Tropical Tropospheric Dynamics

该奖项为最小熵原理和最大熵原理的系统研究提供了支持，因为它们适用于飓风和更大规模热带环流中的潜在涡度混合问题。在正压、非发散模型的背景下，理论预测将从对称扩展到不对称情况。特别令人感兴趣的将是由最大熵涡旋参数预测的对称和非对称结构之间的分岔的确定。这种不对称理论的结果将揭示飓风中可能存在什么样的稳态不对称特征。在非发散模型的范围之外，直接数值积分和理论预测都将推广到浅水方程（在平面和球面上）。这种推广将允许区分涡量和位涡量，以及区分熵和位能，并允许能量约束包括动能和势能。然后从浅水的情况推广到等熵坐标下的准静态原始方程。这项研究的每一步都将有助于提高对大尺度大气流动非线性演化的理解（并最终有助于预测）。

This award provides support for a systematic study of the minimum enstrophy principle and maximum entropy principle as they apply to problems of potential vorticity mixing in hurricanes and larger-scale tropical circulations. Within the context of a barotropic, nondivergent model, theoretical predictions will be extended from the symmetric to the asymmetric case. Of particular interest will be the determination of the bifurcations between the symmetric and asymmetric structures predicted by the maximum entropy vortex arguments. The results of such an asymmetric theory should reveal what kind of steady state asymmetric features are possible in hurricanes. Outside the context of the non-divergent model, both direct numerical integrations and theoretical predictions will be generalized to the shallow water equations (on the plane and on the sphere). This generalization will allow a distinction between vorticity and potential vorticity and a distinction between enstrophy and potential enstrophy, and will allow the energy constraint to include both kinetic and potential energy. The generalization to the quasi-static primitive equations in isentropic coordinates should then follow from the shallow water case. Each step in this investigation will help to improve understanding (and, ultimately, prediction) of the nonlinear evolution of large-scale atmospheric flows.