A Framework for Parameterizing Eddy Potential Vorticity Fluxes
A Framework for Parameterizing Eddy Potential Vorticity Fluxes
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DOI：
10.1175/jpo-d-11-048.1
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发表时间：
2012-04-01
影响因子：
3.5
通讯作者：
Berloff, Pavel S.
中科院分区：
文献类型：
--
作者：
Marshall, David P.;Maddison, James R.;Berloff, Pavel S.
参数化涡位涡通量的框架是一致的能量和动量守恒，同时保留原始涡通量的对称性。该框架涉及将剩余平均涡流力（或等效的涡流位涡通量）重写为涡流应力张量的发散。这个张量的范数是有界的涡流能量，允许的组件的应力张量被重写的涡流能量和无量纲参数描述的平均形状和方向的涡流。如果一个预报方程被求解为涡能，其余的未知数是无量纲的，并在幅度上有界的单位。此外，这些无量纲的几何参数与经典的稳定性理论有很强的联系。当应用到女士问题，它表明，新的框架保留了功能的形式的Eady增长率的线性不稳定性。此外，在Reynolds应力被忽略的限制，该框架减少到一个Gent和McWilliams类型的涡闭合的涡扩散率可以解释为维斯贝克等人提出的形式。模拟三层风驱动的涡旋被用来诊断充分发展的地转湍流的涡的形状和方向。这些领域被发现有大规模的结构，出现相关的平均流的结构。涡动能量决定了涡动应力张量的大小，从而决定了涡动位涡通量的大小。可能的扩展框架，以确保位涡平均混合进行了讨论。
A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Lady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.