Potential vorticity diagnosis of a simulated hurricane. Part I: Formulation and quasi-balanced flow

Because of the lack of three-dimensional (3D) high-resolution data and the existence of highly nonelliptic flows, few studies have been conducted to investigate the inner-core quasi-balanced characteristics of hurricanes. In this study, a potential vorticity (PV) inversion system is developed, which includes the nonconservative processes of friction, diabatic heating, and water loading. It requires hurricane flows to be statically and inertially stable but allows for the presence of small negative PV. To facilitate the PV inversion with the nonlinear balance (NLB) equation, hurricane flows are decomposed into an axisymmetric, gradient-balanced reference state and asymmetric perturbations. Meanwhile, the nonellipticity of the NLB equation is circumvented by multiplying a small parameter epsilon and combining it with the PV equation, which effectively reduces the influence of anticyclonic vorticity. A quasi-balanced omega equation in pseudoheight coordinates is derived, which includes the effects of friction and diabatic heating as well as differential vorticity advection and the Laplacians of thermal advection by both nondivergent and divergent winds. This quasi-balanced PV - omega inversion system is tested with an explicit simulation of Hurricane Andrew (1992) with the finest grid size of 6 km. It is shown that ( a) the PV - v inversion system could recover almost all typical features in a hurricane, and (b) a sizeable portion of the 3D hurricane flows are quasi-balanced, such as the intense rotational winds, organized eyewall updrafts and subsidence in the eye, cyclonic inflow in the boundary layer, and upper-level anticyclonic outflow. It is found, however, that the boundary layer cyclonic inflow and upper-level anticyclonic outflow also contain significant unbalanced components. In particular, a low-level outflow jet near the top of the boundary layer is found to be highly unbalanced ( and supergradient). These findings are supported by both locally calculated momentum budgets and globally inverted winds. The results indicate that this PV inversion system could be utilized as a tool to separate the unbalanced from quasi-balanced flows for studies of balanced dynamics and propagating inertial gravity waves in hurricane vortices.