Mathematical Modeling of Tropical Cyclones on the Basis of Wind Trajectories

Abstract

A mathematical model of the development of a tropical cyclone is considered. It consists of a family of equations obtained by transforming the equation of inviscid non-heat conductive gas (air) motion to the form of equations on wind trajectories in an axially symmetric cylindrical domain. The numerical solution of these equations shows the increase of the wind velocity in accordance with the steam condensation and air warming; later, the velocity becomes stable as the liquid or small pieces of ice accumulate in the air and the friction of water against air decelerates the air updraft.