Interactions Between a Free Surface and a Vortex Sheet Shed in the Wake of a Surface-Piercing Plate
Journal
Journal of Fluid Mechanics
Journal Volume
257
Pages
691-721
Date Issued
1993
Author(s)
Abstract
The nonlinear interactions between a free surface and a shed vortex shear layer in the inviscid wake of a vertical surface-piercing plate are studied numerically using a mixed-Eulerian-Lagrangian method. For a plate with initial submergence d starting abruptly from rest to constant horizontal velocity U , the problem is governed by a single parameter, the Froude number Fn = U /( gd ) ½ , where g is the gravitational acceleration. Depending on Fn , three classes of interaction dynamics (subcritical, transcritical and supercritical) are identified. For subcritical Fn ([lsim ] 0.7), the free surface plunges on both the forward and lee sides of the plate before significant interactions with the vortex sheet occur. For transcritical and supercritical Fn , interactions between the free surface and the starting vortex result in a stretching of the vortex sheet which eventually rolls up into double-branched spirals as a result of Kelvin-Helmholtz instability. In the transcritical range ( Fn ∼ 0.7–1.0), the effect of the free surface on the double-branched spirals remains weak, while for supercritical Fn ([gsim ] 1.0), strong interactions lead to entrainment of the double-branched spiral into the free surface resulting in prominent surface features.
SDGs
Type
journal article