Momentum Balance in Zonal Flows and Resonance of Baroclinic Rossby Waves

Christoph Völker Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven, Germany

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Abstract

Wind-driven flow in a baroclinic quasigeostrophic channel with simple bottom topography is studied in a model with reduced physics and degrees of freedom as an analogy to the Antarctic Circumpolar Current. For a sinusoidal topography an approximate analytical solution is found using a low-order spectral model. Resonance of baroclinic Rossby waves can lead to different flow regimes of which one is a blocked state, where most of the momentum, imparted to the fluid by the wind stress, is transferred to the earth by bottom form stress. For some parameter values there are both resonant and nonresonant solutions to the model equations. It is shown that these results of the low-order model apply also to a more complicated spectral model with sinusoidal but also with Gaussian ridge topography. The steady states of these models are found numerically using a continuation algorithm. In the case of the ridge topography, the resonant and nonresonant steady states coexist over a wide range of topography heights.

Current affiliation: Institut für Meereskunde an der Universität Kiel, Kiel, Germany.

Corresponding author address: Dr. Christoph Völker, Institut für Meereskunde an der Universität Kiel, Dusternbrooker Weg 20, 24105 Kiel, Germany.

Abstract

Wind-driven flow in a baroclinic quasigeostrophic channel with simple bottom topography is studied in a model with reduced physics and degrees of freedom as an analogy to the Antarctic Circumpolar Current. For a sinusoidal topography an approximate analytical solution is found using a low-order spectral model. Resonance of baroclinic Rossby waves can lead to different flow regimes of which one is a blocked state, where most of the momentum, imparted to the fluid by the wind stress, is transferred to the earth by bottom form stress. For some parameter values there are both resonant and nonresonant solutions to the model equations. It is shown that these results of the low-order model apply also to a more complicated spectral model with sinusoidal but also with Gaussian ridge topography. The steady states of these models are found numerically using a continuation algorithm. In the case of the ridge topography, the resonant and nonresonant steady states coexist over a wide range of topography heights.

Current affiliation: Institut für Meereskunde an der Universität Kiel, Kiel, Germany.

Corresponding author address: Dr. Christoph Völker, Institut für Meereskunde an der Universität Kiel, Dusternbrooker Weg 20, 24105 Kiel, Germany.

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  • Charney, J. G., and J. G. DeVore, 1979: Multiple flow equilibra in the atmosphere and blocking. J. Atmos. Sci.,36, 1205–1216.

  • ——, and D. M. Straus, 1980: Form drag instability, multiple equilibra, and propagating planetary waves in baroclinic, orographically forced, planetary wave systems. J. Atmos. Sci.,37, 1157–1176.

  • Davey, M. K., 1980: A quasi-linear theory for rotating flow over topography. Part I: Steady β-plane channel. J. Fluid Mech.,99, 267–292.

  • Doedel, E. J., and X. J. Wang, 1995: AUTO94: Software for continuation and bifurcation problems in ordinary differential equations. Tech. Rep. CRPC-95-2, Center for Research on Parallel Computing, California Institute of Technology. [Available from California Institute of Technology, 12000 East California Boulevard, Pasadena, CA 91125.].

  • Egger, J., 1978: Dynamics of blocking highs. J. Atmos. Sci.,35, 1788–1801.

  • Gille, S. T., and K. A. Kelly, 1996: Scales of spatial and temporal variability in the Southern Ocean. J. Geophys. Res.,101(C), 8759–8773.

  • Hughes, C. W., 1996: The Antarctic Circumpolar Current as a waveguide for Rossby waves. J. Phys. Oceanogr.,26, 1375–1387.

  • Krupitsky, A., and M. A. Cane, 1994: On topographic pressure drag in a zonal channel. J. Mar. Res.,52, 1–23.

  • ——, V. M. Kamenkovich, N. Naik, and M. A. Cane, 1996: A linear equivalent barotropic model of the Antarctic Circumpolar Current with realistic coastlines and bottom topography. J. Phys. Oceanogr.,26, 1803–1824.

  • Marshall, J., 1981: On the parameterization of geostrophic eddies in the ocean. J. Phys. Oceanogr.,11, 257–271.

  • ——, D. Olbers, H. Ross, and D. Wolf-Gladrow, 1993: Potential vorticity constraints on the dynamics and hydrography of the Southern Ocean. J. Phys. Oceanogr.,23, 465–487.

  • McWilliams, J. C., 1977: A note on a consistent quasigeostrophic model in a multiply connected domain. Dyn. Atmos. Oceans,1, 427–441.

  • ——, W. R. Holland, and J. H. S. Chow, 1978: A description of numerical Antarctic Circumpolar Currents. Dyn. Atmos. Oceans,2, 213–291.

  • Munk, W. H., and E. Palmén, 1951: Note on the dynamics of the Antarctic Circumpolar Current. Tellus,3, 53–55.

  • Olbers, D., 1998: Comments on “On the obscurantist physics of ‘form drag’ in theorizing about the Circumpolar Current.” J. Phys. Oceanogr.,28, 1647–1654.

  • ——, and C. Völker, 1996: Steady states and variability in oceanic zonal flows. Decadal Climate Variability, D. L. T. Anderson and J. Willebrand, Eds., NATO ASI series I 44, Springer Verlag, 407–443.

  • Parker, T. S., and L. O. Chua, 1989: Practical Numerical Algorithms for Chaotic Systems. Springer Verlag, 348 pp.

  • Pedlosky J., 1981: Resonant topographic waves in barotropic and baroclinic flows. J. Atmos. Sci.,38, 2626–2641.

  • Stevens, D. P., and V. O. Ivchenko, 1997: The zonal momentum balance in an eddy resolving general circulation model of the Southern Ocean. Quart. J. Roy. Meteor. Soc.,123, 929–951.

  • Treguier, A. M., and J. C. McWilliams, 1990: Topographic influences on wind-driven, stratified flow in β-plane channel: An idealized model for the Antarctic Circumpolar Current. J. Phys. Oceanogr.,20, 321–343.

  • Tung, K. K., and A. J. Rosenthal, 1985: Theories of multiple equilibria—A critical reexamination. Part I: Barotropic models. J. Atmos. Sci.,42, 2804–2819.

  • Völker, C., 1996: Barokline Strömung über periodischer Topographie:Untersuchungen an analytischen und numerischen Modellen. Ph.D. thesis, Universität Bremen, 65 pp.

  • Wang, L., and R. X. Huang, 1995: A linear homogeneous model of wind-driven circulation in a β-plane channel. J. Phys. Oceanogr.,25, 587–603.

  • Wolff, J.-O., and D. Olbers, 1989: The dynamical balance of the Antarctic Circumpolar Current studied with an eddy resolving quasigeostrophic model. Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier Science, 435–458.

  • ——, E. Maier-Reimer, and D. Olbers, 1991: Wind driven flow over topography in a zonal β plane channel: A quasi-geostrophic model of the Antarctic Circumpolar Current. J. Phys. Oceanogr.,21, 236–264.

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