The Continuous Spectrum of Linear Couette Flow with the Beta Effect

Abstract

The previously known analytic solution for the unbounded plane Couette flow [i.e., a mean flow U(y)=Sy, S constant] is extended by 1) inclusion of the beta effect, and 2) more general initial conditions. It is shown that the beta effect and sidewall boundaries in latitude both have little or no effect on the physics of the waves. For large times, as already known, the continuous spectrum always decays away algebraically with time. It is shown, however, that before the final decay, the continuous spectrum may grow rapidly for a finite time interval if the latitudinal length scale of the initial perturbation is small in comparison to the zonal scale.