporally growing disturbances. In this work, the investigations are made for the case of spatially growing disturbances. The neutral curves of the linear stability theory are displayed, and in addition, the downstream development of spatial growing disturbances is provided by using the complete Navier-Stokes equations. It is shown that the behavior of the disturbances is as predicted by the linear stability theory for a certain frequency using small disturbances. The changes in the downstream development of the flow subjected to large disturbances compared to the results using small disturbances is discussed. For large disturbance amplitudes, it was found that for the frequency of the disturbance waves used in the investigations the boundary layer mode clearly dominates the hydrodynamic stability.