The Invertibility Principle for a Simple Hurricane Model
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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A reinterpretation of Ooyamas classic tropical cyclone model is presented in terms of the more recent theoretical notions of the potential thickness equation, the potential radius coordinate and the invertibility principle. This helps place tropical cyclone theory in a theoretical framework closer to that of midlatitude theory. We first present a shallow water model of axisymmetric, frictionless flow of homogeneous incompressible fluid on an f- plane. The potential thickness, the inverse of potential vorticity, is introduced and the equation for its evolution written. We transform the system from physical space to absolute angular momentum or potential radius space. This eliminates the radial component of the wind from the problem and provides better resolution in areas of large vorticity. We derive and solve the invertibility principle using five different methods-solving for a potential function using the shooting method, the fluid depth using the same method, the fluid depth using a nonlinear equation solving black box, a transformed velocity using a tridiagonal matrix equation solver, and the transformed velocity with the nonlinear equation solver. The first four methods can not be generalized to two layers. A short review of Ooyamas model shows how the wind field is determined from the radial mass flux. Then we generalize the concepts of the shallow water case to a two layer model using the nonlinear equation solver to solve the invertibility for the transformed velocity. Theses.