Numerical Simulation of the Life Cycle of Tropical Cyclones

The tropical cyclone is a solitary creature of the tropical oceans accompanied by violent rotating winds and torrential rain. Observational studies and diagnostic analyses leave little doubt that the energy required for driving the vortex comes from the latent heat of condensation released by tall convective clouds around the center, and that the frictionally induced inflow in the vortex plays a major role in supporting the continued activity of convective clouds. This dual character with respect to important scales of motion poses a great difficulty in investigating the dynamics of tropical cyclones as time-dependent phenomena. However, in order to understand the large-scale aspects of tropical cyclones, one may formulate the role of convective clouds in terms of cyclone-scale variables with only implicit consideration of the dynamics of individual clouds. The present study is an attempt to understand the basic mechanism of tropical cyclones by constructing a numerical-dynamical model on such a basis. The model assumes that the large-scale hydrodynamical aspects of a tropical cyclone may be represented by an axisymmetric, quasi-balanced vortex in a stably stratified incompressible fluid, while the effects of moist convection may be formulated through the first law of thermodynamics applied to an implicit model of penetrative convective clouds. The air–sea exchange of angular momentum as well as latent and sensible heat is explicitly calculated in the model with the use of conventional approximations. Results of numerical integration show that the model is capable of simulating the typical life cycle of tropical cyclones, including the mature hurricane stage, with a remarkable degree of reality. The response of the model cyclone to changes in such parameters as the sea surface temperature, the coefficient of air–sea energy exchange, and the initial conditions is tested in a number of numerical experiments to show quite plausible results. A detailed diagnosis of the energy budget of the simulated tropical cyclone is also carried out. The rate of total rainfall, the production and dissipation of kinetic energy, and other energetic characteristics of the computed cyclone compare very well with available estimates for observed tropical cyclones. Because of the restrictive assumption of axisymmetry and other weak approximations, the model is not realistic enough to predict behavior of individual tropical cyclones in nature. The limitation of the present model in this regard is also discussed.