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 compon ent baroclinic point vortices are discriminated from ordinary ones by concentrated potential vorticity instead of concentrated vorticity. Th e former two types of rows always turn out unstable, though the growth rate itself decreases monotonically with increasing F, an index of h orizontal divergence, or the inverse of the deformation radius nondime nsionalized in terms of the longitudinal spacing of the vortex street. As regards a staggered double row, a critical value F-c = 3.04 divid es F into two regimes. Below F-c*, only one value of b* = b(s)* is ne utrally stable, where b = b/a is the aspect ratio of the vortex stree t with a and b the separations between eddies along and perpendicular to the street, respectively. The stable configuration b(s) slowly inc reases with F from the Karman ratio 0.281 at F* = 0 to 0.322 at F* = F-c. For F* above F-c*, the staggered double row is stable for a band of b. The appearance of the stable region is explained by a near-fie ld approximation, where an eddy is assumed to exert its vortex force o nly on adjacent eddies. The near-field approximation yields a stabilit y diagram which agrees well with that obtained from rigorous calculati on for large F. In particular, the configuration b* greater than or e qual to root 3/2 is shown to be unstable irrespective of F.