• Davies, T., 2000: Some aspects of high resolution NWP at the Met Office. Proc. ECMWF Workshop on Developments in Numerical Methods for Very High Resolution Global Models, Reading, United Kingdom, European Centre for Medium-Range Weather Forecasts, 35–46. [Available from ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom.].

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1993: Is the Coriolis force really responsible for the inertial oscillation? Bull. Amer. Meteor. Soc., 74 , 21792184.

  • Eckart, C., 1960: Hydrodynamics of Oceans and Atmospheres. Pergamon Press, 290 pp.

  • Egger, J., 1999: Inertial oscillations revisited. J. Atmos. Sci., 56 , 29512954.

  • Gill, A., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Gossard, E. E., and W. H. Hooke, 1975: Waves in the Atmosphere. Elsevier, 456 pp.

  • Hassid, S., and B. Galperin, 1994: Modeling rotation flows with neutral and unstable stratification. J. Geophys. Res., 99 , 1253312548.

    • Search Google Scholar
    • Export Citation
  • Kamenkovich, V. M., and A. V. Kulakov, 1977: Influence of rotation on waves in a stratified ocean. Oceanology, 17 , 260266.

  • Leibovich, S., and S. K. Lele, 1985: The influence of the horizontal component of earth's angular velocity on the instability of the Ekman layer. J. Fluid Mech., 150 , 4187.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., C. Hill, L. Perelman, and A. Adcroft, 1997: Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res., 102 (C3) 57335752.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Obukhov, 1959: A note on general classification of motions in a baroclinic atmosphere. Tellus, 11 , 159162.

  • Munk, W., and N. Phillips, 1968: Coherence and band structure of inertial motion in the sea. Rev. Geophys., 6 , 447472.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer, 710 pp.

  • Phillips, N. A., 1966: The equations of motion for a shallow rotating atmosphere and the “traditional approximation.”. J. Atmos. Sci., 23 , 626628.

    • Search Google Scholar
    • Export Citation
  • Phillips, N. A., 1973: Principles of large scale numerical weather prediction. Dynamic Meteorology, P. Morel, Ed., Reidel, 1–96.

  • Phillips, N. A., 1990: Dispersion processes in large-scale weather prediction. WMO 700, World Meteorological Organization, 126 pp.

  • Pollard, R. T., 1970: On the generation by winds of inertial waves in the ocean. Deep-Sea Res., 17 , 795812.

  • Thuburn, J., N. Wood, and A. Staniforth, 2002a: Normal modes of deep atmospheres. I: Spherical geometry. Quart. J. Roy. Meteor. Soc., 128 , 17711792.

    • Search Google Scholar
    • Export Citation
  • Thuburn, J., N. Wood, and A. Staniforth, 2002b: Normal modes of deep atmospheres. II: f- F-plane geometry. Quart. J. Roy. Meteor. Soc., 128 , 17931806.

    • Search Google Scholar
    • Export Citation
  • Tolstoy, I., 1973: Wave Propagation. McGraw-Hill, 466 pp.

  • Wang, D., W. G. Large, and J. C. McWilliams, 1996: Large-eddy simulation of the equatorial ocean boundary layer: Diurnal cycling, eddy viscosity, and horizontal rotation. J. Geophys. Res., 101 , 36493662.

    • Search Google Scholar
    • Export Citation
  • White, A. A., and R. A. Bromley, 1995: Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Quart. J. Roy. Meteor. Soc., 121 , 399418.

    • Search Google Scholar
    • Export Citation
  • Wippermann, F., 1969: The orientation of vortices due to instability of Ekman boundary layer. Beitr. Phys. Atmos., 42 , 225244.

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The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models

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  • 1 National Center for Atmospheric Research,* Boulder, Colorado
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Abstract

Roles of the horizontal component of the earth's rotation, which is neglected traditionally in atmospheric and oceanographic models, are studied through the normal mode analysis of a compressible and stratified model on a tangent plane in the domain that is periodic in the zonal and meridional directions but bounded at the top and bottom. As expected, there exist two distinct kinds of acoustic and buoyancy oscillations that are modified by the earth's rotation. When the cos(latitude) Coriolis terms are included, there exists another kind of wave oscillation whose frequencies are very close to the inertial frequency, 2Ω sin(latitude), where Ω is the earth's angular velocity.

The objective of this article is to clarify the circumstance in which a distinct kind of wave oscillation emerges whose frequencies are very close to the inertial frequency. Because this particular kind of normal mode appears only due to the presence of boundary conditions in the vertical, it may be appropriate to call these waves boundary-induced inertial (BII) modes as demonstrated through the normal mode analyses of a homogeneous and incompressible model and a Boussinesq model with thermal stratification. Thus, it can be understood that the BII modes can coexist with the acoustic and inertio-gravity modes when the effect of compressibility is added to the effects of buoyancy and complete Coriolis force in the compressible, stratified, and rotating model.

Corresponding author address: Dr. Akira Kasahara, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: kasahara@ucar.edu

Abstract

Roles of the horizontal component of the earth's rotation, which is neglected traditionally in atmospheric and oceanographic models, are studied through the normal mode analysis of a compressible and stratified model on a tangent plane in the domain that is periodic in the zonal and meridional directions but bounded at the top and bottom. As expected, there exist two distinct kinds of acoustic and buoyancy oscillations that are modified by the earth's rotation. When the cos(latitude) Coriolis terms are included, there exists another kind of wave oscillation whose frequencies are very close to the inertial frequency, 2Ω sin(latitude), where Ω is the earth's angular velocity.

The objective of this article is to clarify the circumstance in which a distinct kind of wave oscillation emerges whose frequencies are very close to the inertial frequency. Because this particular kind of normal mode appears only due to the presence of boundary conditions in the vertical, it may be appropriate to call these waves boundary-induced inertial (BII) modes as demonstrated through the normal mode analyses of a homogeneous and incompressible model and a Boussinesq model with thermal stratification. Thus, it can be understood that the BII modes can coexist with the acoustic and inertio-gravity modes when the effect of compressibility is added to the effects of buoyancy and complete Coriolis force in the compressible, stratified, and rotating model.

Corresponding author address: Dr. Akira Kasahara, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: kasahara@ucar.edu

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