[A-CG38] 海洋と大気の波動・渦・循環の力学

[ACG38-05] 海底地形上の流れの安定性：二層準地衡系における一般的条件と線形解析

*田中 祐希¹ (1.福井県立大学 海洋生物資源学部)

キーワード：二層準地衡流、海底地形、安定性理論、順圧 / 傾圧不安定

Bottom topography is an essential factor that controls the pattern and variability of ocean currents. In the present study, the stability of a two-layer quasi-geostrophic flow over bottom topography is examined by combining a method of obtaining a sufficient condition for stability and a linear stability analysis. First, using a conserved quantity referred to as pseudoenergy that is proportional to the square of the disturbance amplitude, a sufficient condition for stability is derived for the simplest steady background field in which the potential vorticity and the stream function are proportional to each other. The obtained stability condition is unique in that no specific form is assumed for the background field except for the linear relationship between the potential vorticity and the stream function, and that it depends on the minimum possible wavenumber of the disturbance. These features enable us to judge the stability of various background fields by explicitly taking into account the limitation imposed on the disturbance scale by the domain size and/or boundary conditions. Applying the stability condition to a special case of a sinusoidal background field shows that the stable range extends to the area where the currents flow with shallower water on their right in both the upper and lower layers. The stable range is broadened as the disturbance becomes limited to smaller horizontal scales, mainly due to the suppression of barotropic instability which works effectively at large scales. Finally, a linear stability analysis confirms the validity of the stability condition for background fields with a wide range of parameters.