• Argaín, J. L., 2003: Numerical modelling of atmospheric flow: Orographic and boundary layer effects. Ph.D. thesis, University of Algarve, 249 pp.

  • Booker, J. R., , and F. P. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid Mech., 27 , 513539.

    • Search Google Scholar
    • Export Citation
  • Clark, T. L., , and W. R. Peltier, 1984: Critical level reflection and the resonant growth of nonlinear mountain waves. J. Atmos. Sci., 41 , 31223134.

    • Search Google Scholar
    • Export Citation
  • Grubišić, V., , and P. K. Smolarkiewicz, 1997: The effect of critical levels on 3D orographic flows: Linear regime. J. Atmos. Sci., 54 , 19431960.

    • Search Google Scholar
    • Export Citation
  • Keller, T. L., 1994: Implications of the hydrostatic assumption on atmospheric gravity waves. J. Atmos. Sci., 51 , 19151929.

  • Klemp, J. B., , and D. R. Lilly, 1975: The dynamics of wave-induced downslope winds. J. Atmos. Sci., 32 , 320339.

  • Lindzen, R. S., , and K-K. Tung, 1976: Banded convective activity and ducted gravity waves. Mon. Wea. Rev., 104 , 16021617.

  • Miles, J. W., , and H. E. Huppert, 1969: Lee waves in a stratified flow. Part 4. Perturbation approximation. J. Fluid Mech., 35 , 497525.

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

    • Search Google Scholar
    • Export Citation
  • Miranda, P. M. A., , and M. A. Valente, 1997: Critical level resonance in three-dimensional flow past isolated mountains. J. Atmos. Sci., 54 , 15741588.

    • Search Google Scholar
    • Export Citation
  • Öllers, M. C., , L. P. J. Kamp, , F. Lott, , P. F. J. van Velthoven, , H. M. Kelder, , and F. W. Sluijter, 2003: Propagation properties of inertia-gravity waves through a barotropic shear layer and application to the Antarctic polar vortex. Quart. J. Roy. Meteor. Soc., 129 , 24952511.

    • Search Google Scholar
    • Export Citation
  • Phillips, D. S., 1984: Analytical surface pressure and drag for linear hydrostatic flow over three-dimensional elliptical mountains. J. Atmos. Sci., 41 , 10731084.

    • Search Google Scholar
    • Export Citation
  • Sharman, R. D., , and M. G. Wurtele, 2004: Three-dimensional structure of forced gravity waves and lee waves. J. Atmos. Sci., 61 , 664681.

    • Search Google Scholar
    • Export Citation
  • Shen, B-W., , and Y-L. Lin, 1999: Effects of critical levels on two-dimensional back-sheared flow over an isolated mountain ridge on an ƒ plane. J. Atmos. Sci., 56 , 32863302.

    • Search Google Scholar
    • Export Citation
  • Shutts, G., 1995: Gravity-wave drag parameterization over complex terrain: The effect of critical-level absorption in directional wind-shear. Quart. J. Roy. Meteor. Soc., 121 , 10051021.

    • Search Google Scholar
    • Export Citation
  • Shutts, G., 2001: A linear model of back-sheared flow over an isolated hill in the presence of rotation. J. Atmos. Sci., 58 , 32933311.

    • Search Google Scholar
    • Export Citation
  • Shutts, G. J., , and A. Gadian, 1999: Numerical simulations of orographic gravity waves in flows which back with height. Quart. J. Roy. Meteor. Soc., 125 , 27432765.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1984: A theory of lee cyclogenesis. J. Atmos. Sci., 41 , 11591168.

  • Smith, R. B., 1986: Further development of a theory of lee cyclogenesis. J. Atmos. Sci., 43 , 15821602.

  • Teixeira, M. A. C., , and P. M. A. Miranda, 2004: The effect of wind shear and curvature on the gravity wave drag produced by a ridge. J. Atmos. Sci., 61 , 26382643.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., , and P. M. A. Miranda, 2005: Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge. Quart. J. Roy. Meteor. Soc., 131 , 18151820.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., , and P. M. A. Miranda, 2006: A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains. Quart. J. Roy. Meteor. Soc., 132 , 24392458.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., , P. M. A. Miranda, , and M. A. Valente, 2004: An analytical model of mountain wave drag for wind profiles with shear and curvature. J. Atmos. Sci., 61 , 10401054.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., , P. M. A. Miranda, , J. L. Argaín, , and M. A. Valente, 2005: Resonant gravity-wave drag enhancement in linear stratified flow over mountains. Quart. J. Roy. Meteor. Soc., 131 , 17951814.

    • Search Google Scholar
    • Export Citation
  • Wang, T-A., , and Y-L. Lin, 1999: Wave ducting in a stratified shear flow over two-dimensional mountain. Part I: General linear criteria. J. Atmos. Sci., 56 , 412436.

    • Search Google Scholar
    • Export Citation
  • Wurtele, M. G., , A. Datta, , and R. D. Sharman, 2000: The propagation of a gravity–inertia wave in a positively sheared flow. J. Atmos. Sci., 57 , 37033715.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 7 7 3
PDF Downloads 2 2 1

Mountain Waves in Two-Layer Sheared Flows: Critical-Level Effects, Wave Reflection, and Drag Enhancement

View More View Less
  • 1 CGUL, IDL, University of Lisbon, Lisbon, Portugal
  • 2 Department of Physics, University of Algarve, Faro, Portugal
© Get Permissions
Restricted access

Abstract

Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too different from that predicted for an unbounded shear layer, while if it is small the differences are marked, with the drag being enhanced by a considerable factor at low Richardson numbers (Ri). The drag may be further enhanced by nonlinear processes, but its qualitative variation for relatively low Ri is essentially unchanged. However, nonlinear processes seem to interact constructively with shear, so that the drag for a noninfinite but relatively high Ri is considerably larger than the drag without any shear at all.

Corresponding author address: Miguel A. C. Teixeira, Centro de Geofisica da Universidade de Lisboa, Edificio C8, Campo Grande, 1749-016 Lisbon, Portugal. Email: mateixeira@fc.ul.pt

Abstract

Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too different from that predicted for an unbounded shear layer, while if it is small the differences are marked, with the drag being enhanced by a considerable factor at low Richardson numbers (Ri). The drag may be further enhanced by nonlinear processes, but its qualitative variation for relatively low Ri is essentially unchanged. However, nonlinear processes seem to interact constructively with shear, so that the drag for a noninfinite but relatively high Ri is considerably larger than the drag without any shear at all.

Corresponding author address: Miguel A. C. Teixeira, Centro de Geofisica da Universidade de Lisboa, Edificio C8, Campo Grande, 1749-016 Lisbon, Portugal. Email: mateixeira@fc.ul.pt

Save