On the origin of time-dependent behaviour in a barotropically unstable shear layer

Abstract

Abstract. An experimental study on the instability of a detached Stewartson layer, using an annular, rotating tank with flat, rigid upper and lower boundaries, showed an instability to steady vortices at a critical Reynolds number, arranged in a global mode structure along the shear layer. Increasing the Reynolds number resulted in successive transitions to lower modes where time-dependent behaviour was only found for flows with three or less vortices. Previous numerical simulations of a related experiment, using a two-dimensional spectral model of the quasi-geostrophic vorticity equation incorporating Ekman forcing and viscous dissipation, suggested that the boundary conditions at the inner cylinder of the domain could significantly affect the interior flow by the generation and shedding of vorticity at this inner boundary. A comparison of the numerical results with experimental data suggests that the rise of time-dependent behaviour is due to vorticity generation at the inner domain boundary.