軸向溫鹽梯度交互作用所衍生的流場之雙擴散穩定性

Abstract

當冰山在海中融化時，根據海水的溫度和鹽度分佈，在不同深度可能會出現不同類型的雙擴散流。我們提出了一種三維線性穩定性分析，以研究浸沒在溫度和鹽度均勻的海水中的冰山周圍的雙擴散對流的開始。圓柱環狀空間內的流動模擬冰山周圍的邊界層，水平溫度和鹽度梯度相互作用產生雙擴散對流。結果表明，可能會出現三種不同類型的不穩定性：熱不穩定性、雙擴散不穩定性和鹽指不穩定性。軸對稱鹽指在廣泛考慮的條件下普遍存在，並且隨著環形間隙寬度的擴大，其穩定性得到增強。相反，當間隙寬度減小時，非軸對稱鹽指增強了穩定性。當非軸對稱模式具有較小的方位角波長時，增強變得更加強烈。對於冰山上的應用，由於環形間隙寬度與邊界層厚度類似，因此在邊界層厚度較大的冰山上部容易發生不穩定。

When an iceberg melts in the sea, different kinds of double-diffusive flow may occur at different depths depending on the temperature and salinity distributions of the seawater. We propose a three-dimensional linear stability analysis to study the onset of the double-diffusive convections around an iceberg immersing in the seawater of uniform temperature and salinity. The flow within a cylindrical annulus simulates the boundary layer around the iceberg, and the double-diffusive convection is generated by the interaction between the horizontal temperature and salinity gradients. Results show that three different types of instability may occur: thermal, double-diffusive, and salt-finger. The axisymmetric salt-finger prevails in an extensive range of conditions considered, and its stability is enhanced when the annular gap width is enlarged. On the contrary, the non-axisymmetric salt-finger enhances the stability when the gap width reduces. The enhancement becomes more intense when the non-axisymmetric mode has a smaller azimuthal wavelength. For the application on the iceberg, since the annular gap width is analog to the boundary layer thickness, the instability is poised to occur in the upper part of the iceberg where the boundary layer thickness is larger.