Numerical Analyses of Wave Generation and Vortex Formation under the Action of Viscous Fluid Flows over a Depression

Abstract

Transient free-surface deformations and evolving vortices due to the passage of flows over a submerged cavity are simulated. A two-dimensional stream function–vorticity formulation with a free-surface model is employed. Model results are validated against the limiting case of pure lid-driven cavity flow with comparisons of the vortical flow pattern and velocity profiles. The verification of the free-surface computations are also carried out by comparing results with published potential flow solutions for cases of flows over a depressed bottom topography. The agreements are generally good. Investigations are extended to other viscous flow conditions, where the cavity is set to have the normalized dimension of one by one when scaled by the still water depth. The free-surface elevations and streamline patterns for cases with Froude numbers ranging from 0.5 to 1.1 and different Reynolds numbers (Re = 5000 and 500) are calculated. At the condition of near-critical flow (Fr ≈ 1.0), the phenomenon of upstream advancing solitons is produced. Viscous effects on the free-surface profile reveal that at a lower value of Re (e.g., Re = 500) larger advancing solitary waves are generated. Vortical flow patterns in the cavity are examined for the cases with Fr = 1.0 and various values of Re. When Re = 5000, the vortex pattern includes a primary and a weak, but dominated secondary vortices at the time reaching a nearly quasi-steady motion. For the case of lower Re (e.g., Re = 500), a steady-state vortex pattern can be established with a clockwise primary vortex mostly occupied inside the cavity.