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Development of a Shear Instability in Nodal Zones of a Standing Internal Wave

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Abstract

The results of experimentally investigating the initial stage of development of shear instability of the interface between two immiscible fluids relatively oscillating during the parametric excitation of standing internal waves are presented. Three stages of distortion of the sinusoidal wave profile are distinguished: the formation of short secondary waves, their breaking, and transition to large-scale vortex formations. It is shown that in the nodal zones of a standing wave quasi-stationary wave perturbations start to develop at wave steepnesses Γ ∼ 0.08–0.13 and critical Reynolds numbers of the laminar boundary layer R ∼ 90–300. The experimental data are compared with the classical Kelvin-Helmholtz theory.

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REFERENCES

  1. J. D. Woods, “Wave induced shear instability in the summer thermocline,” J. Fluid Mech., 32, Pt. 4, pp. 791–800 (1968).

    ADS  Google Scholar 

  2. J. F. A. Sleath, Sea Bed Mechanics, Wiley, New York (1984).

    Google Scholar 

  3. S. A. Thorpe, “Transitional phenomena and the development of turbulence in stratified fluids: a review,” J. Geophys. Res., 92, No.C5, 5231–5248 (1987).

    ADS  Google Scholar 

  4. J. A. Collins, “Inception of turbulence at the bed under periodic gravity waves,” J. Geophys. Res., 68, No.21, pp. 6007–6014 (1963).

    ADS  Google Scholar 

  5. S. I. Sergeev, “Fluid oscillations in pipes at moderate Reynolds numbers,” Fluid Dynamics, 1, No.1, pp. 121–122 (1966).

    MathSciNet  Google Scholar 

  6. P. Merkli and H. Thomann, “Transition to turbulence in oscillating pipe flow,” J. Fluid Mech., 68, Pt. 3, pp. 567–575 (1975).

    ADS  Google Scholar 

  7. D. Das and J. H. Arakeri, “Transition of unsteady velocity profiles with reverse flow,” J. Fluid Mech., 374, pp. 251–283 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Koneko and H. Honji, “Double structures of steady streaming in the oscillatory viscous flow over a wavy wall,” J. Fluid Mech., 93, Pt. 4, 727–736 (1979).

    ADS  Google Scholar 

  9. M. R. King, D. T. Leighton, and M. J. McCready, “Stability of oscillatory two-phase Couette flow: theory and experiment,” Phys. Fluids, 11, No.4, pp. 833–844 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  10. M. A. Scherer, F. Melo, and M. Marder, “Sand ripples in an oscillating annular sand-water cell,” Phys. Fluids, 11, No.1, pp. 58–67 (1999).

    Article  ADS  Google Scholar 

  11. A. A. Ivanova, V. G. Kozlov, and P. Evesque, “Interface dynamics of immiscible fluids under horizontal vibration,” Fluid Dynamics, 36, No.3, pp. 362–368 (2001).

    Article  Google Scholar 

  12. S. A. Thorpe, “On standing internal waves of finite amplitude,” J. Fluid Mech., 32, Pt. 3, pp. 299–319 (1968).

    Google Scholar 

  13. V. A. Kalinichenko, “Laboratory investigation of a parametric instability in a two-layer fluid,” Izv. Akad. Nauk SSSR, Fizika Atmosfery i Okeana, No. 2, pp. 206–210 (1986).

  14. V. A. Kalinichenko, S. Ya. Sekerzh-Zen'kovich, and A. S. Timofeev, “Experimental study of the velocity field of parametrically excited waves in a two-layer liquid,” Fluid Dynamics, 26, No.5, pp. 771–775 (1991).

    Google Scholar 

  15. A. V. Kravtsov and S. Ya. Sekerzh-Zen'kovich, “Parametric excitation of waves in a viscous two-layer fluid in a closed vessel,” Zh. Vychisl. Mat. Mat. Fiz., 33, No.4, pp. 611–619 (1993).

    MathSciNet  Google Scholar 

  16. H. Lamb, Hydrodynamics, University Press, Cambridge (1924).

    Google Scholar 

  17. P. G. Drazin, “On stability of parallel flow of incompressible fluid of variable density and viscosity,” Proc. Camb. Phil. Soc., 58, Pt. 4, pp. 646–661 (1962).

    MATH  MathSciNet  Google Scholar 

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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2005, pp. 140–149. Original Russian Text Copyright © 2005 by Kalinichenko.

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Kalinichenko, V.A. Development of a Shear Instability in Nodal Zones of a Standing Internal Wave. Fluid Dyn 40, 956–964 (2005). https://doi.org/10.1007/s10697-006-0010-6

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