Potential Vorticity Structure of Simulated Hurricanes

Abstract

Abstract To better understand the processes involved in tropical cyclone development, the authors simulate an axisymmetric tropical-cyclone-like vortex using a two-dimensional model based on nonhydrostatic dynamics, equilibrium thermodynamics, and bulk microphysics. The potential vorticity principle for this nonhydrostatic, moist, precipitating atmosphere is derived. The appropriate generalization of the dry potential vorticity is found to be P = ρ−1 {(−∂υ/∂z) (∂θρ/∂r) + [ f + ∂(rυ)/r∂r] (∂θρ/∂z)}, where ρ is the total density, υ is the azimuthal component of velocity, and θρ is the virtual potential temperature. It is shown that P carries all the essential dynamical information about the balanced wind and mass fields. In the fully developed, quasi-steady-state cyclone, the P field and the θ̇ρ field become locked together, with each field having an outward sloping region of peak values on the inside edge of the eyewall cloud. In this remarkable structure, the P field consists of a narrow, leaning tower in which the value of P can reach several hundred potential vorticity (PV) units. Sensitivity experiments reveal that the simulated cyclones are sensitive to the effects of ice, primarily through the reduced fall velocity of precipitation above the freezing level rather than through the latent heat of fusion, and to the effects of vertical entropy transport by precipitation.