SPIRALS IN POTENTIAL VORTICITY - PART-II - STABILITY

A model of the linear stability of spiral-shaped potential vorticity ( PV) filaments is constructed by using the Kolmogorov capacity as a tim e-independent characterization of their structure, assuming that the d ynamics is essentially barotropic. The angular velocity ''induced'' by the PV spiral has a radial profile that is approximately consistent w ith the advective formation of the spiral itself. The background shear in angular velocity, a: a position along the filament, arising from t he net effect of the remainder of the spiral, suppresses the growth ra re of barotropic instability. However, it is shown here that all such spiral-shaped PV filaments are unstable in isolation and that disturba nce growth rate varies only weakly with spiral shape. Contour dynamics calculations verify these predictions, as well as illustrating the st rong influence of far-field strain on growth rates. The implication is that persistent vortices, associated with PV spirals and to some exte nt isolated from external strain, will mix the air contained within th em at a rate significantly enhanced by filamentary instability. It is also concluded that the Kolmogorov capacity provides a useful geometri cal characterization of atmospheric spirals.