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Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid

Published online by Cambridge University Press:  26 April 2006

P. Bonneton ,
J. M. Chomaz  and
E. J. Hopfinger
P. Bonneton
Affiliation:
Meteo-France CNRM Toulouse, 42 avenue Coriolis, 31057 Toulouse, France
J. M. Chomaz
Affiliation:
Meteo-France CNRM Toulouse, 42 avenue Coriolis, 31057 Toulouse, France LADHYX, Ecole Polytechnique, 91128 Palaiseau-Cedex, France
E. J. Hopfinger
Affiliation:
LEGI-IMG, BP 53, 38041 Grenoble-Cedex, France
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Abstract

The internal gravity wave field generated by a sphere towed in a stratified fluid was studied in the Froude number range 1.5 ≤ F ≤ 12.7, where F is defined with the radius of the sphere. The Reynolds number was sufficiently large for the wake to be turbulent (Re∈[380, 30000]). A fluorescent dye technique was used to differentiate waves generated by the sphere, called lee waves, from the internal waves, called random waves, emitted by the turbulent wake. We demonstrate that the lee waves are well predicted by linear theory and that the random waves due to the turbulence are related to the coherent structures of the wake. The Strouhal number of these structures depends on F when F [lsim ] 4.5. Locally, these waves behave like transient internal waves emitted by impulsively moving bodies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 23 - 40
Copyright
© 1993 Cambridge University Press

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References

Bonneton, P., Chomaz, J. M. & Perrier, M. 1990 Interaction between the internal wave field and the wake emitted behind a moving sphere in a stratified fluid. In Proc. Conf. Engng Turbulence Modelling and Experiments, Dubrovnik, Yugoslavia, (ed. W. Rodi & G. Ganic), pp. 459–466. Elsevier.
Castro, I. P., Snyder, W. H. & Marsh, G. L. 1983 Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261–282.Google Scholar
Chomaz, J. M., Bonneton, P., Butet, A., Hopfinger, E. J. & Perrier, M. 1991 Gravity wave patterns in the wake of a sphere in a stratified fluid. In Proc. Turbulence 89: Organized Structures and Turbulence in Fluid Mech. (ed. M. Lesieur & O. Métais), pp. 489–503. Kluwer.
Chomaz, J. M., Bonneton, P. & Hopfinger, E. J. 1993 The structure of the near wake of a sphere moving in a stratified fluid. J. Fluid Mech. 254, 1–21 (referred to herein as CBH.)Google Scholar
Garrett, C. & Munk, W. 1979 Internal waves in the ocean. Ann. Rev. Fluid Mech. 11, 339–369.Google Scholar
Gilreath, H. E. & Brandt, A. 1985 Experiments on the generation of internal waves in a stratified fluid. AIAA J. 23, 693–700.Google Scholar
Hanazaki, H. 1988 A numerical study of three-dimensional stratified flow past a sphere. J. Fluid Mech. 192, 393–419.Google Scholar
Hartman, R. J. & Lewis, H. W. 1972 Wake collapse in a stratified fluid: linear treatment. J. Fluid Mech. 51, 613–618.Google Scholar
Hopfinger, E. J., Flör, J. B., Chomaz, J. M. & Bonneton, P. 1991 Internal waves generated by a moving sphere and its wake in a stratified fluid. Exps Fluids 11, 255–261.Google Scholar
Hunt, J. C. R. & Snyder, W. H. 1980 Experiments on stably and neutrally stratified flow over a model three-dimensional hill. J. Fluid Mech. 96, 671–704.Google Scholar
Janowitz, G. S. 1984 Lee waves in three-dimensional stratified flow. J. Fluid Mech. 148, 97–108.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Lin, J. T. & Pao, Y. H. 1979 Wakes in stratified fluids. Ann. Rev. Fluid Mech. 11, 317–338.Google Scholar
Lin, Q., Lindberg, W. R., Boyer, D. L. & Fernando, H. J. S. 1992 Stratified flow past a sphere. J. Fluid Mech. 240, 315–354.Google Scholar
Makarov, S. A. & Chashechkin, Yu. D. 1981 Apparent internal waves in a fluid with exponential density distribution. J. Appl. Mech. Techn. Phys. 22, 772–779.Google Scholar
Miles, J. W. 1971 Internal waves generated by a horizontally moving source. Geophys. Fluid Dyn. 2, 63–87.Google Scholar
Peat, K. S. & Stevenson, T. N. 1975 Internal waves around a body moving in a compressible density-stratified fluid. J. Fluid Mech. 70, 673–688.Google Scholar
Schooley, A. H. & Stewart, R. W. 1963 Experiments with a self-propelled body submerged in a fluid with a vertical density gradient. J. Fluid Mech. 15, 83–96.Google Scholar
Smith, R. B. 1980 Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus 32, 348–364.Google Scholar
Smith, R. B. 1989 Hydrostatic airflow over mountains. Adv. Geophys. 31, 1–41.Google Scholar
Smolarkiewicz, P. K. & Rotunno, R. 1989 Low Froude number flow past three-dimensional obstacles. Part I: Baroclinically generated lee vortices. J. Atmos. Sci. 46, 1154–1164.Google Scholar
Stevenson, T. N. 1973 The phase configuration of internal waves around a body moving in a density stratified fluid. J. Fluid Mech. 60, 759–767.Google Scholar
Thual, O., Butet, A., Perrier, M. & Hopfinger, E. 1987 Sillage d'une sphère en milieu stratifié. Rapport DRET 85/105.
Voisin, B. 1991a Rayonnement des ondes internes de gravité. Application aux corps en mouvement. PhD thesis, Paris 6 University.
Voisin, B. 1991b Internal wave generation in uniformly stratified fluids. Part 1. Green's function and point sources. J. Fluid Mech. 231, 439–480.Google Scholar
Voisin, B. 1993 Internal wave generation in uniformly stratified fluids. Part 2. Moving point sources. J. Fluid Mech. (submitted.)Google Scholar
Wu, J. 1969 Mixed region collapse with internal wave generation in a density-stratified medium. J. Fluid Mech. 35, 531–544.Google Scholar
Zavol'skii, N. A. & Zaitsev, A. A. 1984 Development of internal waves generated by a concentrated pulse source in an infinite uniformly stratified fluid. J. Appl. Mech. Tech. Phys. 25, 862–867.Google Scholar