Abstract :
We give a simple method to calculate without approximation the balanced density field of an axisymmetric vortex in
a compressible atmosphere in various coordinate systems given the tangential wind speed as a function of radius and
height and the vertical density profile at large radius. The method is generally applicable, but the example considered is
relevant to tropical cyclones. The exact solution is used to investigate the accuracy of making the anelastic approximation
in a tropical cyclone, i.e. the neglect of the radial variation of density when calculating the gradient wind.
We show that the core of a baroclinic vortex with tangential wind speed decreasing with height is positively buoyant
in terms of density differences compared at constant height, but at some levels may be interpreted as cold-cored or
warm-cored depending on the surfaces along which the temperature deviation is measured. However, it is everywhere
warm-cored if the potential temperature deviation is considered. In contrast, a barotropic vortex in a stably-stratified
atmosphere is cold-cored at all levels when viewed in terms of the temperature deviation at constant height or constant
σ, but warm-cored when viewed in terms of the potential temperature deviation along these surfaces. The calculations
provide a possible explanation for the observed reduction in surface air temperature in the inner core of tropical cyclones
