Collaborative Research: Balanced Models--Theoretical Development, Solution and Application

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Balanced atmospheric models are systems of equations based on an assumption of approximate balance between the wind and mass fields. Existing balanced models have played a key role in advancing our understanding of atmospheric dynamics. Their usefulness, however, is limited by the accuracy of the underlying balance assumption, and none is capable of representing asymmetric flows with large curvature, such as are encountered in hurricanes. The goal of this project is to remedy this situation, by extending the theory of balanced atmospheric models, developing efficient and robust methods for their numerical solution, and using the resulting models to study aspects of hurricane dynamics and midlatitude weather phenomena.The principal theoretical task is to develop two new balanced models in continuous form: a three-dimensional f-plane model for limited-area midlatitude dynamics and tropical cyclones and its generalization to spherical coordinates for global flows. Both will be based on the nonlinear balance assumption. The resulting models will be applied to explore basic dynamical principles, including available potential energy and angular momentum principles, and necessary conditions for combined instability, and wave-mean flow interactions; to study aspects of hurricane dynamics, including potential vorticity rings, secondary eyewalls, the role of asymmetries in the evolution of the mean vortex, responses to lower- and upper-level potential vorticity anomalies, and the role of small-scale fluctuations of temperature and moisture not controlled by the invertibility principle; to investigate weather-scale phenomena, including effects of horizontal shears on frontogenesis in three dimensions; and to high Rossby number turbulence, focusing on the extent to which features of quasi-geostrophic turbulence carry over to the new spherical model.Broader impacts of the project are in developing user-friendly software for the new balanced models, which will be made available to other researchers to facilitate additional studies of atmospheric dynamics. The graduate students involved in this work will receive training which will prepare them for careers in research. Increased knowledge of hurricane dynamics may someday contribute to an improved ability to predict hurricane intensity changes. Finally, this collaborative project will foster increased interaction between the computational mathematics and atmospheric dynamics communities.