Abstract
Often, a combination of waves and turbulence is present in the stably stratified atmospheric boundary layer. The presence of waves manifest itself in the vertical profiles of variances of fluctuations and in low-frequency contributions to the power spectra. In this paper we study internal waves by means of a linear stability analysis of the mean profiles in a stably stratified boundary layer and compare the results with observed vertical variance profiles of fluctuating wind and temperature along a 200 m mast. The linear stability analysis shows that the observed mean flow is unstable for disturbances in a certain frequency and wavenumber domain. These disturbances are expected to the detectable in the measurements. It is shown that indeed the calculated unstable frequencies are present in the observed spectra. Furthermore, the shape of the measured vertical variance profiles, which increase with height, is explained well by the calculated vertical structure of the amplitude of unstable Kelvin-Helmholtz waves, confirming the contribution of waves to the variances. Because turbulence and waves have quite distinct transport properties, estimates of diffusion from measurements of variances would strongly overestimate this diffusion. Therefore it is important to distinguish between them.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bendat, J. S. and Piersol, A. G.: 1966, Measurements and Analysis of Random Data, Wiley and Sons, New York.
Betchov, R. and Criminate, W. O.: 1967, ‘Stability of Parallel Flows’, Applied Math. and Mech. Ser. 10, Acad. Press.
Busch, N. E.: 1969, ‘Waves and Turbulence’, Radio Science 4, 1377–1379.
Caughey, S. J.: 1977, ‘Boundary-Layer Turbulence Spectra in Stable Conditions’, Boundary-Layer Meteorol. 11, 3–14.
Caughey, S. J. and Readings, C. J.: 1975, ‘An Observation of Waves and Turbulence in the Earth's Boundary Layer’, Boundary-Layer Meteorol. 9, 279–296.
Caughey, S. J., Wyngaard, J. C., and Kaimal, J. C.: 1979, ‘Turbulence in the Evolving Stable Boundary Layer’, J. Atmos. Sci. 6, 1041–1052.
Davis, P. A. and Peltier, W. R.: 1976, ‘Resonant Parallel Shear Instability in the Stably Stratified Planetary Boundary Layer’, J. Atmos. Sci. 33, 1287–1300.
Drazin, P. G.: 1958, ‘The Stability of a Shear Layer in an Unbounded Heterogeneous Inviscid Fluid’, J. Fluid Mech. 4, 214–224.
Fritts, D. C.: 1980, ‘Simple Stability Limits for Vertically Propagating Unstable Modes in a tanh(z) Velocity Profile with a Rigid Lower Boundary’, J. Atmos. Sci. 37, 1642–1648.
Fua, D., Chimonas, G., Einaudi, F., and Zeman, O.: 1982, ‘An Analysis of Wave-Turbulence Interaction’, J. Atmos. Sci. 39, 2450–2463.
Gossard, E. E. and Hooke, W. H.: 1975, Waves in the Atmosphere; Atm. Infrasound and Gravity Waves Their Generation and Propagation, Devel. in Atm. Sci. 2, Amsterdam.
Lalas, D. P. and Einaudi, F.: 1976, ‘On the Characteristics of Gravity Waves Generated by Atm. Shear Layers’, J. Atmos. Sci. 13, 1248–1259.
Lambert, J. D.: 1973, Computational Methods in Ordinary Differential Equations, Wiley and Sons, New York.
Miles, J. W. and Howard, L. N.: 1964, ‘Note on a Heterogeneous Shear Flow’, J. Fluid Mech. 20, 331–336.
Stewart, R. W.: 1969, ‘Turbulence and Waves in a Stratified Atmosphere’, Radio Science 4, 1269–1278.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
De Baas, A.F., Driedonks, A.G.M. Internal gravity waves in a stably stratified boundary layer. Boundary-Layer Meteorol 31, 303–323 (1985). https://doi.org/10.1007/BF00120898
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00120898