Wave-induced longitudinal vortices in a shallow current
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Abstract:
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.Keywords:
Dimensionless quantity
Richtmyer–Meshkov instability
Weak, free surface vortices at vertical intakes with a headrace channel are defined by the first observance of a persistent dye core upon dye injection. Dimensionless parameters describing free surface vortex flows are used in an analysis of experimental data. The experimental results indicate that a large dimensionless submergence is required to avoid weak vortices at vertical intakes. Most vertical intakes will therefore require some type of antivortex device if weak vortices are to be avoided. The required dimensionless submergence is also highly dependent upon approach flow angle and headrace length/width ratio.
Dimensionless quantity
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