The Adiabatic Evolution of 3D Annular Vortices with a Double-Eyewall Structure

Tropical cyclones (TCs) can be characterized as a 3D annular structure of elevated potential vorticity (PV). However, strong mature TCs often develop a secondary eyewall, leading to a 3D annular vortex with a double-eyewall structure. Using 2D linear stability analysis, it is shown that three types of barotropic instability (BI) are present for annular vortices with a double-eyewall structure: Type-1 BI across the secondary eyewall, Type-2 BI across the moat of the vortex, and Type-3 BI across the primary eyewall. The overall stability of these vortices (and the type of BI that develops) depends principally upon five vortex parameters: the thickness of the primary eyewall, the thickness of the secondary eyewall, the moat width, the vorticity ratio between the eye and the primary eyewall, and the vorticity ratio between the primary and secondary eyewall. The adiabatic evolution of 3D annular vortices with a double-eyewall structure is examined using a primitive equation model in normalized isobaric coordinates. It is shown that Type-2 BI is the most common type of BI for 3D annular vortices whose vortex parameters mimic TCs with a double-eyewall structure. During the onset of Type-2 BI, eddy kinetic energy budget analysis indicates that barotropic energy conversion from the mean azimuthal flow is the dominant energy source of the eddies, which produces a radial velocity field with a quadrupole structure. Absolute angular momentum budget analysis indicates that Type-2 BI generates azimuthally averaged radial outflow across the moat, and the eddies transport absolute angular momentum radially outward towards the secondary eyewall. The combination of these processes leads to the dissipation of the primary eyewall and the maintenance of the secondary eyewall for the vortex.