Dynamics of Atmospheres and Oceans 40 (2005) 189–208 Buoyancy in tropical cyclones and other rapidly rotating atmospheric vortices Roger K. Smith a,∗ , Michael T. Montgomery b , Hongyan Zhu a,1 a Meteorological Institute, University of Munich, Theresienstr. 37, 80333 Munich, Germany b Department of Atmospheric Science, Colorado State University, USA Received 18 March 2004; accepted 8 March 2005 Abstract Motivated primarily by its application to understanding tropical-cyclone intensification and main- tenance, we re-examine the concept of buoyancy in rapidly rotating vortices, distinguishing between the buoyancy of the symmetric balanced vortex or system buoyancy, and the local buoyancy associated with cloud dynamics. The conventional definition of buoyancy is contrasted with a generalized form applicable to a vortex, which has a radial as well as a vertical component. If, for the special case of axisymmetric motions, the balanced density and pressure distribution of a rapidly rotating vortex are used as the reference state, the buoyancy field then characterizes the unbalanced density perturbations, i.e. the local buoyancy. We show how to determine such a reference state without approximation. The generation of the toroidal circulation of a vortex, which is necessary for vortex amplification, is characterized in the vorticity equation by the baroclinicity vector. This vector depends, inter-alia, on the horizontal (or radial) gradient of buoyancy evaluated along isobaric surfaces. We show that for a tropical-cyclone-scale vortex, the buoyancy so calculated is significantly different from that calculated at constant height or on surfaces of constant σ (σ =(p - p ∗ )/(p s - p ∗ ), where p is the actual pressure, p * some reference pressure and p s is the surface pressure). Since many tropical-cyclone models are formulated using σ-coordinates, we examine the calculation of buoyancy on σ-surfaces and derive an expression for the baroclinicity vector in σ-coordinates. The baroclinic forcing term in the azimuthal vorticity equation for an axisymmetric vortex is shown to be approximately equal to the azimuthal component of the curl of the generalized buoyancy. A scale analysis indicates that the vertical gradient of the radial component of generalized buoyancy makes a comparatively small contribution to the ∗ Corresponding author. E-mail address: roger@meteo.physik.uni-muenchen.de (R.K. Smith). 1 Present address: Department of Meteorology, University of Reading, England. 0377-0265/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.dynatmoce.2005.03.003