The Sawyer-Eliassen Equation (SEQ) is here rederived in height coordinates such that the sea surface is also a coordinate surface. Compared with the conventional derivation in mass field coordinates, this formulation adds some complexity, but arguably less than is inherent in terrain-following coordinates or interpolation to the lower physical boundary. Spatial variations of static stability change the vertical structure of the mass flow streamfunction. This effect leads to significant changes

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... n both secondary-circulation structure and intensification of the primary circulation. The SEQ is solved on a piecewise continuous, balanced mean vortex where the shapes of the wind profiles inside and outside the eye and the tilt of the specified heat source can be adjusted independently. A series of sensitivity studies shows that the efficiency with which imposed heating intensifies the vortex is most sensitive to intensity itself as measured by maximum wind and to vortex size as measured by radius of maximum wind. Vortex shape and forcing tilt have impacts 20%-25% as great as intensity and size, suggesting that the aspects of tropical cyclones that predispose them to rapid intensification are environmental or thermodynamic rather than kinematic.