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 time-independent characterization of their structure, assuming that the dynamics is essentially barotropic. The angular velocity “induced” by the PV spiral has a radial profile that is approximately consistent with the advective formation of the spiral itself. The background shear in angular velocity, at a position along the filament, arising from the net effect of the remainder of the spiral, suppresses the growth rate of barotropic instability. However, it is shown here that all such spiral-shaped PV filaments are unstable in isolation and that disturbance growth rate varies only weakly with spiral shape. Contour dynamics calculations verify these predictions, as well as illustrating the strong influence of far-field strain on growth rates. The implication is that persistent vortices, associated with PV spirals and to some extent isolated from external strain, will mix the air contained within them at a rate significantly enhanced by filamentary instability. It is also concluded that the Kolmogorov capacity provides a useful geometrical characterization of atmospheric spirals.