• Arakawa, A., 1969: Parameterization of cumulus convection. Proc. WMO/IUGG Symp. Numerical Weather Prediction, Tokyo, Japan, Volume IV, Japan Meteorological Agency, 8, 1–6.

    • Search Google Scholar
    • Export Citation
  • ——, and Schubert, W. H., 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci., 31 , 674701.

    • Search Google Scholar
    • Export Citation
  • Baines, P. G., 1995: Topographic Effects in Stratified Flows. Cambridge University Press, 482 pp.

  • ——, and Hoinka, K. P., 1985: Stratified flow over two-dimensional topography in fluid of infinite depth: A laboratory simulation. J. Atmos. Sci., 42 , 16141630.

    • Search Google Scholar
    • Export Citation
  • Bell, R. C., and R. O. Thompson, 1980: Valley ventilation by cross winds. J. Fluid Mech., 96 , 757767.

  • Bretherton, F., 1969: Momentum transport by gravity waves. Quart. J. Roy. Meteor. Soc., 95 , 213243.

  • Clark, T. L., and R. D. Farley, 1984: Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: A possible mechanism for gustiness. J. Atmos. Sci., 41 , 329350.

    • Search Google Scholar
    • Export Citation
  • ——, and Miller, M. J., 1991: Pressure drag and momentum fluxes due to the Alps. II: Representation in large-scale atmospheric models. Quart. J. Roy. Meteor. Soc., 117 , 527552.

    • Search Google Scholar
    • Export Citation
  • Eisenstat, S. C., H. C. Elman, and M. H. Schultz, 1983: Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal., 20 , 345357.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., and E. Palm, 1961: On the transfer of energy in stationary mountain waves. Geofys. Publ., 22 , 123.

  • Epifanio, C. C., and D. R. Durran, 2001: Three-dimensional effects in high-drag-state flows over long ridges. J. Atmos. Sci., 58 , 10511065.

    • Search Google Scholar
    • Export Citation
  • Falcone, M., and R. Ferretti, 1998: Convergence analysis for a class of high-order semi-Lagrangian advection schemes. SIAM J. Numer. Anal., 35 , 909940.

    • Search Google Scholar
    • Export Citation
  • Gal-Chen, T., and R. Somerville, 1975: On the use of a coordinate transformation for the solutions of the Navier-Stokes equations. J. Comput. Phys., 17 , 209228.

    • Search Google Scholar
    • Export Citation
  • Garner, S. T., 1995: Permanent and transient upstream effects in nonlinear stratified flow over a ridge. J. Atmos. Sci., 52 , 227246.

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

  • Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75 , 18251830.

    • Search Google Scholar
    • Export Citation
  • Kim, Y-J., and A. Arakawa, 1995: Improvement of orographic gravity wave parameterization using a mesoscale gravity wave model. J. Atmos. Sci., 52 , 18751902.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and P. Manins, 1988: Blocking in periodic valleys. Bound.-Layer Meteor., 44 , 137169.

  • Klinker, E., and P. D. Sardeshmukh, 1992: The diagnosis of mechanical dissipation in the atmosphere from large-scale balance requirements. J. Atmos. Sci., 49 , 608627.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86 , 97079714.

  • Lott, F., and M. J. Miller, 1997: A new subgrid-scale orographic drag parameterization: Its formulation and testing. Quart. J. Roy. Meteor. Soc., 123 , 101127.

    • Search Google Scholar
    • Export Citation
  • McFarlane, N., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44 , 17751800.

    • Search Google Scholar
    • Export Citation
  • Miller, M., T. Palmer, and R. Swinbank, 1989: Parametrization and influence of subgrid-scale orography in general circulation and numerical weather prediction models. Meteor. Atmos. Phys., 40 , 84109.

    • Search Google Scholar
    • Export Citation
  • Miranda, P., and I. James, 1992: Non-linear three-dimensional effects on gravity-wave drag: Splitting flow and breaking waves. Quart. J. Roy. Meteor. Soc., 118 , 10571081.

    • Search Google Scholar
    • Export Citation
  • Palmer, T., G. Shutts, and R. Swinbank, 1986: Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parameterization. Quart. J. Roy. Meteor. Soc., 112 , 10011039.

    • Search Google Scholar
    • Export Citation
  • Peltier, W., and T. Clark, 1979: The evolution and stability of finite-amplitude mountain waves. Part II: Surface wave drag and severe downslope windstorms. J. Atmos. Sci., 36 , 14981529.

    • Search Google Scholar
    • Export Citation
  • Pierrehumbert, R., 1986: An essay on the parameterization of orographic gravity wave drag. Proc. Seminar/Workshop on Observation, Theory and Modeling of Orographic Effects, Vol. 1, Shinfield Park, Reading, United Kingdom, ECMWF, 251–282.

    • Search Google Scholar
    • Export Citation
  • ——, and Wyman, B., 1985: Upstream effects of mesoscale mountains. J. Atmos. Sci., 42 , 9771003.

  • Queney, P., 1948: The problem of airflow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc., 29 , 1626.

  • Sawyer, J., 1959: The introduction of the effects of topography into methods of numerical forecasting. Quart. J. Roy. Meteor. Soc., 85 , 3143.

    • Search Google Scholar
    • Export Citation
  • Schumann, U., 1991: Subgrid length-scales for large-eddy simulation of stratified turbulence. Theor. Comput. Fluid Dyn., 2 , 279290.

  • Scinocca, J., and N. McFarlane, 1999: Anisotropy in the parameterization of drag due to freely propagating gravity waves and low-level dynamics. Preprints, 12th Conf. on Atmospheric and Oceanic Fluid Dynamics, New York, NY, Amer. Meteor. Soc., 123–126.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., P. K. Smolarkiewicz, and J. B. Klemp, 1997: Preconditioned conjugate-residual solvers for Helmholtz equations in nonhydrostatic models. Mon. Wea. Rev., 125 , 587599.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1977: The steepening of hydrostatic mountain waves. J. Atmos. Sci., 34 , 16341654.

  • ——,. 1979: The influence of mountains on the atmosphere. Advances in Geophysics, Vol. 21, Academic Press, 87–230.

  • ——,. 1985: On severe downslope winds. J. Atmos. Sci., 42 , 25972603.

  • ——,. 1990: Why can't stably stratified air rise over high around? Atmospheric Processes over Complex Terrain, Meteor. Monogr., No. 45, Amer. Meteor. Soc., 105—107.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., 1991: On forward-in-time differencing for fluids. Mon. Wea. Rev., 119 , 25052510.

  • ——, and Margolin, L. G., 1993: On forward-in-time differencing for fluids: Extension to a curvilinear framework. Mon. Wea. Rev., 121 , 18471859.

    • Search Google Scholar
    • Export Citation
  • ——, and ——,. 1994: Variational solver for elliptic problems in atmospheric flows. Appl. Math. Comput. Sci., 4 , 527551.

  • ——, and ——,. 1997: On forward-in-time differencing for fluids: An Eulerian/semi-Lagrangian non-hydrostatic model for stratified flows. Atmos.–Ocean, XXXV , 127152.

    • Search Google Scholar
    • Export Citation
  • ——, Grubisic, V., and L. G. Margolin, 1997: On foreward-in-time differencing for fluids: Stopping criteria for iterative solutions of anelastic pressure equations. Mon. Wea. Rev., 125 , 647654.

    • Search Google Scholar
    • Export Citation
  • Snyder, W. H., R. S. Thompson, R. E. Eskridge, R. E. Lawson, I. P. Castro, J. Lee, J. C. Hunt, and Y. Ogawa, 1985: The structure of strongly stratified flow over hills: Dividing-Streamline concept. J. Fluid Mech., 152 , 249288.

    • Search Google Scholar
    • Export Citation
  • Trüb, J., and H. Davies, 1995: Flow over a mesoscale ridge: Pathways to regime transition. Tellus, 47A , 502524.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 174 35 4
PDF Downloads 69 20 1

The Large-Scale Effects of Flow over Periodic Mesoscale Topography

Wendell T. WelchDepartment of Geology and Geophysics, Yale University, New Haven, Connecticut

Search for other papers by Wendell T. Welch in
Current site
Google Scholar
PubMed
Close
,
Piotr SmolarkiewiczNational Center for Atmospheric Research,+ Boulder, Colorado

Search for other papers by Piotr Smolarkiewicz in
Current site
Google Scholar
PubMed
Close
,
Richard RotunnoNational Center for Atmospheric Research,+ Boulder, Colorado

Search for other papers by Richard Rotunno in
Current site
Google Scholar
PubMed
Close
, and
Byron A. BovilleNational Center for Atmospheric Research,+ Boulder, Colorado

Search for other papers by Byron A. Boville in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Airflow over two-dimensional sinusoidal mesoscale topography is studied using simulations from a numerical model, with an eye toward quantification of the net effect on the large-scale flow. Analytic formulas are derived for the amount of form drag, that is, the total slowdown of the flow, as a function of mountain height, and predictions from such formulas are shown to agree well with model results. The vertical distribution of drag, due to gravity wave breaking at various altitudes, is briefly discussed.

The flow is divided into two regimes: a “linear” regime for small mountain heights, and a “blocked” regime for taller mountains. The latter is always accompanied by a layer of stagnant fluid in the valleys. Separate analytic arguments are used in each regime, and together they provide a prediction of form drag over a wide range of parameter space. The cutoff mountain height between the two regimes is also argued analytically.

A key difference from flow over isolated mountains is explained. This suggests that studies of flow over both isolated and periodic topography are needed in the development of orographic parameterizations for large-scale models.

Current affiliation: Colorado Research Associates Division, Northwest Research Associates, Inc., Boulder, Colorado.

Corresponding author address: Dr. Wendell Welch Orlando, Colorado Research Associates Division, Northwest Research Associates, Inc., 3380 Mitchell Lane, Boulder, CO 80301. Email: orlando@co-ra.com

Abstract

Airflow over two-dimensional sinusoidal mesoscale topography is studied using simulations from a numerical model, with an eye toward quantification of the net effect on the large-scale flow. Analytic formulas are derived for the amount of form drag, that is, the total slowdown of the flow, as a function of mountain height, and predictions from such formulas are shown to agree well with model results. The vertical distribution of drag, due to gravity wave breaking at various altitudes, is briefly discussed.

The flow is divided into two regimes: a “linear” regime for small mountain heights, and a “blocked” regime for taller mountains. The latter is always accompanied by a layer of stagnant fluid in the valleys. Separate analytic arguments are used in each regime, and together they provide a prediction of form drag over a wide range of parameter space. The cutoff mountain height between the two regimes is also argued analytically.

A key difference from flow over isolated mountains is explained. This suggests that studies of flow over both isolated and periodic topography are needed in the development of orographic parameterizations for large-scale models.

Current affiliation: Colorado Research Associates Division, Northwest Research Associates, Inc., Boulder, Colorado.

Corresponding author address: Dr. Wendell Welch Orlando, Colorado Research Associates Division, Northwest Research Associates, Inc., 3380 Mitchell Lane, Boulder, CO 80301. Email: orlando@co-ra.com

Save