Dynamics of Laminar Jets in Stratified Fluids

Abstract

We consider the flow of a planar buoyant jet in a stable density stratified fluid. The jet undergoes acceleration then deceleration. The flow exhibits a pair of rotors adjacent to the nozzle and near the jet termination point. This recirculation maintains an entrained conduit of less dense water from near the nozzle that surrounds the denser jet core. The flow is found to have three different instability modes: a symmetric instability in the jet core, an antisymmetric instability in the jet core and a symmetric shear type instability on the edge of the entrained conduit. A local linear stability analysis shows the presence of the three modes with the symmetric and anti-symmetric modes in the jet core exhibiting comparable growth rates. However, the anti-symmetric is found to dominate. Direct numerical simulation of Bousinessq equations was used to map the stability of the flow as a function of jet Reynolds number and Grashof number. In addition, the flow is considered for two different stratification strengths and two different Schmidt numbers. The stratification length was not found to have a significant impact on flow stability. Higher Schmidt numbers led to decreased stability, primarily due to the increased acceleration of the more dense jet core. In addition, possible methods for accurate global stability analysis are presented.