Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

The linear dynamics of non‐symmetric wave and vortex mode perturbations in spectrally stable geostrophic zonal flows with a constant horizontal shear along the meridional direction, when a fluid is incompressible and stratified, is investigated. Specific features of these dynamics are closely related to the non‐normality of the linear operators governing perturbation evolution in shear flows and are well interpreted in the framework of the non‐modal approach—by tracing the linear dynamics of spatial Fourier harmonics of perturbations in time. If the Rossby number Ro1, in addition, there takes place an exponential/explosive transient growth of the waves that precedes the time interval of algebraic amplification. We also describe the evolution of pure vortex mode perturbations imposed initially on the mean flow. It is shown that at Ro∼1, pure vortex (aperiodic) perturbations are able to gain basic flow energy and then generate non‐symmetric shear internal waves. The studied linear phenomena are specific to geostrophic zonal flows and cast doubt on the filtering of fast wave perturbations in the traditional quasi‐geostrophic models of geophysical hydrodynamics. Copyright © 2006 Royal Meteorological Society