Counterpropagating Rossby waves in confined plane wakes

In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163-185 (2007)] and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)] by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171-195 (2006)]: it is well predicted by the mean group velocity of the uncoupled CRWs. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729617]