Linear stability analysis of turbulent mixing layers and jets in shallow water layers

Abstract

Free turbulent shear flows, such as mixing layers or jets, can exist in a shallow fluid layer. Flows of these types have many hydraulic, environmental or geophysical applications. The instability characteristics of these laterally sheared flow types have been studied by means of a modified depth-averaged Orr-Sommerfeld equation that describes spatial and temporal growth of disturbances in the nominally parallel flow. Two major parameters, a bed-friction parameter and a Reynolds number control the flow behavior. In addition, the width of the flow domain relative to the sheared zone width can have secondary influences. Results are presented as stability diagrams for the separate and joint effects of viscosity and bed-friction, respectively. Comparisons with available experimental evidence are given.