THE INFLUENCE OF CIRCULATION ON THE STABILITY OF VORTICES TO MODE-ONEDISTURBANCES

The initial value problem for the two-dimensional inviscid vorticity e quation, linearized about an azimuthal basic velocity field with monot onic angular velocity, is solved exactly for mode-one disturbances. Th e solution behaviour is investigated for large time using asymptotic m ethods. The circulation of the basic state is found to govern the ulti mate fate of the disturbance: for basic state vorticity distributions with non-zero circulation, the perturbation tends to the steady soluti on first mentioned in Michalke & Timme (1967), while for zero circulat ion, the perturbation grows without bound. The latter case has potenti ally important implications for the stability of isolated eddies in ge ophysics.