A Piecewise Potential Vorticity Inversion Algorithm and Its Application to Hurricane Inner-Core Anomalies

In this study, a piecewise potential vorticity (PV) inversion algorithm for an arbitrary number of PV pieces is developed by extending Wang and Zhang's PV inversion scheme, and then the nonlinear responses to various types and magnitudes of axisymmetric PV anomalies (PVAs) in hurricane vortices are investigated. Results show that the upper- and lower-level PVAs in the eye help enhance cyclonic flows in the eyewall, but with weak vertical interactions between them. The balanced flows corresponding to the PVAs in the eyewall appear to account for a substantial portion of the warm core and the minimum pressure in the eye. However, the lower-level PVA in the eye inversion layer is more effective in contributing to the hurricane intensity than that at the upper levels. Results also show that the radius of the balanced response of PVAs is more sensitive to the mean vortex intensity than the vertical penetration; the weaker the mean vortex intensity, the larger the radius of the influence will be. Similar behaviors are also observed for the quasi-balanced secondary circulations. That is, given a diabatic heating profile in the eyewall, the weaker the background vortex or the PVAs, the stronger the secondary circulations will be. It is found that the development of an outer eyewall (or spiral rainbands) could be inimical to the inner eyewall in several ways, such as by 1) adding an anticyclonic flow inside to offset the cyclonic rotation of the inner eyewall, 2) enhancing a ring of a lower pressure zone underneath to broaden the inner-core lower pressure region, 3) inducing an inward (outward) radial flow outside (inside) in the PBL (upper level) to block the energy supply to (outflow of) the inner eyewall, and 4) generating subsidence between the two eyewalls to suppress the development of deep convection in the inner eyewall.