Assessing the frictional and baroclinic contributions to stratified wake formation: A parameter-space study

The baroclinic and surface-frictional contributions to stratified wake formation are considered as a function of the non-dimensional height (epsilon = Nh/U) and aspect-ratio (delta = h/L) of the barrier. Numerical simulations are computed for a wide range of the epsilon-delta parameter space, including both unstratified (epsilon = 0) and highly stratified (epsilon = 4) flows and for terrain slopes characteristic of both geophysical (delta = 0.1) and laboratory scale (delta = 2.0) obstacles. All simulations are conducted both with and without applied surface stresses in an effort to clarify the separate contributions of friction and baroclinicity to the production of the wake. Particular emphasis is given to the changes in kinematic wake structure, mechanisms of vorticity generation, and relative contributions of skin and pressure drag observed as the various control parameters are varied.

Preliminary work confirms the results of previous studies showing that for small epsilon, wakes are formed only when stress is applied at the surface, while for large epsilon, wakes develop both and without applied surface stresses. However, the critical obstacle height separating these two regimes is a function of delta, with increasing delta implying a greater critical epsilon. For values of epsilon greater than the critical value the application of stress at the terrain surface produces a weakening of the wake flow relative to the corresponding free-slip case. However, this difference between the free-slip and surface-stress flows diminishes with increasing delta. At delta = 2.0 (terrain slope of roughly unity) the wakes with and without the applied surface-stresses are qualitatively similar (and feature nearly identical pressure drags) for epsilon at least as large as four.