The heating field in an asymmetric hurricane — Part I: Scale analysis
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A closed system of equations describing an asymmetric disturbance in cylindrical geometry is expanded about a small parameter. The small parameter describes the ratio of the magnitude of divergence in the boundary layer to that above that layer. A low order system describes a gradient wind balance in the radial direction and is quasi-symmetric with respect to the pressure and temperature fields. This system can be solved as an inverse problem for a mature steady state hurricane. The procedure entails asking the questions what structure and heating distributions are required to maintain a given asymmetric distribution of the tangential velocity (i. e. the angular momentum) in steady state. The method of characteristics enables us to solve for the vertical motion. That in turn determines the radial motion from the mass continuity equation. Application of the hydrostatics to the cylindrical thermal wind equation determines the pressure and the thermal fields and finally the required heating fields are deduced from the first law. This entire system of inverse dynamics is linear although no nonlinear terms are dropped from the original direct set of equations. The real data applications of this procedure will be described in part II (to be published in the next issue).
KeywordsTangential Velocity Flight Data Order Partial Differential Equation Rain Band Frictional Torque
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