Abstract

The effect of the vertical transport of horizontal momentum by cumulus clouds on the development of a symmetric model hurricane is investigated. This is accomplished by using Sundqvist's symmetric hurricane model with parameterized cumulus friction. The scheme used to include cumulus friction in the model is essentially the same as that given by Stevens and Lindzen in 1978 and Lindzen in 1981. The results of two sets of numerical integrations are presented. In one, the initial wind and moisture distributions were derived from atmospheric observations in Atlantic intensifying cyclones as composited by McBride. In the other, the initial vortex was specified as that which corresponds to the linearly most unstable mode in Mak's 1980 linear analysis of the effect of cumulus friction on hurricane formation. Given each initial wind, temperature and moisture distribution, numerical integrations were performed with and without cumulus friction present in the model.

With cumulus friction included, the growth rates of the initial disturbances and their final intensities are smaller than those obtained in the absence of cumulus friction. The Atlantic intensifying cyclone with cumulus friction reaches storm strength, whereas without cumulus friction it develops into a hurricane. In the second pair of numerical integrations with the initial vortex specified as described above, the model develops hurricanes with and without cumulus frictions, but the rate of intensification and final strength of the vortex are significantly smaller when cumulus friction is included. The damping effect of cumulus friction is attributed to the fact that the angular momentum transported from the lower into the upper troposphere by cumulus mixing is not fully replenished in the lower troposphere by the cumulus induced secondary (radial) circulation. This contrasts with the effect of the inward eddy flux of momentum, reported on previously, which was found to enhance the intensification of hurricanes. The crucial difference between the two mechanisms, both of which induce secondary radial circulations due to a vertical differential in cyclonic torque, appears to be the net increase of momentum in the vortex due to inward eddy flux of momentum, which is not present in the case of cumulus friction. The latter mechanism simply redistributes the momentum vertically, actually reducing the strength of both the low-level cyclone and the upper-level anticyclone.

Abstract

The results of numerical integrations of Sundqvist's (1970) symmetric model for hurricane development modified to include parameterized large-scale eddy fluxes of momentum are presented. The initial wind and moisture distributions, and the prescribed eddy fluxes of momentum, were taken from atmospheric observations of Atlantic developing (prehurricane) and non-developing tropical disturbances as composited by McBride (1981a,b) and McBride and Zehr (1981). For the purposes of the present study, the data for individual stages in the evolution of developing and non-developing disturbances were combined to form a single composite developing hurricane and a single composite non-developing disturbance.

The data reveal the presence of intense, well organized inward eddy fluxes of momentum in developing Atlantic hurricanes and weak, poorly organized fluxes in non-developing disturbances. In the developing disturbances, the eddy fluxes of momentum are organized such that they act as a forcing function for driving the radial circulation, drawing moist air in toward the center of the vortex in the lower troposphere and pumping drier air outward aloft, thereby providing fuel for the explosive growth of the hurricane. In order to test the efficacy of this mechanism, and of Ekman suction and cooperative instability, numerical integrations were performed using the data for the composite developing hurricane, with and without the observed eddy fluxes of momentum, and for the composite non-developing disturbance with the observed eddy fluxes corresponding to this disturbance.

Without eddy flux forcing, the prehurricane developing vortex fails to intensify into a hurricane, even after 20 days of integration. With the observed eddy fluxes of momentum, the same initial vortex intensifies rapidly, reaching hurricane strength within 4 days. Moreover, because of the weak and diffuse pattern of the eddy fluxes of momentum in non-developing tropical disturbances, the initial vortex characterizing these disturbances also fails to develop into a hurricane.

The kinetic energy budgets corresponding to the integrations with the composite developing and non-developing disturbances are presented as a function of time. The calculations reveal that, during the early stages of development of the model hurricane, the conversion (E_k ) from eddy kinetic energy to the kinetic energy of the mean hurricane circulation is larger than the conversion (C_A ) from potential to kinetic energy. The eddy process is, therefore, directly responsible for the early growth of the model hurricane. This is followed by an explosive increase in the rate of conversion from potential to kinetic energy and in the rate of kinetic energy dissipation (F). During the latter period, C_A and F become almost an order of magnitude greater than the peak attained earlier by E_k , and the kinetic energy tendency reaches its peak. Without the eddy momentum flux forcing, no such explosive growth takes place.

The results of these integrations provide evidence that properly organized large-scale eddy fluxes of momentum may be an essential ingredient id the development of Atlantic hurricanes.

Abstract

The nonlinear effects of asymmetries associated with synoptic-scale waves in which hurricanes usually form are simulated by introducing steady-state and time varying eddy fluxes of angular momentum in a parameterized way into Sundqvist's (1970) symmetric model for hurricane development. The equations are integrated numerically using different initial conditions and different distributions of the parameterized eddy fluxes.

It is found that angular momentum flux convergences, with magnitudes comparable to those measured from atmospheric data, markedly accelerate hurricane development, and can initiate a model hurricane when the sea surface temperature is slightly subcritical such that the purely symmetric model fails to produce a vortex of hurricane intensity. Different distributions of the eddy flux of momentum produce different rates of growth, different final intensifies and different vortex sizes. The most effective distributions are those in which the vertical derivative of the angular momentum flux convergence is large near sea level, where it acts as a forcing function for the symmetric radial circulation, drawing moist boundary-layer air into the hurricane from the surroundings. In this way, it enhances the Ekman layer inflow, particularly at the early stages when the sea level vortex is weak. On the other hand, an angular momentum flux divergence produced by the eddies is found to suppress model hurricane development, even when the sea surface temperature is supercritical such that the purely symmetric model yields explosive hurricane growth. This is because it produces a radial circulation which opposes the Ekman layer inflow.

The contributions of the different terms in the kinetic energy equation in the purely symmetric integration are compared with those in one of the integrations with an eddy flux convergence of angular momentum. The calculations reveal that the kinetic energy production and dissipation are both larger in the latter case than in the former, and that the production exceeds the dissipation by a greater amount in the latter case, leading to a larger kinetic energy tendency and thereby more explosive hurricane growth.

Abstract

The role of large scale eddy processes in the transformation of cloud clusters and depressions into hurricanes is investigated by using different initial conditions in numerical integrations of the Naval Research Laboratory limited-area hurricane model. With initial conditions specified from the Colorado State University composite datasets of Professor William Gray for Atlantic nondeveloping cloud clusters, wave trough clusters and depressions, no hurricane formation takes place in any of the model integrations. With initial conditions specified from the datasets for Atlantic developing cloud clusters and depressions, a hurricane develops in the course of each model integration. One characteristic difference between the developing and nondeveloping disturbances is that the former exhibit large, well-organized eddy flux convergences of angular momentum associated with wavelike disturbances in the upper troposphere and lower stratosphere, whereas the latter exhibit weak, poorly organized eddy momentum fluxes.

In order to assess the role played in hurricane formation by the large-scale eddy processes in the developing cases, we performed additional integrations with initial conditions in which the eddies were removed from the datasets for the developing cloud cluster and depression. This was accomplished by using only the symmetric components of the wind and moisture fields in these datasets. In these integrations, the initial disturbances failed to develop. We take this as evidence to support the view that wavelike asymmetries in the upper troposphere and lower stratosphere may be necessary for hurricane development from Atlantic cloud clusters and depressions. Such asymmetries may act through the agency of eddy fluxes of heat and/or eddy fluxes of momentum. In this paper, we concentrate mainly on the role of eddy fluxes of momentum. Mechanistically, these fluxes exert an upper-level cyclonic torque on the initially weak vortex. Such a process induces upper level divergence and lower level convergence. The air converging in the lower boundary layer over a broad stretch of warm ocean brings moisture inward, organizing and concentrating the convection which fuels the development of the hurricane.

Abstract

The radial circulation equation for a balanced vortex is solved with forcing functions obtained from numerical simulations of hurricane formation from prehurricane cloud clusters and depressions. The simulations were made with the Naval Research Laboratory hurricane model using initial conditions derived from the Colorado State University composite datasets. Separate solutions of the radial circulation equation using different forcing functions provide evidence that large-scale eddy fluxes of heat and momentum serve to trigger the formation of the model hurricanes. Such fluxes, found in the Colorado State University datasets, induce a radial circulation with surface inflow over a broad stretch of warm ocean. This inflow picks up water vapor and concentrates it in the region of the vortex where the resulting release of latent heat by cumulus convection serves as an additional driving force that further enhances the radial circulation. Mechanisms such as CISK and finite-amplitude instability, which depend upon Ekman pumping by a symmetric vortex, are less efficient, given the observed strength of the initial vortex. In the absence of eddy fluxes of heat and momentum, the radial circulation forced by heating and friction in the simulations from both cloud clusters and depressions decreases in intensity with time and the initial vortex weakens. In the presence of the observed eddy fluxes, the radial circulation intensifies and a hurricane forms in both simulations.

Abstract

Numerical simulations and diagnostics are performed for Typhoon Tip and Tropical Storm Faye, both of which occurred during 1979, the year of the First Global GARP (Global Atmosphere Research Program) Experiment (FGGE). The simulations are started from early in the life cycles of both disturbances, the former of which developed into a super typhoon, and the latter of which did not develop beyond the tropical storm stage. The numerical model employed was that of Madala et al. and is a modification of the one used in previous simulations by the authors. The primary modifications are the inclusion of a more sophisticated boundary layer parameterization, based on similarity theory, and the inclusion in the Kuo cumulus parameterization scheme of the nonmeasurable mesoscale latent heat release, as described by Krishnamurti et al. The initial conditions for both simulations were derived from the FGGE dataset of the European Centre for Medium-Range Weather Forecasts and from monthly mean sea surface temperatures provided by the National Meteorological Center (now the National Centers for Environmental Prediction). The initial intensities and the underlying sea surface temperatures were approximately the same for the two disturbances. In the simulations, Tip developed into an intense typhoon and Faye did not develop, as observed in the atmosphere, although the minimum surface pressures and maximum wind speeds attained do not agree quantitatively with the reported values.

The primary question the authors set out to answer is what special conditions exist at the early stages of the life cycles of tropical disturbances that allow one system to develop and another to fail to develop into a typhoon. The most significant difference found in the initial states of Tip and Faye was a large-scale eddy flux of angular momentum from the surroundings into the former and out of the latter, with maximum amplitudes located around 200 mb at radial distances from the vortex centers greater than 1000 km. These fluxes persisted for at least 24 h prior to the time the numerical simulations were started. While there were differences in the eddy heat fluxes as well, these were less significant. Diagnostic calculations reveal that the secondary radial circulation induced by the eddy fluxes of momentum and heat transported water vapor inward for Tip and outward for Faye, with the result that convection broke out at an early stage in the vortex center of Tip, but not in Faye. The convection intensified with time in Tip and subsequently became the dominant factor contributing to the moisture inflow and rapid vortex intensification.

The authors’ interpretation of the results of their numerical simulations and diagnostic calculations is that the secondary radial circulation induced by large-scale eddy fluxes of heat and momentum can serve either as a catalyst for typhoon formation or as a mechanism for inhibiting the further development of an incipient tropical disturbance, depending on the direction of the water vapor transport (into or out of the vortex core).