Fluid Dynamics

, Volume 41, Issue 6, pp 949–956 | Cite as

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

  • A. Yu. Vasil’ev
  • Yu. D. Chashechkin
Article
  • 33 Downloads

Abstract

An analytical solution of a linearized problem of the emission of periodic internal waves by part of a plane which oscillates with a small amplitude in an arbitrary direction in a viscous exponentially stratified fluid is constructed. Solutions of the dispersion equation are given for all positions of the emitting surface (arbitrary, vertical, horizontal, and critical when one of the beam propagation directions is collinear with the emitting surface). The possibility of transition to the case of a uniform fluid, which is important for applications, is analyzed.

Keywords

viscous stratified fluid periodic internal waves boundary layers exact solutions 

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References

  1. 1.
    J. Lighthill, Waves in Fluids, Cambridge Univ. Press, (Cambridge) (1978).MATHGoogle Scholar
  2. 2.
    B. Voisin, “Limit states of internal waves beams,” J. Fluid. Mech., 496, 243–293 (2003).MATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    A. V. Aksenov, V. A. Gorodtsov, and I. V. Sturova, Modeling of the Flow of a Stratified Inviscid Incompressible Fluid Past a Cylinder [in Russian], Preprint IPM AS USSR No. 282, Institute for Problems in Mechanics AS USSR (1986).Google Scholar
  4. 4.
    D. G. Hurley and G. Keady, “The generation of internal waves by vibrating elliptic cylinders. Pt 2. Approximate viscous solution,” J. Fluid Mech., 351, 119–138 (1997).MATHCrossRefMathSciNetADSGoogle Scholar
  5. 5.
    D. G. Hurley and M. J. Hood, “The generation of internal waves by vibrating elliptic cylinders. Pt 3. Angular oscillations and comparison of theory with recent experimental observations,” J. Fluid Mech., 433, 61–75 (2001).MATHMathSciNetADSGoogle Scholar
  6. 6.
    Yu. V. Kistovich and Yu. D. Chashechkin, “The generation of monochromatic internal waves in a viscous fluid,” Prikl. Mekh. Tekh. Fiz., 40, No. 6, 31–40 (1999).MATHMathSciNetGoogle Scholar
  7. 7.
    Yu. S. Il’inykh, Yu. V. Kistovich, and Yu. D. Chashechkin, “Comparison of an exact solution of one problem of the generation of periodic internal waves with experiment,” Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana, 35, No. 5, 649–655 (1999).Google Scholar
  8. 8.
    G. G. Stokes, “On the effect of internal friction of fluids on the motion of pendulums,” Trans. Cambr. Phil. Soc., 9, Pt 2, 8–106 (1851).Google Scholar
  9. 9.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Some exactly solved problems of the generation of three-dimensional periodic internal waves,” Prikl. Mekh. Tekh. Fiz., 42, No. 2, 52–61 (2001).MATHGoogle Scholar
  10. 10.
    A. Yu. Vasil’ev and Yu. D. Chashechkin, “The generation of beams of three dimensional periodic internal waves in an exponentially stratified fluid,” Prikl. Matem. Mekh., 67, No. 3, 442–452 (2003).MATHMathSciNetGoogle Scholar
  11. 11.
    D. D. Holm and Y. Kimura, “Zero-helicity Lagrangian kinematics of three-dimensional advection,” Phys. Fluids. A, 3, No. 5, 1033–1038 (1991).CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    Yu. D. Chashechkin and A. V. Kistovich, “Classification of three-dimensional periodic motions in a fluid,” Dokl. Acad. Nauk, 395, No. 1, 55–58 (2004).Google Scholar
  13. 13.
    A. H. Nayfeh, Perturbation Methods, Wiley, New York et al. (1973).MATHGoogle Scholar
  14. 14.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Reflection of beams of internal gravitational waves on a plane rigid surface,” Prikl. Matem. Mekh., 59, No. 4, 607–613 (1995).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. Yu. Vasil’ev
  • Yu. D. Chashechkin

There are no affiliations available

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