In this paper, the nonlinear evolution of two-dimensional instability waves in a submerged shear flow is studied numerically, through direct simulation often incompressible Euler equations subject to the dynamic and kinematic boundary conditions at the ocean surface. In a submerged shear flow with a free surface, the sinuous mode of linear instability is the dominant one, but depending on the submergence depth of the mean shear flow and the Froude number of the flow, the nonlinear evolution of the instability waves exhibit substantially different behavior. More specifically, for large submergence depth and low Froude number, the flow reaches an equilibrium state, and the free-surface signature of the instability has the form of a propagating water wave but the free-surface elevation is small. However, for the same large submergence depth, increasing the Froude number beyond a certain value causes breaking of the free-surface wave. For very high Froude numbers, the breaking of the free-surface wave is caused by the presence of a sharp vertical velocity shear at the free surface. For a small submergence depth, on the other hand, the free-surface elevation breaks even for low Froude numbers, because of the sharp horizontal velocity shear, which is induced at the free surface by the vortices of the flow.


The flow in the wake of bluff and streamlined objects in unbounded fluid is characterized by self-induced unsteadiness, which results in the formation of a vortex street. Vortex streets can cause vibrations of flexible structures, and have been the subject of extensive investigations for this reason (see Sarpkaya (1979) and Bearman (1984) for reviews of the subject). Components of offshore structures exposed to a current often generate wakes parallel to the ocean surface.

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