An analytical model for the rapid intensification of tropical cyclones

The nonlinearity and complexity of the primitive equations have been key obstacles to our understanding of tropical cyclones (TCs), particularly in relation to the dynamical processes leading to their rapid intensification. In this study, an axisymmetric model, in which all nonlinear terms in the horizontal momentum equations are retained, is used to examine analytically the effects of organized deep convection on TC rapid intensification. By prescribing a vertical profile of the vertical motion with exponential growth in the core region, a class of exact time-dependent solutions for the primary circulations of TCs are obtained. The analytical solutions are shown to capture well many observed dynamical structures in both the core and outer regions and the rapid growth of TCs in terms of maximum winds and central pressure drops. The analytical solutions reveal that (1) the rotational flows in the inner-core region grow double-exponentially, and the central pressure drops occur at rates much faster than the rotational growth; (2) the amplification rates of the primary circulations differ profoundly from those of the secondary circulations; (3) the rotational flows tend to grow from the bottom upwards with the fastest growth occurring at the lowest levels; and (4) the TC growth rates depend critically on the vertical structure of tangential flows, with a faster rate for a lower-level peak rotation. The nonlinear dynamics are shown to play an important role in the rapid growth of TCs. It is demonstrated that the analytical solutions can also be used to construct dynamically consistent vortices for the initialization of TC models. Limitations and possible improvements of the analytical model are also discussed. Copyright (C) 2009 Royal Meteorological Society