Meteorology and Atmospheric Physics

, Volume 45, Issue 1–2, pp 65–74 | Cite as

The effect of moist layer location on the stability of trapped gravity waves in an almost saturated atmosphere

  • C. P. Jacovides
  • D. P. Lalas


The stability characteristics of trapped gravity waves, generated by an isothermal bounded tanh (z) velocity profile in the presence of a saturated finite layer, are studied. The saturated layer is introduced at different levels above the inlection point and the variations of moisture content, layer thickness and distance from the origin are examined. The growthyrates and phase speeds of the unstable modes are obtained by solving numerically the equations of motion in the linear, inviscid, Boussinesq limit, via the technique of Lalas and Einaudi (1976).

It is shown that the presence of the saturated layer can significantly affect the stability characteristics of the waves. inereases in moisture, layer thickness and distance of the layer from the inflection point are found to amplify the wave response because the saturated layer behaves as a top boundtry to the shear flow. The presence of such effective boundaries is found to stabilize short wavelengths and destabilize longer wavelengths. Finally, an application of the results to a rainband case produces values of the wave parameters in good agreement with the observed ones.


Layer Thickness Velocity Profile Short Wavelength Inflection Point Shear Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Balanchadran, N. K., 1980: Gravity Waves from thunderstorms.Mon. Wea. Rev.,108, 804–816.Google Scholar
  2. Brethehon, F. P. 1966: The propagation of groups of internal gravity waves in a shear flow.Quart. J. Roy. Meteor. Soc.,92, 466–480.Google Scholar
  3. Chimonas, G., 1970: The extension of the Miles-Howard Theorem to compressible flows.J. Fluid Mech.,43, 833–836.Google Scholar
  4. Drazin, P. G., 1958: The stability of a shear layer in an unbounded heterogenous inviscid fluids.J. Fluid Mech.,4, 214–224.Google Scholar
  5. Drazin, P. G., Howard, L. N., 1966: Hydrodynamic stability of parallel flow of inviscid fluids,Adv. Mech.,9, 1–89.Google Scholar
  6. Durran, D. R., Klemp, J. B., 1982: On the effects of moisture on the Brunt-Vaisala frequency.J. Atmos. Sci.,39, 2152–2158.Google Scholar
  7. Einaudi, F., Lalas, D. P., 1973: The propagation of acoustic-gravity waves in a moist atmosphere.J. Atmos. Sci.,30, 365–376.Google Scholar
  8. Einaudi, F., Lalas, D. P., 1975: Wave induced instabilities in an atmosphere near saturation.J. Atmos. Sci.,32, 536–547.Google Scholar
  9. Einaudi, F., Lalas, D. P., 1976: The effects of boundaries on the stability of inviscid stratified shear flow.J. Appl. Mech.,98, 243–248.Google Scholar
  10. Hines, C. O., 1960: Internal gravity waves at ionospheris heights.Can. J. Phys.,38, 1441–1481.Google Scholar
  11. Hines, C. O., 1963: The upper atmosphere in motion. In: Geophys. Monog. 18, Amer. Geophys. Union. Washington D.C., 248–328.Google Scholar
  12. Howard, L. N., 1961: Note on a paper of John Miles.J. Fluid Mech.,10, 509–512.Google Scholar
  13. Jacovides, C. P., 1986: The effects of moisture on the gravity waves in an atmospheric shear layer. Ph.D. Thesis (in Greek), University of Athens, 173pp.Google Scholar
  14. Jacovides, C. P., Lalas, D. P., 1988: On the effects of moisture-saturation on trapped gravity waves generated by a tanh(y) velocity profile with a lower rigid surface. Annales Geophysicae, XIII General Assembly of EGS, Bologna, 21–55 March.Google Scholar
  15. Koch S. E., 1979: Mesoscale gravity waves as a possible trigger of severe convection along a dryline. Ph.D. Thesis, University of Oklahoma, 195pp.Google Scholar
  16. Lalas, D. P., Einaudi, 1973: On the stability of a moist atmosphere in the presence of a background wind.J. Atmos. Sci.,30, 795–800.Google Scholar
  17. Lalas, D. P., Einaudi, 1974: On the correct use of the wet adiabatic lapse rate in the stability criteria of a saturated atmosphere.J. Appl. Meteor.,13, 318–324.Google Scholar
  18. Lalas, D. P., Einaudi, 1976: On the characteristics of gravity waves generated by atmospheric shear layers.J. Atmos. Sci.,33, 1248–1259.Google Scholar
  19. Lindzen, R. S., Rosenthal, A. J., 1976: On the instability of Helmholtz velocity profiles in stably-stratified fluids when a lower boundary is present.J. Geophys. Res.,81, 1561–1571.Google Scholar
  20. Miles, J. W., 1961: On the stability of heterogenous shear flow.J. Fluid Mech.,10, 496–508.Google Scholar
  21. Narayanan, A. S., Sachdev, P. L., 1982: Instability induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows.Phys. Fluids.,25, 1317–1321.Google Scholar
  22. Parsons, D. B., Hobbs, P. V., 1983: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones, 11: Comparisons between observational and theoretical aspects of rainbands.J. Atmos. Sci.,40, 2377–2397.Google Scholar
  23. Pellacani, C., Tebaldi, C., Tosi, E., 1978: Shear instabilities in the atmosphere in the presence of a jump in the Brunt-Vaisala frequency.J. Atmos. Sci.,35, 1633–1643.Google Scholar
  24. Stobie, J. G., Einaudi, F., Uccellini, L. W., 1983: A case study of gravity waves convective storms interaction: May 9, 1979.J. Atmos. Sci.,40, 2804–2830.Google Scholar
  25. Testud, J., Breger, G., Amayenc, P., Chong, M., Nutten, B., Sauvaget, A., 1980: A Doppler radar observation of a cold front: three-dimensional air circulation, related precipitation system and associated wavelike motions.J. Atmos. Sci.,37, 78–98.Google Scholar
  26. Thorpe, S. A., 1969: Experiments on the stability of stratified shear flows.Radio Sci.,4, 1327–1331.Google Scholar
  27. Uccellini, L. W., Johnson, D. R., 1979: The coupling of upper and lower tropospheric jet streaks and implications for the development of severe convective storms.Mon. Wea. Rev.,107, 682–703.Google Scholar
  28. Wang, P. T., Parsons, D. B. Hobbs, P. V., 1983: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones, 6: Wave-like rainbands associated with a cold-frontal zone.J. Atmos. Sci.,40, 543–558.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • C. P. Jacovides
    • 1
  • D. P. Lalas
    • 1
  1. 1.Department of PhysicsUniversity of AthensGreece

Personalised recommendations