Analytical model of the intensification of a tropical cyclone

Abstract

A description of the dynamic stage of the intensification of a tropical cyclone (TC) amounts to describing an interaction between radial (in the vertical plane) and tangential (rotational) circulation fields. In an axisymmetric TC, the structure of radial circulation is given by a streamfunction; the evolution of tangential velocity is expressed by the angular-momentum transfer equation. In this paper, analytical solutions to the equation of transfer of angular momentum are derived for several model streamfunction distributions imitating the TC radial circulation. The features of TC intensification are described on the basis of these solutions. In particular, in the TC-specific steady radial circulation, cyclonic rotation in the axial zone of the vortex encompasses the entire troposphere with time. The low-level TC intensification is accompanied by an exponential growth of maximum tangential velocity and by a fall in the radius of the maximum wind (vortex contraction). Numerical estimates are obtained which show that the Coriolis force plays a crucial role in TC cyclonic rotation. It is shown that a vortex with hurricane velocity forms from a state of rest in two days owing to a steady mass flux to the center and the deflecting effect of the Coriolis force. A rapid superexponential growth of maximum vortex velocity is possible with a nonstationary (increasing) mass inflow. The influence of friction is also studied using a simple phenomenological model. It is found that for TC intensification in the friction model it is necessary for the radial flow velocity at the lower level to be higher than a particular threshold (critical) value.