Numerical Simulations of Upstream Blocking, Columnar Disturbances, and Bores in Stably Stratified Shear Flows over an Obstacle

Abstract

A two-dimensional, nonhydrostatic, elastic numerical model has been used to study the generation of gravity waves for a stably stratified shear flow over an obstacle. When a low-level wind shear is included in the simulation, we find that the predictions for noticeable upstream effects based on Froude number for a uniform flow are no longer accurate. Upstream effects are encountered in the form of upstream propagating columnar disturbances and internal bores away from the obstacle. The limited parameter space studies conducted in this study suggest that the ratio of the shear depth to the obstacle height (d/H), the obstacle aspect ratio (H/L), and the Froude number (U/NH) are instrumental in determining the strength and the existence of these upstream disturbances. Thus, the present theoretical and empirical understanding of the importance of the Froude number for determining the nature of upstream effects should be modified substantially to include additional nondimensional parameters when shear is present.