Balanced and unbalanced aspects of tropical cyclone intensification

Abstract

ABSTRACT:We investigate the extent to which the azimuthally-averaged fields from a three-dimensional, nonhydrostatic, tropical cyclone model can be captured by axisymmetric balance theory. The secondary (overturning) circulation and balanced tendency for the primary circulation are obtained by solving a general form of the Sawyer-Eliassen equation with the diabatic heating, eddy heat fluxes and tangential momentum sources (eddy momentum fluxes, boundary-layer friction and subgrid-scale diffusion) diagnosed from the model. The occurrence of regions of weak symmetric instability at low levels and in the upper-tropospheric outflow layer requires a regularization procedure so that the Sawyer-Eliassen equation remains elliptic. The balanced calculations presented capture a major fraction of the azimuthally-averaged secondary circulation of the three-dimensional simulation except in the boundary layer, where the balanced assumption breaks down and where there is an inward agradient force. In particular, the balance theory is shown to significantly underestimate the low-level radial inflow and therefore the maximum azimuthal-mean tangential wind tendency. In the balance theory, the diabatic forcing associated with the eyewall convection accounts for a large fraction of the secondary circulation. The findings herein underscore both the utility of axisymmetric balance theory and also its limitations in describing the axisymmetric intensification physics of a tropical cyclone vortex.

The vorticity budget of developing typhoon Nuri (2008)

“…Uncertainties in the vertical distribution of surface stress are insufficient to explain this discrepancy, particularly for Nuri 2. We note that significant imbalance was found in the boundary layer of a simulated, intensifying tropical storm (Bui et al, 2009) in agreement with our observations. The effects of tilting are generally insufficient to change these qualitative results, at least at low levels.…”

Asymmetric and axisymmetric dynamics of tropical cyclones

“…10e and f. The main contribution to the spin-up of the maximum tangential wind is associated with the import of mean cyclonic absolute vorticity in the boundary layer and its vertical advection into the eyewall updraught. This result corroborates that of Bui et al (2009, Fig. 9a, c, g and e).…”

“…This mechanism has been articulated previously by many authors (e.g., Willoughby, 1979;Shapiro and Willoughby, 1982). It explains why the vortex expands in radial extent as measured by an increase in tangential winds beyond the radius of maximum winds and may be interpreted in terms of axisymmetric balance dynamics (Bui et al, 2009;Smith et al, 2011).…”

“…Previous studies of the conventional spin-up process have tended to use an approach based on the Sawyer-Eliassen equation for the balanced overturning circulation forced by heat and momentum sources (Willoughby, 1979;Bui et al, 2009). Here we follow Shapiro and Montgomery (1993) and Vigh and Schubert (2009) and adopt an alternative approach based on the geopotential tendency equation.…”

“…On the basis of the foregoing discussion, in lieu of a full inversion of the geopotential tendency equation (as employed for the Sawyer-Eliassen equation by Bui et al (2009) or using coarse resolution data with a cumulus parameterization derived from the Geophysical Fluid Dynamics Laboratory Hurricane model by Möller and Shapiro, 2002), we will use a bulk measure of the spinup function in order to assess the balanced contribution of the mean heating rate to the change in the mass field in the 3-D and AX simulations.…”