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On internal waves generated by travelling wind

Published online by Cambridge University Press:  26 April 2006

Pijush K. Kundu
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Abstract

Oceanic internal waves forced by a latitude-independent wind field travelling eastward at speed U is investigated, extending the hydrostatic f-plane model of Kundu & Thomson (1985). The ocean has a well-mixed surface layer overlying a stratified interior with a depth-dependent buoyancy frequency N(z), and f can vary with latitude. Solutions are found by decomposition into vertical normal modes. Problems discussed are (i) the response to a slowly moving line front, and (ii) the response in a variable f ocean.

For the slowly moving line front assuming a depth-independent N, the trailing waves are found to have large frequencies, and the vertical acceleration ∂w/∂t is important (that is the dynamics are non-hydrostatic) if the frequency ω is larger than a few times (Nf)½. The wake contains waves associated with all vertical modes, in contrast to hydrostatic dynamics in which slowly moving line fronts do not generate trailing waves of low-order modes. It is argued that slowly moving wind fields can provide an explanation for the frequently observed broad peak in the spectrum of vertical motion at a frequency somewhat smaller than N, and of the vertical coherence of the associated waves in the upper ocean.

To study lower-frequency internal waves, the hydrostatic constant-f model of Kundu & Thomson is extended to variable f. Various sections through such a flow clearly illustrate the development of a meridional wavelength λy = 2π/βt as predicted by D'Asaro (1989), in addition to the zonal wavelength λx due to translation of the wind. The two effects combine to cause a greater horizontal inhomogeneity, so that energy from the surface layer descends quickly, travelling equatorward and downward. Since waves at any point arrive from different latitudes, spectra no longer consist of discrete peaks but are more continuous and broader than those in the constant-f model. The waves are more intermittent because of the larger spectral width, and vertically less correlated in the thermocline because of a larger bandwidth of vertical modes. The vertical correlation in the deep ocean, however, is still high because the response is dominated by one or two low-order modes after 30 days of integration. As U decreases, the larger bandwidth of frequency increases the intermittency, and the larger bandwidth of vertical wavenumber decreases the vertical correlation. A superposition of travelling wind events intensifies the high-frequency end of the spectrum; a month-long travelling series of realistic strength can generate waves with amplitudes of order 4 cm/s in the deep ocean.

It is suggested that propagating winds and linear dynamics are responsible for the generation of a large fraction of internal waves in the ocean at all depths. The main effect of nonlinearity and mean flow may be to shape the internal wave spectra to a ω-2 form.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 529 - 559
Copyright
© 1993 Cambridge University Press

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References

Anderson, D. L. T. & Gill, A. 1979 Beta dispersion of inertial waves. J. Geophys. Res. 84, 1836–1842.Google Scholar
Cairns, J. L. & Williams, G. O. 1976 Internal wave observations from a mid-water float. Part 2. J. Geophys. Res. 81, 1943–1950.Google Scholar
Cornish, C. R. & Larsen, M. F. 1989 Observations of low-frequency waves in the lower stratosphere over Arecibo. J. Atmos. Sci. 46, 2428–2439.Google Scholar
D'asaro, E. A. 1985 The energy flux from the wind to near-inertial motions in the surface mixed layer. J. Phys. Oceanogr. 15, 1043–1959.Google Scholar
D'asaro, E. A. 1989 The decay of wind-forced mixed layer inertial oscillations due to the β effect. J. Geophys. Res. 94, 2045–2056.Google Scholar
Desaubies, Y. J. F. 1975 A linear theory of internal wave spectra and coherences near Väisälä frequency. J. Geophys. Res. 80, 895–899.Google Scholar
Eriksen, C. C. 1988a On wind forcing and observed wavenumber spectra. J. Geophys. Res. 93, 4985–4992.Google Scholar
Eriksen, C. C. 1988b Variability in the upper-ocean internal wave field at a Sargasso sea site. J. Phys. Oceanogr. 18, 1495–1513.Google Scholar
Eriksen, C. C. 1993 Equatorial ocean response to rapidly translating wind bursts. J. Phys. Oceanogr. 23, 1208–1230.Google Scholar
Fennel, W. & Lass, H. U. 1989 Analytical Theory of Forced Oceanic Waves. Berlin: Akademie.
Fu, L. L. 1981 Observations and models of inertial waves in the deep ocean. Rev. Geophys. Space Phys. 19, 141–170.Google Scholar
Garrett, C. J. R. & Munk, W. H. 1972 Space-time scales of internal waves. Geophys. Fluid Dyn. 2, 225–264.Google Scholar
Garrett, C. J. R. & Munk, W. H. 1979 Internal waves in the ocean. Ann. Rev. Fluid Mech. 11, 339–369.Google Scholar
Geisler, J. E. 1970 Linear theory of the response of a two-layer ocean to a moving hurricane. Geophys. Fluid Dyn. 1, 249–272.Google Scholar
Geisler, J. E. & Dickinson, R. E. 1972 The role of variable Coriolis parameter in the propagation of inertia-gravity waves during the geostrophic adjustment. J. Phys. Oceanogr. 2, 263–272.Google Scholar
Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic.
Gill, A. E. 1984 On the behavior of internal waves in the wakes of storms. J. Phys. Oceanogr. 14, 1129–1151.Google Scholar
Gould, W. J., Schmitz, W. J. & Wunch, C. 1974 Preliminary field results for a Mid-Ocean Dynamics Experiment (MODE-0). Deep-Sea Res. 21, 911–932.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
Kundu, P. K. 1976 An analysis of inertial oscillations observed near Oregon coast. J. Phys. Oceanogr. 6, 879–893.Google Scholar
Kundu, P. K. 1984 Generation of coastal inertial oscillations by time-varying wind. J. Phys. Oceanogr. 14, 1901–1913.Google Scholar
Kundu, P. K. 1986 A two-dimensional model of inertial oscillations generated by a propagating wind field. J. Phys. Oceanogr. 16, 1399–1411.Google Scholar
Kundu, P. K. 1990 Fluid Mechanics. Academic.
Kundu, P. K. & Thomson, R. E. 1985 Inertial oscillations due to a moving front. J. Phys. Oceanogr. 15, 1076–1084 (referred to herein as KT85.)Google Scholar
Kunze, E. 1985 Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr. 15, 544–565.Google Scholar
Kunze, E. & Sanford, T. B. 1986 Near-inertial wave interactions with mean flow and bottom topography near Caryn seamount. J. Phys. Oceanogr. 16, 109–120.Google Scholar
Levine, M. D., Paulson, C. A., Briscoe, M. G., Weller, R. A. & Peters, H. 1983a Internal waves in JASIN. Phil. Trans. R. Soc. Lond. A 308, 389–405.Google Scholar
Levine, M. D., Szoeke, R. A. de & Niiler, P. P. 1983b Internal waves in the upper ocean during MILE. J. Phys. Oceanogr. 13, 240–257.Google Scholar
McComas, C. H. & Bretherton, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 82, 1397–1412.Google Scholar
McCreary, J. P. 1981 A linear stratified ocean model of the equatorial undercurrent. Phil. Trans. R. Soc. Lond. A 298, 603–635.Google Scholar
Munk, W. H. 1980 Internal wave spectra at the buoyant and inertial frequencies. J. Phys. Oceanogr. 10, 1718–1728.Google Scholar
Munk, W. H. 1981 Internal waves. In Evolution of Physical Oceanography (ed. B. A. Warren & C. Wunch), p. 623. MIT Press.
Munk, W. H. & Phillips, N. 1968 Coherence and band structure of inertial motion in the sea. Rev. Geophys. Space Phys. 6, 447–472.Google Scholar
Olbers, D. 1983 Internal gravity waves. In Oceanography, vol. 3 (ed. J. Sündermann). Springer.
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21, 251–269.Google Scholar
Paduan, J. D., Szoeke, R. A. de & Weller, R. A. 1989 Inertial oscillations in the upper ocean during the Mixed Layer Experiment. J. Geophys. Res. 94, 4835–4842.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Pinkel, R. 1975 Upper ocean internal wave observations from FLIP. J. Geophys. Res. 80, 3892–3910.Google Scholar
Pinkel, R. 1981 Observations of the near-surface internal wavefield. J. Phys. Oceanogr. 11, 1248–1257.Google Scholar
Pinkel, R. 1985 A wavenumber-frequency spectrum of upper ocean shear. J. Phys. Oceanogr. 15, 1453–1469.Google Scholar
Pollard, R. T. 1970 On the generation by winds of inertial waves in the ocean. Deep-Sea Res. 17, 795–812.Google Scholar
Price, J. F. 1983 Internal wave wake of a moving storm. Part I: Scales, energy budget and observations. J. Phys. Oceanogr. 13, 949–965.Google Scholar
Sanford, T. B. 1975 Observations of the vertical structure of internal waves. J. Geophys. Res. 80, 3861–3871.Google Scholar
Shen, C. Y. & Holloway, G. 1986 A numerical study of the frequency and the energetics of nonlinear internal gravity waves. J. Geophys. Res. 91, 953–973.Google Scholar
Smith, R. 1973 Evolution of inertial frequency oscillations. J. Fluid Mech. 60, 383–389.Google Scholar
Thomson, R. E. & Huggett, W. S. 1981 Wind-driven inertial oscillations of large spatial coherence. Atmos. Ocean. 19, 281–306.Google Scholar
Thorpe, S. A. 1975 The excitation, dissipation, and interaction of internal waves in the open ocean. J. Geophys. Res. 80, 328–338.Google Scholar
Wunch, C. & Gill, A. E. 1976 Observations of equatorially trapped waves in Pacific sea level variations. Deep-Sea Res. 23, 371–390.Google Scholar