Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-06-03T10:24:03.597Z Has data issue: false hasContentIssue false
  • English
  • Français

The effects of terrain shape on nonlinear hydrostatic mountain waves

Published online by Cambridge University Press:  19 April 2006

D. K. Lilly  and
J. B. Klemp
D. K. Lilly
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307
J. B. Klemp
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307
Get access Rights & Permissions [Opens in a new window]

Abstract

Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength. Nonlinear lower and upper (radiative) boundary conditions are utilized and found to have a strong influence on the wave structure at large amplitudes. The results for symmetric and asymmetric mountain profiles reveal that the wave amplitude and wave drag are significantly enhanced for mountains with gentle windward and steep leeward slopes. These results confirm and explain those obtained by Raymond (1972) using a different solution method. Several results obtained by Smith (1977) from perturbation analysis are also confirmed and extended to large amplitudes. The methods are also applied to investigate the nonlinear nature of the singularity predicted by linear theory for flow over a step.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 2 , 28 November 1979 , pp. 241 - 261
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alaka, M. A. 1960 The airflow over mountains. Tech. Notes Wld met. Org. no. 34.Google Scholar
Bretherton, F. P. 1969 Momentum transport by gravity waves. Q. J. Roy. Met. Soc. 95, 213.Google Scholar
Drazin, P. G. & Su, C. H. 1975 A note on long-wave theory of airflow over a mountain. J. Atmos. Sci. 32, 437.Google Scholar
Harrison, H. T. 1965 N.A.S.A. Contractor Rep. NASA CR-315.
Hodges, R. R. 1967 Generation of turbulence in the upper atmosphere by internal gravity waves. J. Geophys. Res. 72, 3455.Google Scholar
Huppert, H. E. & Miles, J. W. 1969 Lee waves in a stratified flow. 3. Semi-elliptical obstacle. J. Fluid Mech. 35, 481.Google Scholar
Klemp, J. B. & Lilly, D. K. 1975 The dynamics of wave-induced down-slope winds. J. Atmos. Sci. 32, 320.Google Scholar
Klemp, J. B. & Lilly, D. K. 1978 Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78.Google Scholar
Lester, P. F. 1976 Evidence of long lee waves in southern Alberta. Atmosphere 14, 28.Google Scholar
Lilly, D. K. 1972 Wave momentum flux — a GARP problem. Bull. Amer. Meteor. Soc. 53, 17.Google Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation. Tellus 5, 42.Google Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradient. Tellus 7, 341.Google Scholar
Mcintyre, M. E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. 52, 209.Google Scholar
Miles, J. W. 1968 Lee waves in a stratified flow. 1. Thin barrier. J. Fluid Mech. 32, 549.Google Scholar
Miles, J. W. 1969 The lee-wave regime for a slender body in a rotating flow. J. Fluid Mech. 36, 265.Google Scholar
Miles, J. W. & Huppert, H. E. 1968 Lee waves in a stratified flow. 2. Semi-circular obstacle. J. Fluid Mech. 33, 804.Google Scholar
Miles, J. W. & Huppert, H. E. 1969 Lee waves in a stratified flow. 4. Perturbation approximations. J. Fluid Mech. 35, 497.Google Scholar
Raymond, D. 1972 Calculations of airflow over an arbitrary ridge including diabatic heating and cooling. J. Atmos. Sci. 29, 837.Google Scholar
Smith, R. B. 1977 The steepening of hydrostatic mountain waves. J. Atmos. Sci. 34, 1634.Google Scholar
Smith, R. B. 1979 Some aspects of the quasi-geostrophic flow over mountains. To appear in J. Atmos. Sci.Google Scholar
Titchmarsh, E. C. 1937 Introduction of the Theory of Fourier Integrals. Oxford University Press.