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Eady (1949)的斜壓不穩定（baroclinic instability）理論是海洋與大氣科學家了解海洋渦旋和中緯度天氣系統形成（包含其空間尺度、成長率等）的重要理論基礎。例如，在圖一中可見，延著密度鋒面發展的各種尺度渦漩結構，經常是透過斜壓不穩定產生。

在海洋與大氣環境中，流體與介面的摩擦和地形變化是重要的物理過程，這些過程對不穩定現象的發展可能有所影響，因此，文獻中已有許多 Eady 的延伸理論探討摩擦、地形斜率等效應。然而，當斜壓不穩定發生在大陸棚或大陸斜等水深較淺的區域，這些大尺度理論的適用性在很大的程度上並未經過仔細檢驗，為此，Chen et al. (2020) 藉由理想化的數值實驗，分別探討底部摩擦和地形斜率的效應，其提供直接的證據顯示：定性上，如古典理論，淺水斜壓不穩定的成長可藉由邊界上Rossby wave的共振來解釋，亦即，上下邊界的不穩定波相互加強彼此而使震幅指數成長（圖二）。值得注意的是，這些理論有其定量上的限制。因為理論模型忽略了Ekman邊界層的反饋與水平流切的影響，使得成長率明顯被高估。另外，針對理論的不足之處，Chen et al. (2020) 也提出了可能的修正。

Chen, S. N*., C. J. Chen, and J. A. Lerczak, 2020: On baroclinic instability over continental shelves: Testing the utility of Eady-type models. Journal of Physical Oceanography, 50, 3-33.

Fig. 1. Examples of coastal currents: (a) unstable Middle Atlantic Bight Shelf Break Jet (Garvine et al. 1988); (b) unstable Leeuwin Current (Pearce and Griffiths 1991); (c)unstable Alaska Coastal Current (fed by coastal discharge); (d) stable Chesapeake Bay outflow (fed by coastal discharge; Donato and Marmorino (2008).

Fig. 2. An example of baroclinically unstable coastal current. In this setup, the basic flow (e) has a constant isopycnal slope (color contour is salinity), is purely along-shore with no horizontal shear (u denoted by white contours) in a wide central region, and is inviscid. This example therefore mimics the Eady basic flow. Panels (a)-(d) show the top views of surface salinity, taken at day 7, 11, 13, and 15. (f) and (g) are the time series of eddy kinetic energy budget and estimated growth rate (black) and wavelength (red). In (h), the estimated most unstable mode (star symbols taken in (g)) agrees with Eady’s theory (i.e. max of black curve).