On the stability of baroclinic vortex streets composed of quasi-geostrophic point eddies

The stability of quasi-geostrophic vortex streets is investigated for a single, a symmetric double, and a staggered double row, where component baroclinic point vortices are discriminated from ordinary ones by concentrated potential vorticity instead of concentrated vorticity. The former two types of rows always turn out unstable, though the growth rate itself decreases monotonically with increasing F∗, an index of horizontal divergence, or the inverse of the deformation radius nondimensionalized in terms of the longitudinal spacing of the vortex street. As regards a staggered double row, a critical value Fc∗ = 3.04 divides F∗ into two regimes. Below Fc∗, only one value of b∗ = bs∗ is neutrally stable, where b = ba is the aspect ratio of the vortex street with a and b the separations between eddies along and perpendicular to the street, respectively. The stable configuration bs∗ slowly increases with F∗ from the Kármán ratio 0.281 at F∗ = 0 to 0.322 at F∗ = Fc∗. For F∗ above Fc∗, the staggered double row is stable for a band of b∗. The appearance of the stable region is explained by a near-field approximation, where an eddy is assumed to exert its vortex force only on adjacent eddies. The near-field approximation yields a stability diagram which agrees well with that obtained from rigorous calculation for large F∗. In particular, the configuration b∗ ≥ √32 is shown to be unstable irrespective of F∗.