Beta平面上中尺度渦旋傳遞的不對稱性——以淺水方程模擬探討

Chelton et al. (2011) 以衛星高度計資料分析中尺度渦旋的特徵與現象，分析結果顯示，氣旋式渦旋（cyclonic eddies，下稱低壓渦旋）與反氣旋式渦旋（anticyclonic eddies，下稱高壓渦旋）皆向西傳遞，且傳遞速度趨近於羅士比長波速度（long Rossby wave speed，β〖L_d〗^2）。高壓渦旋的生命期與傳遞距離皆較低壓渦旋長，顯示渦旋傳遞性質存在不對稱性。本研究使用減重力淺水方程模式（reduced-gravity shallow-water model）研究渦旋傳遞的不對稱性，並特別針對渦旋的東西向傳遞速度做探討。具體而言，我們在模式中測試了Davey and Killworth (1984) （下稱DK84）對於渦旋傳遞速度的理論推導，其中高壓渦旋傳遞速度會比 β〖L_d〗^2 快，低壓渦旋則比 β〖L_d〗^2 慢。理論中透過 F_β 與 F_C 的力平衡關係解釋渦旋傳遞速度：F_β 為渦旋質量異常（mass anomaly）內流體運動產生的南北向科氏加速度（即beta效應）積分，F_C 為渦漩質量異常向西傳遞所產生的科氏力。模擬結果顯示，高壓渦旋和低壓渦旋均向西傳遞，且傳遞速度與 β〖L_d〗^2 接近，與觀測結果相符。β〖L_d〗^2 的傳遞速度對應於 F_β 中，渦旋旋轉速度為純地轉流速，而高度異常（height anomaly）為零。模擬中高壓渦旋與低壓渦旋的傳遞速度確實存在不對稱：高壓渦旋傳遞比 β〖L_d〗^2 快，低壓渦旋則比 β〖L_d〗^2 慢，定性上與DK84理論結果相符。渦旋傳遞速度與 β〖L_d〗^2 的偏差可以超過30％。定量上，高壓渦旋傳遞速度區間和DK84理論預測結果相符，低壓渦旋卻與理論有很大的偏差。進一步分析發現，高壓渦旋傳遞速度大於 β〖L_d〗^2 的主要原因為：高壓渦旋的高度異常和其對應的地轉流速能使 F_β 增強，其傳遞速度與 β〖L_d〗^2 的偏差隨著渦旋高度異常相對於平均水深之無因次化參數增加而增加。另一方面，DK84理論則高估了低壓渦旋的傳遞速度，模擬中低壓渦旋傳遞速度亦與渦旋高度異常無關。在研究中發現，低壓渦旋的質量散失和隨著渦旋傳遞輻射羅士比波的現象，可能導致低壓渦旋的能量散失，從而減弱低壓渦旋的傳遞速度。

關鍵字

中尺度渦旋；渦旋傳遞不對稱性；羅士比長波速度；淺水方程模擬； beta 效應

並列摘要

Chelton et al.’s (2011) analyses of global sea-surface height fields have shown that cyclonic and anticyclonic mesoscale eddies have their westward propagation speeds approaching that for the long Rossby wave (β〖L_d〗^2). Yet, the lifetime and propagation distance of anticyclones are longer than cyclones, suggesting that marked asymmetry exists. In this study, properties of the asymmetry are studied using a reduced-gravity shallow-water model. The focus is on zonal propagation. Specifically, we examine the utility of a theory by Davey and Killworth (1984; DK84) who predicted an anticyclone to be faster than long wave while a cyclone to be slower. Their model based on the balance of two forces, F_β and F_C, are also evaluated: F_β arises from the north-south variations of Coriolis acceleration (i.e. beta effect) associated with eddy’s rotational velocity integrated over the entire mass, whereas F_C represents the Coriolis force acting on the translating eddy mass anomaly. In our numerical experiments, the zonal propagation speeds for both cyclones and anticyclones are not far from β〖L_d〗^2, consistent with Chelton et al.’s global observation. The long wave speed corresponds to F_β where eddy’s rotational velocity is purely geostrophic and height anomaly is zero. However, clear asymmetric propagation does exist: simulated anticyclones are faster than β〖L_d〗^2 while cyclones are slower as predicted by DK84. The speed deviations can be more than 30 percent. Quantitatively, the speed of a range of anticyclones is well represented by DK84’s theory, but large discrepancies are found for cyclones. Further analyses reveal that the positive speed deviations for anticyclones are mainly due to positive correlations of eddy’s height anomaly and geostrophic rotational velocity which reinforces F_β. The deviations thus increase with a dimensionless parameter characterizing the height anomaly relative to eddy’s mean thickness. By contrast, for cyclones, the theory significantly overestimates the propagation speeds, and the speed deviations show no dependence on the height anomaly. A large fraction of mass leakage and radiation of Rossby wave are found along the trails of cyclones, which may lead to significant energy loss and thus contribute to the slow-down of cyclones.

並列關鍵字

mesoscale eddies ； asymmetric eddy propagation ； long Rossby wave speed ； shallow-water model ； beta effect

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Beta平面上中尺度渦旋傳遞的不對稱性——以淺水方程模擬探討

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