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

平衡大气模型是基于风场和质量场之间近似平衡的假设的方程组。现有的平衡模式在促进我们对大气动力学的理解方面发挥了关键作用。然而，它们的用处受到基本平衡假设的准确性的限制，而且没有一个能够表示飓风中遇到的具有大曲率的不对称流动。该项目的目标是通过扩展平衡大气模式的理论，开发高效和稳健的数值解方法，并将所产生的模式用于研究飓风动力学和中纬度天气现象，来纠正这种情况。主要的理论任务是发展两个新的连续形式的平衡模式：有限区域中纬度动力学和热带气旋的三维f平面模式，并将其推广到全球流动的球坐标。两者都将基于非线性平衡假设。所产生的模式将用于探索基本的动力学原理，包括可用势能和角动量原理，以及组合不稳定和波-均流相互作用的必要条件；研究飓风动力学的各个方面，包括位涡环、二次眼壁、不对称在平均涡旋演变中的作用、对低层和高层位涡异常的响应，以及不受可逆性原理控制的温度和湿度的小尺度波动的作用；研究天气尺度现象，包括三维水平切变对锋生的影响；和高Rossby数湍流，重点是准地转湍流的特征在多大程度上延续到新的球面模式。该项目的主要影响是为新的平衡模式开发用户友好的软件，该软件将提供给其他研究人员，以促进对大气动力学的进一步研究。参与这项工作的研究生将接受培训，为他们从事研究工作做好准备。增加对飓风动力学的了解，有朝一日可能有助于提高预测飓风强度变化的能力。最后，这一合作项目将促进计算数学和大气动力学社区之间加强互动。

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.