Instabilities in non-rotating and rotating shallow shear flows

Numerical simulations for the wave radiation effect on the linear and nonlinear instabilities of rotating and non-rotating shallow flows are conducted using shallow-water equations. At a low convective Froude number, the results of the instabilities is a string of eddies. The coalescence between the neighbouring eddies decides the transverse mixing of the shallow shear flow. At a higher convective Froude number, the development of the shear flow is characterized by wave radiation and the production of shocklets. The radiation of waves in the non-rotating shallow flow is a phenomenon analogous to the radiation of sound in gas dynamics. In the rotating flow on the other hand, the shallow-flow instabilities are intensified due to rotational interference within a window of instability over a narrow range of Rossby numbers.