Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On secondary vorticity in internal waves

Authors: B. D. Dore and M. A. Al-Zanaidi
Journal: Quart. Appl. Math. 37 (1979), 35-50
MSC: Primary 76V05; Secondary 76C05
DOI: https://doi.org/10.1090/qam/530667
MathSciNet review: 530667
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Abstract: The generation of secondary vorticity in maintained and temporally-decaying wave motions is investigated for internal waves in fluid of great depth. In the case of two semi-infinite, homogeneous fluids of different density, the interfacial boundary layers generate a second-order, mean vorticity which diffuses inwards into the interior of both fluids, and the net vorticity produced is zero. For a continuously-stratified fluid, the free surface layer plays an indirect role and secondary vorticity, initially generated only within stratified regions by the action of a Reynolds stress, diffuses, in general, over the whole fluid, and no steady-state vorticity field is established. In finite depths, a steady state ultimately exists for maintained waves, and the mass transport velocity field is investigated.

References [Enhancements On Off] (What's this?)

  • [1] M. S. Longuet-Higgins, Mass transport in the boundary layer at a free oscillating surface., J. Fluid Mech. 8 (1960), 293–306. MR 0113438, https://doi.org/10.1017/S002211206000061X
  • [2] O. M. Phillips, The dynamics of the upper ocean, Cambridge University Press, 1966
  • [3] M. S. Longuet-Higgins, Mass transport in water waves, Phil. Trans. Roy. Soc. Lond. 1953
  • [4] M. S. Longuet-Higgins, A nonlinear mechanism for the generation of sea waves. Proc. Roy. Soc. Lond. 1969
  • [5] B. D. Dore, Mass transport in layered fluid systems, J. Fluid Mech. 1970
  • [6] B. D. Dore, A contribution to the theory of viscous damping of stratified wave flows. Acta Mech. 1969
  • [7] S. A. Thorpe, On the shape of progressive internal waves, Phil. Trans. Roy. Soc. Lond., 1968
  • [8] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947. MR 0022294
  • [9] M. A. Al-Zanaidi and B. D. Dore, Some aspects of internal wave motions. Pure and Appl. Geophys. 1976
  • [10] M. A. Al-Zanaidi, Some aspects of internal wave motions, M. Phil. Dissertation, University of Reading, 1975
  • [11] B. D. Dore, Viscous damping of small amplitude waves in a non-homogeneous fluid of infinite depth, Deep-Sea Res. 1968
  • [12] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Publications, 1965
  • [13] R. E. Kelly, Wave-induced boundary layers in a stratified fluid, J. Fluid Mech. 1970
  • [14] U. Ünlüata and C. C. Mei, Mass transport in water waves, J. Geophys. Res. 1970
  • [15] C. C. Mei, P. L.-F. Liu and T. G. Carter, Mass transport in water waves, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Report 146, 1972
  • [16] B. O. Dore, Some effects of the air-water interface on gravity waves, Geophys. Astrophys. Fluid Dyn. 1978

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DOI: https://doi.org/10.1090/qam/530667
Article copyright: © Copyright 1979 American Mathematical Society

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