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Baroclinic instability of axially symmetric flow over sloping bathymetry

Published online by Cambridge University Press:  22 June 2016

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: asolodoch@atmos.ucla.edu

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.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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References

Benilov, E. S. 2005 On the stability of oceanic vortices: a solution to the problem? Dyn. Atmos. Oceans 40 (3), 133149.CrossRefGoogle Scholar
Blumsack, S. L. & Gierasch, P. J. 1972 Mars: the effects of topography on baroclinic instability. J. Atmos. Sci. 29 (6), 10811089.2.0.CO;2>CrossRefGoogle Scholar
Bower, A. S., Armi, L. & Ambar, I. 1997 Lagrangian observations of Meddy formation during a Mediterranean undercurrent seeding experiment. J. Phys. Oceanogr. 27 (12), 25452575.2.0.CO;2>CrossRefGoogle Scholar
Bower, A. S., Lozier, M. S., Gary, S. F. & Böning, C. W. 2009 Interior pathways of the North Atlantic meridional overturning circulation. Nature 459 (7244), 243247.CrossRefGoogle ScholarPubMed
Chelton, D. B., Schlax, M. G. & Samelson, R. M. 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91 (2), 167216.CrossRefGoogle Scholar
Choboter, P. F. & Swaters, G. E. 2000 On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope. J. Fluid Mech. 408, 149177.CrossRefGoogle Scholar
Cushman-Roisin, B. 1994 Introduction to Geophysical Fluid Dynamics. Prentice Hall.Google Scholar
Dewar, W. K. & Killworth, P. D. 1995 On the stability of oceanic rings. J. Phys. Oceanogr. 25 (6), 14671487.2.0.CO;2>CrossRefGoogle Scholar
Dong, C., Mcwilliams, J. C., Liu, Y. & Chen, D. 2014 Global heat and salt transports by eddy movement. Nat. Commun. 5, 3294.CrossRefGoogle ScholarPubMed
Eady, E. T. 1949 Long waves and cyclone waves. Tellus A 1 (3), 3352.Google Scholar
Farrell, B. F. & Ioannou, P. J. 1996 Generalized stability theory. Part I: autonomous operators. J. Atmos. Sci. 53 (14), 20252040.2.0.CO;2>CrossRefGoogle Scholar
Isachsen, P. E. 2011 Baroclinic instability and eddy tracer transport across sloping bottom topography: How well does a modified Eady model do in primitive equation simulations? Ocean Model. 39 (1), 183199.CrossRefGoogle Scholar
James, I. N. 1987 Suppression of baroclinic instability in horizontally sheared flows. J. Atmos. Sci. 44 (24), 37103720.2.0.CO;2>CrossRefGoogle Scholar
James, I. N. & Gray, L. J. 1986 Concerning the effect of surface drag on the circulation of a baroclinic planetary atmosphere. Q. J. R. Meteorol. Soc. 112 (474), 12311250.CrossRefGoogle Scholar
Lavender, K. L, Davis, R. E. & Owens, W. B. 2000 Mid-depth recirculation observed in the interior Labrador and Irminger seas by direct velocity measurements. Nature 407 (6800), 6669.CrossRefGoogle ScholarPubMed
Lavender, K. L., Owens, W. B. & Davis, R. E. 2005 The mid-depth circulation of the subpolar North Atlantic ocean as measured by subsurface floats. Deep-Sea Res. I 52 (5), 767785.CrossRefGoogle Scholar
Mcdowell, S. E. & Rossby, H. T. 1978 Mediterranean water: an intense mesoscale eddy off the Bahamas. Science 202 (4372), 10851087.CrossRefGoogle Scholar
McWilliams, J. C. 1977 A note on a consistent quasigeostrophic model in a multiply connected domain. Dyn. Atmos. Oceans 1 (5), 427441.CrossRefGoogle Scholar
Mcwilliams, J. C. 1985 Submesoscale, coherent vortices in the ocean. Rev. Geophys. 23 (2), 165182.CrossRefGoogle Scholar
Mcwilliams, J. C. 2008 The nature and consequences of oceanic eddies. In Ocean Modeling in an Eddying Regime (ed. Hecht, M. W. & Hasumi, H.), chap. 1, Wiley.Google Scholar
Mechoso, C. R. 1980 Baroclinic instability of flows along sloping boundaries. J. Atmos. Sci. 37 (6), 13931399.2.0.CO;2>CrossRefGoogle Scholar
Molemaker, M. J., Mcwilliams, J. C. & Dewar, W. K. 2015 Submesoscale instability and generation of mesoscale anticyclones near a separation of the California undercurrent. J. Phys. Oceanogr. 45 (3), 613629.CrossRefGoogle Scholar
Moler, C. B. & Stewart, G. W. 1973 An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10 (2), 241256.CrossRefGoogle Scholar
Mysak, L. A. & Schott, F. 1977 Evidence for baroclinic instability of the Norwegian current. J. Geophys. Res. 82 (15), 20872095.CrossRefGoogle Scholar
Olson, D. B 1991 Rings in the ocean. Annu. Rev. Earth Planet. Sci. 19, 283311.CrossRefGoogle Scholar
Paldor, N. & Nof, D. 1990 Linear instability of an anticyclonic vortex in a two-layer ocean. J. Geophys. Res. 95 (C10), 1807518079.CrossRefGoogle Scholar
Pedlosky, J. 1964 The stability of currents in the atmosphere and the ocean: Part I. J. Atmos. Sci. 21 (2), 201219.2.0.CO;2>CrossRefGoogle Scholar
Pedlosky, J.1970 Flow in rotating stratified systems. Notes on the 1970 Summer Study Program in GFD at WHOI, pp. 1–68; https://darchive.mblwhoilibrary.org/handle/1912/3000.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer.CrossRefGoogle Scholar
Phillips, N. A. 1951 A simple three-dimensional model for the study of large-scale extratropical flow patterns. J. Meteorol. 8 (6), 381394.2.0.CO;2>CrossRefGoogle Scholar
Pichevin, T. 1998 Baroclinic instability in a three layer flow: a wave approach. Dyn. Atmos. Oceans 28 (3), 179204.CrossRefGoogle Scholar
Poulin, F. J., Stegner, A., Hernández-Arencibia, M., Marrero-Díaz, A. & Sangrà, P. 2014 Steep shelf stabilization of the coastal Bransfield current: linear stability analysis. J. Phys. Oceanogr. 44 (2), 714732.CrossRefGoogle Scholar
Rayleigh, L. 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 5770.Google Scholar
Sherwin, T. J., Williams, M. O., Turrell, W. R., Hughes, S. L. & Miller, P. I. 2006 A description and analysis of mesoscale variability in the Färoe-Shetland channel. J. Geophys. Res. 111 (C3), C03003.Google Scholar
Smith, P. C. 1976 Baroclinic instability in the Denmark Strait overflow. J. Phys. Oceanogr. 6 (3), 355371.2.0.CO;2>CrossRefGoogle Scholar
Spall, M. A. 2010 Non-local topographic influences on deep convection: an idealized model for the Nordic Seas. Ocean Model. 32 (1), 7285.CrossRefGoogle Scholar
Stegmann, P. M. & Schwing, F. 2007 Demographics of mesoscale eddies in the California current. Geophys. Res. Lett. 34 (14), L14602.CrossRefGoogle Scholar
Stern, A., Nadeau, L. & Holland, D. 2015 Instability and mixing of zonal jets along an idealized continental shelf break. J. Phys. Oceanogr. 45 (9), 23152338.CrossRefGoogle Scholar
Stewart, A. L., Dellar, P. J. & Johnson, E. R. 2011 Numerical simulation of wave propagation along a discontinuity in depth in a rotating annulus. Comput. Fluids 46, 442447.CrossRefGoogle Scholar
Stewart, A. L., Dellar, P. J. & Johnson, E. R. 2014 Large-amplitude coastal shelf waves. In Modeling Atmospheric and Oceanic Flows (ed. von Larcher, T. & Williams, P. D.), pp. 229253. Wiley.CrossRefGoogle Scholar
Stipa, T. 2004a Baroclinic adjustment in the Finnish coastal current. Tellus A 56 (1), 7987.CrossRefGoogle Scholar
Stipa, T.2004b On the sensitivity of coastal quasigeostrophic edge wave interaction to bottom boundary characteristics: possible implications for eddy parameterizations. Preprint, arXiv:physics/0401119.Google Scholar
Stommel, H. & Arons, A. B. 1972 On the abyssal circulation of the world ocean. V: the influence of bottom slope on the broadening of inertial boundary currents. Deep Sea Res. 19 (10), 707718.Google Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578584.CrossRefGoogle ScholarPubMed
Williams, P. D., Read, P. L. & Haine, T. W. N. 2010 Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime. J. Fluid Mech. 649, 187203.CrossRefGoogle Scholar
Xu, X., Rhines, P. B., Chassignet, E. P. & Schmitz, W. J. Jr 2015 Spreading of Denmark strait overflow water in the western subpolar North Atlantic: insights from eddy-resolving simulations with a passive tracer. J. Phys. Oceanogr. 45 (2015), 29132932.CrossRefGoogle Scholar