Interactions between a free surface and a vortex sheet shed in the wake of a surface-piercing plate

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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.

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