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An experiment on the stability of small disturbances in a stratified free shear layer

Published online by Cambridge University Press:  29 March 2006

R. S. Scotti  and
G. M. Corcos
R. S. Scotti
Affiliation:
Division of Fluid Mechanics, University of California, Berkeley Present address: Woods Hole Oceanographic Institution, Woods Hole, Massachussetts
G. M. Corcos
Affiliation:
Division of Fluid Mechanics, University of California, Berkeley
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Abstract

A statically stable stratified free shear layer was formed within the test section of a wind tunnel by merging two uniform streams of air after uniformly heating the top stream. The two streams were accelerated side by side in a contraction section. The resulting sheared thermocline thickened gradually as a result of molecular diffusion and was characterized by nearly self-similar temperature (odd), velocity (odd) and Richardson number (even) profiles. The minimum Richardson number J0 could be adjusted over the range 0·07 ≥ J0 ≥ 0·76; the Reynolds number Re varied between 30 and 70. Small periodic disturbances were introduced upstream of the test section by a fine wire oscillating in the thermocline. The wire generated a narrow horizontal beam of internal waves, which propagated downstream and remained confined within the thermocline. The growth or decay of these waves was observed in the test section. The results confirm the existence of a critical Richardson number the value of which is in plausible agreement with theoretical predictions (J0 ≅ 0·22 for the Reynolds number of the experiment). The growth rate is a function of the wavenumber and is somewhat different from that computed for the same Reynolds and Richardson numbers, but the calculation assumed velocity and density profiles which were also somewhat different.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 3 , 11 April 1972 , pp. 499 - 528
Copyright
© 1972 Cambridge University Press

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References

Clark, J. W. 1969 Laboratory investigation of atmospheric shear flows using an open water channel. AGARD-NATO Meeting, Munich, 15.
Davis, R. E. 1969 J. Fluid Mech. 36, 337.
Drazin, P. G. 1961 Tellus, 13, 239.
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic Stability of Parallel Flow of Inviscid Fluids. In Advances in Applied Mechanics, vol. 9 (ed. G. Kuerti). Academic.
Gage, K. S. 1971 J. Fluid Mech. 47, 1.
Gage, K. S. & Reid, W. H. 1968 J. Fluid Mech. 33, 21.
Hazel, P. 1972 J. Fluid Mech. 51, 39.
Koppel, D. 1964 J. Math. Phys. 5, 963.
Lamb, H. 1932 Hydrodynamics, 6th edn., p. 378. Dover.
Long, R. R. 1954 Tellus, 6, 97.
Longuet-Higgins, M. S. & Stewart, R. W. 1960 J. Fluid Mech. 8, 565.
Longuet-Higgins, M. S. & Stewart, R. W. 1961 J. Fluid Mech. 10, 529.
Maslowe, S. A. 1969 A theoretical study of the stability of stratified shear layers. Doctoral dissertation, University of California, Los Angeles.
Maslowe, S. A. & Kelly, R. E. 1971 J. Fluid Mech. 48, 405.
Maslowe, S. A. & Thompson, J. M. 1971 Phys. Fluids, 14, 453.
Miles, J. W. 1963 J. Fluid Mech. 16, 209.
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. N.A.D.A. Rep. no. 1191.
Schwember, H. E. 1969 The interaction of buoyancy, shear and diffusion in stratified flows. College of Engineering, University of California, Berkeley. Rep. no. AS-69-2.
Scotti, R. S. 1969 An experimental study of a stratified free shear layer. College of Engineering, University of California, Berkeley Rep. no. AS-69-1.
Segur, H. 1971 J. Fluid Mech. 48, 161.
Thomson, W. 1910 Mathematics and Physics Papers, vol. 4, pp. 76–85. Cambridge
Thorpe, S. A. 1969 J. Fluid Mech. 39, 25.
Thorpe, S. A. 1971 J. Fluid Mech. 46, 299.
Tritton, D. J. 1959 J. Fluid Mech. 6, 547.
Webster, C. A. G. 1964 J. Fluid Mech. 19, 221–245.
Whitham, G. B. 1962 J. Fluid Mech. 12, 135.
Yih, C.-S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.