17B.2
Potential vorticity in a moist atmosphere
Wayne H. Schubert, Colorado State University, Fort Collins, CO; and S. A. Hausman, M. Garcia, K. V. Ooyama, and H. C. Kuo
The potential vorticity principle for a nonhydrostatic, moist, precipitating atmosphere is derived. The appropriate generalization of the well-known (dry) Ertel potential vorticity is found to be $P=\rho^{-1}(2{\bf \Omega}+\nabla\times{\bf u})\cdot\nabla\theta_\rho$, where $\rho$ is the total density, consisting of the sum of the densities of dry air, airborne moisture (vapor and cloud condensate) and precipitation, where ${\bf u}$ is the density-weighted-mean velocity of dry air, airborne moisture, and precipitation, and where $\theta_\rho$ is the virtual potential temperature, defined in such a way as to annihilate the solenoidal term. The $\theta_\rho$-surfaces are impermeable to $\rho P$. For balanced flows, there exists an invertibility principle which determines the total pressure (the sum of the partial pressures of dry air and water vapor) from the spatial distribution of $P$. In the special case of an absolutely dry atmosphere, $P$ reduces to the usual (dry) Ertel potential vorticity.
Session 17B, Convective Processes III (Parallel with Sessions 17A and 17C)
Saturday, 27 May 2000, 10:30 AM-12:30 PM
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