从准地转动力学直接推导 Gent-McWilliams/Redi 扩散张量
A direct derivation of the Gent-McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics
AI总结：
本文从准地转动力学直接推导出 Gent-McWilliams/Redi 扩散张量，证明其仅含两个随深度变化的系数，并揭示二者满足 Taylor-Bretherton 关系且在边界附近相等。
摘要：
海洋中尺度涡旋引起的输运在大多数最先进的气候模式中仍未得到解析，因此需要对其进行参数化。强迫与涌现湍流之间的自然尺度分离要求采用扩散型参数化，其中涡致通量通过扩散张量与大尺度梯度相联系。气候模拟中的标准参数化方案是采用 Gent-McWilliams/Redi（GM/R）形式的扩散张量，该形式最初基于物理直觉和有根据的猜测提出，后来才通过厚度加权平均（TWA）方法建立在坚实的解析基础之上。在本文中，我们直接从准地转（QG）动力学出发推导了这一扩散张量，所考虑的系统是 beta 平面上一个水平均匀的三维海洋区域，其中包含大尺度垂直剪切纬向流。尽管不如 TWA 方法具有一般性，但本文的 QG 框架对扩散张量给出了严格的约束。首先，在低粘性和小尺度扩散率条件下，QG GM/R 张量中不会出现跨密度面扩散率。此时扩散张量仅包含两个随深度变化的系数，即 GM 输运系数 $K_{GM}(z)$ 和 Redi 扩散率 $K_R(z)$。其次，正如先前作者已经指出的，这两个系数的垂直结构通过所谓的 Taylor-Bretherton 关系相互联系。最后，尽管这两个系数在水柱内部通常不同，我们证明当耗散系数足够低时，它们在区域表面附近和底部附近彼此相等。我们通过数值模拟一个水平均匀海洋区域的 QG 动力学来说明这些结果，该区域包含一股类似于南极绕极流的垂直剪切纬向流。
英文摘要：
The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parameterized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a diffusive parameterization, where the eddy-induced fluxes are related to the large-scale gradients by a diffusion tensor. The standard parameterization scheme in climate modeling consists in adopting the Gent-McWilliams/Redi (GM/R) form for the diffusion tensor, initially put forward based on physical intuition and educated guesses before being put on firm analytical footing using thickness-weighted average (TWA). In the present contribution we provide a direct derivation of this diffusion tensor from the quasi-geostrophic (QG) dynamics of a horizontally homogeneous three-dimensional patch of ocean hosting a large-scale vertically-sheared zonal flow on the beta plane. While less general than the TWA approach, the present QG framework leads to rigorous constraints on the diffusion tensor. First, there is no diapycnal diffusivity arising in the QG GM/R tensor for low viscosity and small-scale diffusivities. The diffusion tensor then involves only two vertically dependent coefficients, namely the GM transport coefficient $K_{GM}(z)$ and the Redi diffusivity $K_R(z)$. Secondly, as already identified by previous authors the vertical structures of the two coefficients are related by the so-called Taylor-Bretherton relation. Finally, while the two coefficients generically differ in the interior of the water column, we show that they are equal to one another near the surface and near the bottom of the domain for low-enough dissipative coefficients. We illustrate these findings by numerically simulating the QG dynamics of a horizontally homogeneous patch of ocean hosting a vertically sheared zonal current resembling the Antarctic Circumpolar Current.
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