Buoyancy and the warm-core structure of hurricanes

In this talk I will review the concept of parcel buoyancy in rapidly-rotating vortices. Parcel buoyancy arises naturally in the vertical momentum equation when pressure and density are defined relative to any hydrostatically-balanced reference fields for these quantities. Accordingly the magnitude of the force depends on the reference state used in the definition and is not a universally unique quantity. For a hurricane one might choose as reference profiles the mean of any environmental soundings for the storm, or the climatological mean profiles at the storm's current position at the particular time of year. In either case, one might expect the storm to have positive buoyancy and this would include the eyewall clouds as well as the eye, at least in the upper troposphere. Since the largest temperature anomalies occur in the eye, it is a more subtle question to ask whether the eyewall clouds have positive buoyancy in a local sense? To answer this question one needs to take into consideration that much of the thermal field of the vortex is in thermal wind balance with the tangential wind field, which typically decays in magnitude with height. To estimate the effective local buoyancy requires the use of balanced reference pressure and density fields that vary also with radius (and possibly azimuth and time). I will show an accurate method for calculating such a reference state given the azimuthally-averaged tangential wind field as a function of radius and height.

A typical calculation for a hurricane-scale vortex shows that the warm-core nature of a hurricane in the lower troposphere depends on the vertical coordinate used to depict the radial temperature gradient. In particular it is shown that such a balanced vortex is cold-cored at the surface with temperature falls comparable with those observed. Such a calculation provides an alternative explanation for the observations of cool air near the surface to those based on the evaporation of spray.

For a rapidly-rotating vortex such as a tornado or a hurricane one can define generalized buoyancy, which has a radial as well as a vertical component and which is normal to the isobaric surfaces. Accordingly, air parcels that are less dense (denser) than their immediate environment experience a radially-inward (radially-outward) force component. A scale analysis suggests that the radial component is small in hurricanes, but not for tornadoes.