The stability analysis of an inflexion-free velocity profile and its application to the night-time boundary layer in the atmosphere
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The characteristics of waves excited in a stratified shear flow with a velocity profile monotonically increasing above the ground are calculated numerically. It is shown that unstable modes exist when the Brunt-Väisälä frequency of the ambient atmosphere decreases sufficiently fast with height. Their growth rates as a function of the horizontal wavelength and the local Richardson number are given, and a comparison between them and experimental data obtained for the night-time-boundary layer of the Earth's atmosphere is carried out. Finally, the characteristics of the singular neutral modes that the system can support are presented.
- Acton, F. S.: 1970, Numerical Methods that Work, Harper and Row, Publishers, New York.
- Bulirsch, R. and Stoer, J.: 1966, Numerical Treatment of Ordinary Differential Equations by Extrapolation Methods, Num. Math. 8, 1–13.
- Case, K. M.: 1960, Stability of an Idealized Atmosphere. I: Discussion of Results, Phys. Fluids 3, 149–154.
- Chimonas, G.: 1970, The Extension of the Miles-Howard Theorem to Compressible Flows, J. Fluid Mech. 43, 833–836.
- Chimonas, G.: 1972, The Stability of a Coupled Wave-Turbulence System in a Parallel Shear Flow, Boundary-Layer Meteorol. 2, 444–452.
- Chimonas, G.: 1974, Considerations of the Stability of Certain Heterogeneous Shear Flows Including Some Inflexion-free Profiles, J. Fluid Mech. 65, 65–69.
- Einaudi, F. and Lalas, D. P.: 1976, The Effect of Boundaries on the Stability of Inviscid Stratified Shear Flows, accepted for publication in J. Appl. Mech.
- Emmanuel, C. B., Bean, B. R., McAllister, L. G., and Pollard, J. R.: 1972, Observations of Helmholtz Waves in the Lower Atmosphere with an Acoustic Sounder, J. Atmos. Sci. 29, 886–892.
- Gage, K. S. and Reid, W. H.: 1968, The Stability of Thermally Stratified Plane Poiseuille Flow, J. Fluid Mech. 33, 21–32.
- Gage, K. S.: 1971, The Effect of Stable Thermal Stratification on the Stability of Viscous Parallel Flows, J. Fluid Mech. 47, 1–20.
- Hall, F. F. and Owens, E. J.: 1975, ‘Atmospheric Acoustic Echo Soundings Investigations at the South Pole’, Proc. of the Workshop on Polar Meteorology, National Science Foundation, University of Nevada, May, 1975.
- Hines, C. O.: 1960, Internal Atmospheric Gravity Waves at Ionospheric Heights, Can. J. Phys. 38, 1441–1481.
- Hines, C. O.: 1974, The Upper Atmosphere in Motion, Geophysical Monograph 18, American Geophysical Union, Washington, D. C., pp. 248–328.
- Hooke, W. H., Hall, F. F., and Gossard, E. E.: 1973, Observed Generation of an Atmospheric Gravity Wave by Shear Instability in the Mean Flow of the Planetary Boundary Layer, Boundary-Layer Meteorol. 5, 29–41.
- Howard, L. N.: 1961, Note on a Paper of John W. Miles, J. Fluid Mech. 10, 509–512.
- Hull, T. E., Enright, W. H., Fellen, B. M. and Sedgwick, A. E.: 1972, Comparing Numerical Methods for Ordinary Differential Equations, SIAM J. Numer. Anal. 9, 603–637.
- Ince, E. L.: 1956, Ordinary Differential Equations, Dover Publications, Inc., New York.
- Jones, W. L.: 1968, Reflexion and Stability of Waves in Stably Stratified Fluids with Shear Flow: A Numerical Study, J. Fluid Mech. 34, 609–624.
- Lalas, D. P. and Einaudi, F.: 1975, On the Characteristics of Gravity Waves Generated by Atmospheric Shear Layers, submitted for publication.
- Maslowe, S. A. and Thompson, J. M.: 1971, Stability of a Stratified Free Shear Layer, Phys. Fluids 14, 453–458.
- Merrill, J. T.: 1975, ‘Observational Study of Shear Instability Events in the Planetary Boundary Layer’, 55th Annual Meeting Amer. Meteorol. Soc., Denver, Colo., June 20–23.
- Miles, J. W.: 1961, On the Stability of Heterogeneous Shear Flows, J. Fluid Mech. 10, 496–508.
- Miles, J. W.: 1963, On the Stability of Heterogeneous Shear Flows. Part 2, J. Fluid Mech. 16, 209–227.
- Miles, J. W.: 1967, Internal Waves in a Continuously Stratified Atmosphere or Ocean, J. Fluid Mech. 28, 305–310.
- Rayleigh, Lord: 1880, On the Stability, or Instability, of Certain Fluid Motions, Proc. London Math. Soc. 11, 57–70. (See also: Rayleigh, Lord, 1964, Scientific Papers 1, Dover Publications, pp. 474–487.)
- Schlichting, H.: 1935, Turbulenz bei Wärmeschichtung, Zeitschrift Angew. Math. Mech. 15, 313–338. (See also: ‘Turbulence and Heat Stratification’, Tech. Mem. 1262, National Advisory Committee for Aeronautics, Washington, D.C., 1950.)
- Stankov, B.: 1975, ‘Study of the Nocturnal Boundary Layer’, 55th Annual Meeting Amer. Meteorol. Soc., Denver, Colo., June 20–23.
- Synge, J. L.: 1933, The Stability of Heterogeneous Liquids, Trans. Royal Soc. Canada 27, 1–18.
- Thorpe, S. A.: 1969a, Experiments on the Stability of Stratified Shear Flows, Radio Science 4, 1327–1331.
- Thorpe, S. A.: 1969b, Neutral Eigensolutions of the Stability Equation for Stratified Shear Flow, J. Fluid Mech. 36, 673–683.
- Wagner, K. K.: Inflection Point Instability within an Inversion Layer, Atmospheric Research Laboratory Report, University of Oklahoma, Norman, Oklahoma, May 1975.
- Yih, C.-S.: 1970, Stability of and Waves in Stratified Flows, 8th Symposium on Hydrodynamics in the Ocean Environment, paper ARC-179, pp. 219–237.
- The stability analysis of an inflexion-free velocity profile and its application to the night-time boundary layer in the atmosphere
Volume 10, Issue 1 , pp 35-54
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Industry Sectors
- Author Affiliations
- 1. Cooperative Institute for Research in Environmental Sciences, University of Colorado/NOAA, Boulder, Co., USA
- 2. Cooperative Institute for Research in Environmental Sciences, University of Colorado/NOAA and Aeronomy Laboratory, NOAA, Boulder, Co., USA
- 3. Dept. of Mechanical Engineering Sciences, Wayne State University, Detroit, Mich., USA