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Evolution of near-inertial waves

Published online by Cambridge University Press:  26 April 2006

R. C. Kloosterziel  and
P. Müller
R. C. Kloosterziel
Affiliation:
School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, USA
P. Müller
Affiliation:
School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, USA
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Abstract

The three-dimensional evolution of near-inertial internal gravity waves is investigated for the case of a laterally unbounded fluid layer of constant finite depth. A general Green's function formulation is derived which can be used to solve initial value problems or study the effect of forcing. The Green's function is expanded in vertical normal modes, and is very singular. Convolutions with finite-sized initial conditions lead however to well-behaved solutions. Expansions in similarity solutions of the diffusion equation are shown to be an alternative for finding exact solutions to initial value problems, with respect to one normal mode. For the case of constant buoyancy frequency normal modes expansions are shown to be equivalent to expansions in an alternative series of which the first term is the response on the infinite domain, all the others being corrections to account for the no-flux boundary condition on the upper and lower boundaries.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 301 , 25 October 1995 , pp. 269 - 294
Copyright
© 1995 Cambridge University Press

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References

Cahn, A. 1945 An investigation of the free oscillations of a simple current system. J. Met. 2, 113–119.Google Scholar
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw-Hill.
Fu, L. L. 1981 Observations and models of inertial waves in the deep ocean. Rev. Geophys. Space Phys. 19, 141–170.Google Scholar
Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic Press.
Gill, A. E. 1984 On the behavior of internal waves in the wake of storms. J. Phys. Oceanogr. 14, 1129–1151.Google Scholar
Greatbatch, R. J. 1983 On the response of the ocean to a moving storm: the nonlinear dynamics. J. Phys. Oceanogr. 13, 357–367.Google Scholar
Greatbatch, R. J. 1984 On the response of the ocean to a moving storm: parameters and scales. J. Phys. Oceanogr. 14, 59–78.Google Scholar
Hasselmann, K. 1970 Wave-driven inertial oscillations. Geophys. Fluid Dyn. 1, 463–502.Google Scholar
Kloosterziel, R. C. 1990 On the large-time asymptotics of the diffusion equation on infinite domains. J. Engng Maths 24, 213–236.Google Scholar
Kundu, P. K. 1993 Internal waves generated by traveling wind. J. Fluid Mech. 254, 529–559.Google Scholar
Kundu, P. K. & Thomson, R. E. 1985 Inertial oscillations due to a moving front. J. Phys. Oceanogr. 15, 1076–1084.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Phyics. McGraw-Hill.
Pollard, R. T. 1970 On the generation by winds of inertial waves in the ocean. Deep Sea Res. 17, 795–812.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. A. 1990 Numerical Recipes: the Art of Scientific Computing. Cambridge University Press.
Price, J. F. 1983 Internal wave wake of a moving storm. Part 1: scales, energy budget and observations. J. Phys. Oceanogr. 13, 949–965.Google Scholar
Rubenstein, D. M. 1983 Vertical dispersion of inertial waves in the upper ocean. J. Geophys. Res. 88, 4368–4380.Google Scholar
Watson, G. M. 1966 Theory of Bessel Functions. Cambridge University Press.