Features of nonlinear interactions between a free surface and a shed vortex shear layer

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Abstract
The nonlinear interaction between a free surface, under gravitational acceleration g, and the vortex shear layer shed by a thin surface‐piercing plate, initial submergence h, started abruptly from rest to a constant horizontal velocity U, is studied numerically. The problem is governed by a single parameter, the Froude number Fn = U/√gh. Depending on Fn, three classes of interaction dynamics are identified in the wake of the plate. For subcritical Fn(≲0.7), a plunging breaker forms on the free surface before significant interaction with the vortex sheet occurs. For both transcritical and supercritical Fn, the deformation of the free surface stretches the vortex sheet, and finite‐amplitude Kelvin–Helmholtz instabilities arise, which roll up into double‐branch spirals. In the transcritical range (Fn∼ 0.7–1.0), the interactions between the free surface and the Kelvin–Helmholtz instabilities remain weak, which allows the latter to roll up continuously into a series of double‐branch spirals. For supercritical Fn(≳1.0), the double‐branch spiral becomes entrained into the free surface resulting in large surface deformations.

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