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Wave-induced longitudinal vortices in a shallow current

An instability theory is presented for the initiation of longitudinal vortices due to waves interacting with a turbulent current in an open channel of finite depth. With a simple model of eddy viscosity the dimensionless shearing rate of the basic current is much weaker than the dimensionless velocity almost everywhere except near the bed. We shall show that in addition to the internal vortex force, a mean shear stress exists on the mean sea level, owing to nonlinear wave–current interactions, despite the absence of wind. This stress adds vertical vorticity to the interior and augments the vortex force mechanism of instability significantly. Effects of current strength and wave conditions on the unstable growth are studied by numerical examples.