Abstract
Internal waves generated by the turbulent wake of a sphere travelling horizontally through a linearly stratified fluid were studied using shadowgraph and particle-streak photography. The Reynolds and internal Froude number ranges considered were 2,000 ≤ Re ≤ 12,900 and 2.0 ≤ Fi ≤ 28.0, respectively. Two quite distinct flow regimes based on the structure of the turbulent wake were identified. In one, the wake is characterized by “large-scale coherent structures”. In the other, the wake, as viewed on a side-view shadowgraph, grows in a roughly symmetric fashion to a maximum height and then collapses slowly; such flows are termed the “smallscale structures” regime.
Wave lengths and maximum wave heights of the internal waves were measured as functions of Nt and Fi, where N is the Brunt-Väisälä frequency and t the time. It was found that the wave lengths scale well with the streamwise dimension of the spiralling coherent structures. The maximum amplitude of the internal waves were found to scale with the vertical dimension of the turbulent wake, upon varying the internal Froude number.
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References
Brighton, P. W. M. 1978: Strongly stratified flow past three-dimensional obstacles. Q. J. Roy. Met. Soc. 104, 289–307
Castro, I. P.; Snyder, W. H.; Marsh, G. L. 1983: Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261–282
Chomaz, J. M.; Bonneton, P.; Butet, A.; Hopfinger, E. J.; Perrier, M. 1990: Gravity wave patterns in the wake of a sphere in a stratified fluid. Proceedings of Turbulence 89, (edEds. Lesieur, M.; Metais, O.). Kluwer Academic Publishers, Dordrecht, The Netherlands
Crapper, G. D. 1959: A three-dimensional solution for waves in the lee of mountains. J. Fluid Mech. 6, 51–76
Gilreath, H. E.; Brandt, A. 1985: Experiments on the generation of internal waves in a stratified fluid. AIAA J. 23, 693–700
Hanazaki, H. 1988: A numerical study of three-dimensional stratified flow past spheres. J. Fluid Mech. 192, 303–419
Hopfinger, E. J.; Flor, J. B.; Chomaz, J. M.; Bonneton, P. 1991: Internal waves generated by a moving sphere and its wake in a stratified fluid. Exp. Fluids 11, 255–261
Kim, H. J.; Durbin, P. A. 1988: Observations of the frequency in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 31, 3260–3265
Lighthill, M. J. 1978: Waves in fluids. London: Cambridge University Press
Lin, Q.; Boyer, D. L.; Fernando, H. J. S. 1992a: Stratified flow past a sphere. J. Fluid Mech. 240, 315–355
Lin, Q.; Boyer, D. L.; Fernando, H. J. S. 1992b: Turbulent wakes of linearly stratified flow past a sphere. Phys. Fluids (A) 4 (8), 1687–1696
Mowbray, D. E.; Rarity, B. S. 1967: A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28, 1–16
Sakamoto, H.; Haniu, H. 1990: A study on vortex shedding from spheres in a uniform flow. J. Fluids Eng. (Trans. ASME) 112, 386–392
Schooley, A. H.; Hughes, B. A. 1972: An experimental and theoretical study of internal waves generated by the collapse of a two-dimensional mixed region in a density gradient. J. Fluid Mech. 51, 159–175
Taneda, S. 1978: Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106. J. Fluid Mech. 85, 187–192
Wu, J. 1969: Mixed region collapse with internal wave generation in a density stratified medium. J. Fluid Mech. 35, 531–544
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Lin, Q., Boyer, D.L. & Fernando, H.J.S. Internal waves generated by the turbulent wake of a sphere. Experiments in Fluids 15, 147–154 (1993). https://doi.org/10.1007/BF00190954
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DOI: https://doi.org/10.1007/BF00190954