Tropical Tropospheric Dynamics

该奖项支持系统地研究最小拟能原理和最大熵原理，因为它们适用于飓风和较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，理论预测将从对称情形扩展到非对称情形。特别令人感兴趣的将是确定由最大熵涡旋自变量预测的对称和非对称结构之间的分叉。这种不对称理论的结果应该揭示出飓风中可能存在什么样的稳态不对称特征。在无散度模型之外，直接数值积分和理论预测都将推广到浅水方程(平面上和球面上)。这一推广将允许区分涡度和位涡以及拟能和势能，并将允许能量约束既包括动能又包括势能。然后，推广到等熵坐标下的准静态原始方程，然后从浅水情况出发。这项研究的每一步都将有助于提高对大尺度大气流动的非线性演化的理解(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.