The initiation of cyclonic circulation in a vertically unstable stagnant air mass

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Abstract
Equations of motion are derived in cylindrical co‐ordinates and they are applied to investigate the perturbations in a vertically unstable stagnant air mass having infinite lateral extent and confined between two horizontal planes. A complete solution of the perturbation equation with the boundary conditions is derived. The boundary conditions are then varied by surrounding and surmounting the unstable air mass by stable air. It is shown that the horizontal extent of the unstable air mass has a definite upper limit which depends on the magnitude of instability, height of the disturbance, and the Coriolis parameter.The mathematical analysis is then applied to show that a tropical cyclone may originate from vertical instability. It is shown by a numerical illustration that the distribution and order of magnitude of the different meteorological elements are the same in the mathematical model as observed in the initial stages of a tropical cyclone.

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