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.
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M. A. Al-Zanaidi and B. D. Dore, Some aspects of internal wave motions. Pure and Appl. Geophys. 1976
M. A. Al-Zanaidi, Some aspects of internal wave motions, M. Phil. Dissertation, University of Reading, 1975
B. D. Dore, Viscous damping of small amplitude waves in a non-homogeneous fluid of infinite depth, Deep-Sea Res. 1968
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Publications, 1965
R. E. Kelly, Wave-induced boundary layers in a stratified fluid, J. Fluid Mech. 1970
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B. O. Dore, Some effects of the air-water interface on gravity waves, Geophys. Astrophys. Fluid Dyn. 1978
M. S. Longuet-Higgins, Mass transport in the boundary layer at a free oscillating surface, J. Fluid Mech. 1960
O. M. Phillips, The dynamics of the upper ocean, Cambridge University Press, 1966
M. S. Longuet-Higgins, Mass transport in water waves, Phil. Trans. Roy. Soc. Lond. 1953
M. S. Longuet-Higgins, A nonlinear mechanism for the generation of sea waves. Proc. Roy. Soc. Lond. 1969
B. D. Dore, Mass transport in layered fluid systems, J. Fluid Mech. 1970
B. D. Dore, A contribution to the theory of viscous damping of stratified wave flows. Acta Mech. 1969
S. A. Thorpe, On the shape of progressive internal waves, Phil. Trans. Roy. Soc. Lond., 1968
H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, Oxford University Press (2nd ed.), 1959
M. A. Al-Zanaidi and B. D. Dore, Some aspects of internal wave motions. Pure and Appl. Geophys. 1976
M. A. Al-Zanaidi, Some aspects of internal wave motions, M. Phil. Dissertation, University of Reading, 1975
B. D. Dore, Viscous damping of small amplitude waves in a non-homogeneous fluid of infinite depth, Deep-Sea Res. 1968
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Publications, 1965
R. E. Kelly, Wave-induced boundary layers in a stratified fluid, J. Fluid Mech. 1970
U. Ünlüata and C. C. Mei, Mass transport in water waves, J. Geophys. Res. 1970
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
B. O. Dore, Some effects of the air-water interface on gravity waves, Geophys. Astrophys. Fluid Dyn. 1978
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Article copyright:
© Copyright 1979
American Mathematical Society
