Evaluation of a time-dependent model for the intensification of tropical cyclones

Axisymmetric and three-dimensional simulations are used to evaluate the theory of tropical cyclone (TC) intensification proposed by K. A. Emanuel, which is based on gradient wind balance and moist-neutral ascent along angular momentum (M) surfaces. According to the numerical model results, the intensification of the TC can be divided into two periods, phase I and phase II. During phase I, the TC intensifies while the M and saturation entropy (s*) surfaces evolve from nearly orthogonal to almost congruent. During phase II, the M and s* surfaces in the eyewall and outflow are congruent as the TC intensifies, which is consistent with Emanuel's study. Therefore, the condition of moist slantwise neutrality in Emanuel's study is sufficiently satisfied throughout the intensification in phase II. It is also found that the sensitivity of the intensification rates to the surface exchange coefficient for entropy C_k matches Emanuel's theoretical result, which is that the intensification rate is proportional to C_k. However, the intensification rate varies in proportion to the surface exchange coefficient for momentum C_d, while the Emanuel model growth rate is insensitive to C_d. Furthermore, although the tendency diagnosed by Emanuel is qualitatively similar to the numerical model result during phase II, it is not quantitatively similar. The present analysis finds the inclusion of non-gradient wind effects in the theoretical framework of Emanuel's study produces an intensification rate that is quantitatively similar to the numerical model results. The neglect of non-gradient wind effects in Emanuel's study may be the reason for the different dependence of its intensification rate on C_d compared to that of the numerical model. Other aspects of Emanuel's study in the context of recent research on TC intensification are discussed.