Inertial Instability of Horizontally Sheared Flow away from the Equator

Abstract

We investigate the temporal and spatial characteristics of unstable normal modes in a horizontally sheared flow on a sphere using the shallow water equations. Both inertial and barotropic instabilities are identified in cases where the appropriate necessary conditions are satisfied. A primary focus is determining what conditions favor asymmetric modes of inertial instability rather than symmetric modes. With the Bickley jet profile, the region of instability [f(f + &xi) ≤ 0] is confined to the anticyclonic side of the jet in a limited region. We find that symmetric instability is preferred only for modes of very small vertical wide, for which the pressure gradient force is secondary. Relatively small dissipation is needed to stabilize these modes. With deeper vertical scales, asymmetric instabilities are preferred in which the zonal scale of the instability is comparable to the width of the unstable region. This study extends previous results for linear shear on an equatorial beta plane to the midlatitude jet case. Our results suggest that deep atmospheric circulations in spatially confined regions of negative potential vorticity may develop as asymmetric rather than symmetric instabilities.