**Observational Evidence for Horizontal Mixing in the Hurricane Near-Core

Intense tropical cyclones often exhibit concentric eyewall patterns in their radar reflectivity. Deep convection within the inner, or primary eyewall is surrounded by an echo-free moat, which in turn is surrounded by an outer, or secondary ring of deep convection. Both convective regions typically contain well-defined tangential wind maxima. The primary wind maximum is associated with large vorticity just inside the radius of maximum wind, while the secondary wind maximum is usually associated with relatively enhanced vorticity embedded in the outer ring. In contrast, the moat is a region of low vorticity. If the vorticity profile across the eye and inner eyewall is approximated as monotonic, the resulting radial profile of vorticity still satisfies the Rayleigh necessary condition for instability as the radial gradient twice changes sign.

Here we investigate the stability of such structures and, in the case of instability, we simulate the nonlinear evolution into a more stable structure using a nondivergent barotropic model. Because the radial gradient of vorticity changes sign twice, two types of instability and vorticity rearrangement are identified: (1) instability across the outer ring of enhanced vorticity, and (2) instability across the moat. Type 1 instability occurs when the outer ring of enhanced vorticity is sufficiently narrow and when the circulation of the central vortex is sufficiently weak (compared to the outer ring) that it does not induce enough differential rotation across the outer ring to stabilize it. The nonlinear mixing associated with type 1 instability results in a broader and weaker vorticity ring but still maintains a significant secondary wind maximum. The central vortex induces strong differential rotation (and associated enstrophy cascade) in the moat region which then acts as a barrier to inward mixing of small (but finite) amplitude asymmetric vorticity disturbances. Type 2 instability occurs when the radial extent of the moat is sufficiently narrow so that unstable interactions may occur between the central vortex and the inner edge of the ring. Because the vortex induced differential rotation across the ring is large when the ring is close to the vortex, type 2 instability typically precludes type 1 instability except in the case of very thin rings. The nonlinear mixing from type 2 instability perturbs the vortex into a variety of shapes. In the case of contracting rings of enhanced vorticity, the vortex and moat typically evolve into a nearly steady tripole structure thereby offering a possible mechanism for the formation and persistence of elliptical eyewalls.