Generalized LSG models with spatially varying Coriolis parameter
Generalized LSG models with spatially varying Coriolis parameter
复制标题
具有空间变化科里奥利参数的广义 LSG 模型
DOI：
10.1080/03091929.2012.722210
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发表时间：
2013
影响因子：
1.3
通讯作者：
S. Vasylkevych
中科院分区：
文献类型：
--
作者：
M. Oliver;S. Vasylkevych
在本文中，我们推导和研究了近地转浅水流的近似平衡模型，其中允许Coriolis参数在整个区域内变化，只要它保持不退化。例如，这种情况包括对中纬度浅水方程的β平面近似。我们的方法是基于改变基本变分原理中的位形空间坐标，使得变换后的拉格朗日一致的渐近导致简并的拉格朗日结构。在本文中，我们的注意力仅限于一阶模型。我们表明，所得到的模式可以用平流势涡度和非线性涡度反演关系来表示。我们研究了相关的可解性条件，并确定了满足这些条件的模型子族，而不需要对数据进行额外的限制。最后，我们给出了我们的框架与约束哈密顿系统理论之间的联系。
In this paper, we derive and study approximate balance models for nearly geostrophic shallow water flow where the Coriolis parameter is permitted to vary across the domain as long as it remains nondegenerate. This situation includes, for example, the β-plane approximation to the shallow water equations at mid-latitudes. Our approach is based on changing configuration space coordinates in the underlying variational principle in such a way that consistent asymptotics in the transformed Lagrangian leads to a degenerate Lagrangian structure. In this paper, we restrict our attention to first-order models. We show that the resulting models can be formulated in terms of an advected potential vorticity with a nonlinear vorticity inversion relation. We study the associated solvability conditions and identify a subfamily of models for which these conditions are satisfied without additional restrictions on the data. Finally, we provide the link between our framework and the theory of constrained Hamiltonian systems.