几何拉格朗日平均Euler-Boussinesq和原始方程
Geometric Lagrangian averaged Euler-Boussinesq and primitive equations
摘要：
在这篇文章中，我们推导出的方程的旋转分层流体的无粘欧拉-Boussinesq和原始方程，占的影响，扰动后的平均值。我们的方法是基于几何广义拉格朗日平均的概念，最近引入的Gilbert和Vanneste，结合广义泰勒和水平各向同性的波动湍流闭合假设。我们得到的模型产生的欧拉-庞加莱方程，并继承其父系统的能量和位涡守恒定律。它们在结构和几何上类似于Euler-Boussinesq- $α$和原始方程- $α$模型，但是具有不同的正则化二阶算子。
英文摘要：
In this article we derive the equations for a rotating stratified fluid governed by inviscid Euler-Boussinesq and primitive equations that account for the effects of the perturbations upon the mean. Our method is based on the concept of geometric generalized Lagrangian mean recently introduced by Gilbert and Vanneste, combined with generalized Taylor and horizontal isotropy of fluctuations as turbulent closure hypotheses. The models we obtain arise as Euler-Poincaré equations and inherit from their parent systems conservation laws for energy and potential vorticity. They are structurally and geometrically similar to Euler-Boussinesq-$α$ and primitive equations-$α$ models, however feature a different regularizing second order operator.
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