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Baroclinic instability of axially symmetric flow over sloping bathymetry

Published online by Cambridge University Press:  22 June 2016

Aviv Solodoch ,
Andrew L. Stewart  and
James C. McWilliams
Aviv Solodoch*
Affiliation:
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA
Andrew L. Stewart
Affiliation:
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA
James C. McWilliams
Affiliation:
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical two-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Non-zero barotropic flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Quasi-geostrophic flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , pp. 265 - 296
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Copyright
© 2016 Cambridge University Press 

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