Generalised Lagrangian solutions for atmospheric and oceanic flows
Generalised Lagrangian solutions for atmospheric and oceanic flows
复制标题
大气和海洋流的广义拉格朗日解
DOI：
10.1137/0151002
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发表时间：
1991
影响因子：
2
通讯作者：
J. Norbury
中科院分区：
文献类型：
--
作者：
M. Cullen;R. Purser;J. Norbury
受旋转和层结强烈约束的大气或海洋流动可以用一组称为半地转方程的拉格朗日偏微分方程来描述。在这些方程中，必须隐式地确定轨迹。这些方程的广义解被定义为流体的重排序列，它不需要是光滑的。这些解决方案是密切相关的广义解决方案的蒙赫-安培方程。证明了该解的存在唯一性。的演变被证明是一个序列的最低能量状态的流体，提供强的物理可扩展性的解决方案。
Atmospheric or oceanic flows strongly constrained by rotation and stratification can be described by a set of Lagrangian partial differential equations called the semigeostrophic equations. In these equations the trajectories must be determined implicitly. Generalised solutions of these equations are defined as a sequence of rearrangements of the fluid, which need not be smooth. These solutions are closely related to generalised solutions of the Monge-Ampere equation. Existence and uniqueness of such solutions is proved. The evolution is shown to be a sequence of minimum energy states of the fluid, giving strong physical plausibility to the solutions.