The Eliassen-Palm flux tensor
The Eliassen-Palm flux tensor
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Eliassen-Palm 通量张量
DOI：
10.1017/jfm.2013.259
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发表时间：
2013
影响因子：
3.7
通讯作者：
Maddison J
中科院分区：
文献类型：
--
作者：
Maddison J
本文的目的是导出Eliassen-Palm通量张量的一般坐标不变形式，从而刻画流体静压Boussinesq旋转流体中涡流-均流相互作用的真实几何性质。在准地转极限下，通过规范变换证明了Eliassen-Palm通量张量的前人形式是相互联系的；提出了一种一般形式，并讨论了它的几何性质。将类似的方法应用于流体静力学Boussinesq Navier-Stokes方程，重新推导出坐标不变形式的残差平均方程。通过体积形式加权平均的定义，仔细地描述了浮力坐标中的厚度加权平均，其构造是为了与矢量的协变散度交换。讨论了导致厚度-重量平均方程的过程，并确定了产生的Eliassen-Palm通量张量的形式。
The aim of this paper it to derive general coordinate-invariant forms of the Eliassen–Palm flux tensor and thereby characterize the true geometric nature of the eddy–mean-flow interaction in hydrostatic Boussinesq rotating fluids. In the quasi-geostrophic limit previous forms of the Eliassen–Palm flux tensor are shown to be related to each other via a gauge transformation; a general form is stated and its geometric properties are discussed. Similar methodology is applied to the hydrostatic Boussinesq Navier–Stokes equations to re-derive the residual-mean equations in a coordinate-invariant form. Thickness-weighted averaging in buoyancy coordinates is carefully described, via the definition of a volume-form-weighted average, constructed so as to commute with the covariant divergence of a vector. The procedures leading to the thickness-weight averaged equation are discussed, and forms of the Eliassen–Palm flux tensor which arise are identified.