Absolute and convective instabilities of plane turbulent wakes in a shallow water layer

In shallow turbulent wake flows, typically island wakes, the flow patterns depend mainly on a shallow wake parameter which is the ratio of the product of quadratic law friction coefficient and the island diameter to the water depth. To understand this, the Orr-Sommerfeld equation is modified with the depth averaged equations of motion yielding a shallow water stability equation with terms describing bottom friction. Numerical investigations reveal a stability diagram with two dividing lines, one defining the boundary between absolute and convective instabilities and the other defining the boundary between convectively unstable and stable wake flow. Vortex shedding is shown to be the end product of absolute instability.