Japan Geoscience Union Meeting 2021

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[J] Oral

A (Atmospheric and Hydrospheric Sciences ) » A-CG Complex & General

[A-CG38] Dynamics of Oceanic and Atmospheric Waves, Vortices, and Circulations

Sun. Jun 6, 2021 10:45 AM - 12:15 PM Ch.10 (Zoom Room 10)

convener:Yuki Tanaka(Faculty of Marine Science and Technology, Fukui Prefectural University), Kunihiro Aoki(Japan Agency for Marine Earth Science and Technology), Yukiharu Hisaki(University of the Ryukyus), Norihiko Sugimoto(Keio University, Department of Physics), Chairperson:Kunihiro Aoki(Japan Agency for Marine Earth Science and Technology), Yukiharu Hisaki(University of the Ryukyus), Yuki Tanaka(Faculty of Marine Science and Technology, Fukui Prefectural University)

11:45 AM - 12:00 PM

[ACG38-05] Stability of a Flow over Bottom Topography: A General Condition and a Linear Analysis in a Two-Layer Quasi-Geostrophic Model

*Yuki Tanaka1 (1.Faculty of Marine Science and Technology, Fukui Prefectural University)

Keywords:Two-Layer Quasi-Geostrophic Flow, Bottom Topography, Stability Theory, Barotropic and Baroclinic Instability

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.