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Nonlinear Response of Atmospheric Vortices to Heating by Organized Cumulus Convection

James J. HackNational Center for Atmospheric Research, Boulder, CO 80307

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Wayne H. SchubertDepartment of Atmospheric Science, Colorado State University, Fort Collins, CO 80523

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Abstract

Using an axisymmetric primitive tropical cyclone model, we first illustrate the way in which nonlinear processes contribute to the development of an atmospheric vortex. These numerical experiment show that nonlinearities allow a given diabatic beat source to induce larger tangential wind (and kinetic energy) changes as the vortex develops and the inertial stability becomes large. In an attempt to gain a deeper theoretical understanding of this process, we consider the energy cycle in the balanced vortex equations of Eliassen. The temporal behavior of the total potential energy P is governed by dP/dt=HC where H is the rate of generation of total potential energy by diabatic heating, and C is the rate of conversion to kinetic energy. We define a time-dependent system efficiency parameter as η¯(t)=C/H. Then, using the dynamical simplifications of balanced vortex theory, we express η¯(t) as a weighted average of a dynamic efficiency factor η(r, z, t). The dynamic efficiency factor is a measure of the efficacy of diabatic heating at any point in generating kinetic energy and can be determined by solving a second-order partial differential equation whose coefficients and right-hand side depend only on the instantaneous vortex structure. The diagnostic quantities η¯(t) and η(r, z, t) are utilized in the analysis of several balanced numerical experiments with different vertical and radial distributions of a diabatic heat source.

Abstract

Using an axisymmetric primitive tropical cyclone model, we first illustrate the way in which nonlinear processes contribute to the development of an atmospheric vortex. These numerical experiment show that nonlinearities allow a given diabatic beat source to induce larger tangential wind (and kinetic energy) changes as the vortex develops and the inertial stability becomes large. In an attempt to gain a deeper theoretical understanding of this process, we consider the energy cycle in the balanced vortex equations of Eliassen. The temporal behavior of the total potential energy P is governed by dP/dt=HC where H is the rate of generation of total potential energy by diabatic heating, and C is the rate of conversion to kinetic energy. We define a time-dependent system efficiency parameter as η¯(t)=C/H. Then, using the dynamical simplifications of balanced vortex theory, we express η¯(t) as a weighted average of a dynamic efficiency factor η(r, z, t). The dynamic efficiency factor is a measure of the efficacy of diabatic heating at any point in generating kinetic energy and can be determined by solving a second-order partial differential equation whose coefficients and right-hand side depend only on the instantaneous vortex structure. The diagnostic quantities η¯(t) and η(r, z, t) are utilized in the analysis of several balanced numerical experiments with different vertical and radial distributions of a diabatic heat source.

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