论文标题
具有全科利亚力的三维Euler-Boussinesq方程的变分平衡模型
Variational balance models for the three-dimensional Euler-Boussinesq equations with full Coriolis force
论文作者
论文摘要
我们为在刚性盖近似下的非传统$ f $平面上的三维Euler- boussinesq方程提供了一个半地球变异平衡模型。该模型是通过汉密尔顿原理中的小罗斯比数量扩展获得的，没有其他近似值。我们允许完全非静态流动，并且不要忽略科里奥利参数的水平成分，即，我们不做所谓的“传统近似”。最终的平衡模型与原始方程的“ $ L_1 $平衡模型”具有相同的结构：运动平衡关系，三维示踪剂领域的预后方程，以及在二维水平域上为标量域而定的额外预后方程，该方程与二维水平域上的整体相关性相关性相关性相关性相关性不足。在所有预后领域的稳定分层和足够小的波动的假设下，平衡关系是椭圆形的。
We derive a semi-geostrophic variational balance model for the three-dimensional Euler--Boussinesq equations on the non-traditional $f$-plane under the rigid lid approximation. The model is obtained by a small Rossby number expansion in the Hamilton principle, with no other approximations made. We allow for a fully non-hydrostatic flow and do not neglect the horizontal components of the Coriolis parameter, i.e., we do not make the so-called "traditional approximation". The resulting balance models have the same structure as the "$L_1$ balance model" for the primitive equations: a kinematic balance relation, the prognostic equation for the three-dimensional tracer field, and an additional prognostic equation for a scalar field over the two-dimensional horizontal domain which is linked to the undetermined constant of integration in the thermal wind relation. The balance relation is elliptic under the assumption of stable stratification and sufficiently small fluctuations in all prognostic fields.
