測試現有渦漩尺度理論在非均勻背景流場之準地轉模式中的可用性

Abstract

海洋與大氣中偏離緯向平均或時間平均值中的擾動場被稱之為渦旋，它們對於中緯度大氣和海洋的南北向熱傳運輸扮演著重要的角色，並且塑造了現今的平均溫度結構。這些熱傳輸一直被當成是宏觀渦漩熱擴散的結果，現今絕大部分的渦旋擴散理論幾乎都是基於此觀點出發。透過在均勻背景平均場之準地轉平衡模式中的渦漩研究，前人提出了各種參數化理論（被稱為局部擴散理論）。然而，這些理論以背景場為定值為前提，現今仍缺乏將局部擴散理論應用到非均勻流場中的嚴謹分析。

為了測試局部擴散理論在非均勻背景流場中的可用性，我們利用Dedalus（Python 偏微分方程求解工具）撰寫均勻背景流場與非均勻背景流場之兩層準地轉平衡模式。首先我們在均勻背景場中驗證Gallet和Ferrari（2021）提出的局部擴散理論，接著將局部擴散理論預測之渦漩擴散率，帶入熱通量輻散與差異加熱的平衡式，可以重新構建南北向溫度剖面，並將其與真實剖面進行比較。我們發現在弱β值的實驗中，重新構建的溫度剖面與真實剖面較為接近，可以驗證局部擴散性理論的實用性。然而，當β值增加，可預測性則隨之降低。由於β值的增加產生了噴流，使背景非均勻性增加，實際上阻礙了經向渦旋熱傳輸，導致擴散性大幅減小，而局部擴散性理論則不考慮背景場的變化，因此對溫度梯度的估計出現顯著高估。

Eddies, defined as disturbances from zonal or time mean, play an important role in meridional heat transport for the midlatitude atmosphere and ocean, thereby helping to shape the mean temperature structure. This eddy transport has long been studied as a result of diffusion due to macroturbulence, and from this perspective, a theory for the eddy diffusivity is of fundamental importance. Various scaling laws for the diffusivity have been proposed by studying turbulence generated from homogeneous mean flows (referred to as local scaling theory). But, there is a lack of rigorous analysis on the applicability of these local scaling theory back to more realistic, inhomogeneous mean flows. To test the utility of local scaling theory in inhomogeneous turbulence, the evolution of two-layer, quasi-geostrophic potential vorticity, forced by a meridionally varying forcing, is implemented into a spectral PDE solver. The solutions of the resulting turbulence fields were validated against a prior study of Gallet and Ferrari (2021). The local scaling theory are evaluated as follows: Using an equilibrated mean state as an input, we apply the local scaling theory to estimate the meridional profile of diffusivity. From a balance between diffusive transport and forcing, we can then re-construct the meridional temperature profile, and the re-construction is evaluated against the true profile. It is found that, for weak β, the re-constructed temperature profiles closely resemble the true profiles, supporting the utility of local scaling theory. However, as β increases, the comparisons deteriorate. Emergence of zonal jets appears to block the meridional eddy transport near the jet cores, leading to large reduction in diffusivity there and thus a large overestimation of temperature gradient using the local scaling theory.