Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-20T05:19:09.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Radiation damping of inertial oscillations in the upper ocean

Published online by Cambridge University Press:  19 April 2006

T. H. Bell
T. H. Bell
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington, D.C. 20375
Get access Rights & Permissions [Opens in a new window]

Abstract

Turbulent motions within the wind-mixed layer, which is advected by near-surface inertial oscillations, excite internal gravity waves in the underlying ocean layers. Momentum transport in the radiated wave field results in a drag force on the inertial currents. Because the magnitude of the inertial currents is large compared with the turbulence intensity, the resultant rate of dissipation of inertial oscillation energy is approximately equal to the energy flux in the radiated wave field. Using linear internal wave theory, asymptotic results are derived for the energy flux in terms of the Brunt-Väisälä frequency N below the mixed layer, the magnitude U0 of the inertial current, the integral length scale l of the mixed-layer turbulence and the mean-square displacement 〈ζ20〉 of the base of the mixed layer. For representative conditions, we estimate an energy flux of 1-10 erg/cm2 s into relatively short (wavelength of order 2πU0/N) high frequency (of order, but less than, N) internal waves. The resultant decay times for inertial oscillation energy range from a day to a week or so, in agreement with reported observations on the decay of inertial oscillations in the upper ocean. The estimated energy flux is comparable in magnitude to estimates for other internal wave generation mechanisms, indicating that, in addition to being a significant sink of inertial energy, this process may locally represent a significant source of internal wave energy in the open ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 2 , 27 September 1978 , pp. 289 - 308
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Assaf, G., Gerard, R. & Gordon, A. L. 1971 Some mechanisms of oceanic mixing revealed in aerial photographs. J. Geophys. Res. 76, 6550–6572.Google Scholar
Bell, T. H. 1975a Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 65, 705–722.Google Scholar
Bell, T. H. 1975b Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320–327.Google Scholar
Blumen, W. 1972 Geostrophic adjustment. Rev. Geophys. Space Phys. 10, 485–528.Google Scholar
Copson, E. T. 1967 Asymptotic Expansions. Cambridge University Press.
Dillon, T. M. & Powell, T. M. 1976 Low-frequency turbulence spectra in the mixed layer of Lake Tahoe, California-Nevada. J. Geophys. Res. 81, 6421–6427.Google Scholar
Faller, A. J. 1971 Oceanic turbulence and the Langmuir circulations. Ann. Rev. Ecology Systematics 2, 201–236.Google Scholar
Fofonoff, N. P. 1969 Spectral characteristics of internal waves in the ocean. Deep-Sea Res. Suppl. 16, 59–71.Google Scholar
Garrett, C. & Munk, W. 1972 Space-time scales of internal waves. Geophys. Fluid Dyn. 3, 225–264.Google Scholar
Gonella, J. 1971 A local study of inertial oscillations in the upper layers of the oceans. Deep-Sea Res. 18, 775–788.Google Scholar
Halpern, D. 1974 Observations of the deepening of the wind-mixed layer in the northeast Pacific Ocean. J. Phys. Ocean. 4, 454–466.Google Scholar
Hayes, S. & Halpern, D. 1976 Observations of internal waves and coastal upwelling off the Oregon coast. J. Mar. Res. 34, 247–267.Google Scholar
Krauss, W. 1972 Wind-generated internal waves and inertial-period motions. Dtsche Hydro. Z. 25, 241–250.Google Scholar
Kroll, J. 1975 The propagation of wind-generated inertial oscillations from the surface into the deep ocean. J. Mar. Res. 33, 15–51.Google Scholar
Kundu, P. K. 1976 An analysis of inertial oscillations observed near Oregon coast. J. Phys. Ocean. 6, 879–893.Google Scholar
Lighthill, M. J. 1964 Fourier Analysis and Generalised Functions. Cambridge University Press.
Mcleish, W. 1968 On the mechanics of wind-slick generation. Deep-Sea Res. 15, 461–469.Google Scholar
Müller, P. & Olbers, D. J. 1975 On the dynamics of internal waves in the deep ocean. J. Geophys. Res. 80, 3848–3860.Google Scholar
Nihoul, J. C. J. 1972 The effect of wind blowing on turbulent mixing and entrainment in the upper layer of the ocean. Mem. Soc. Roy. Sci. Liège 6 (4), 115–124.Google Scholar
Niiler, P. P. 1977 One-dimensional models of the seasonal thermocline. In The Sea, vol. 6 (ed. E. D. Goldberg et al.), pp. 97–115.
Oberhettinger, F. 1973 Fourier Expansions: A Collection of Formulas. Academic Press.
Phillips, O. M. 1955 The irrotational motion outside a free turbulent boundary. Proc. Camb. Phil. Soc. 51, 220–229.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
Pollard, R. T. 1974 The Joint-Air-Sea Interaction Trial-JASIN 1972. Mém. Soc. Roy. Sci. Liège 6 (6), 17–34.Google Scholar
Pollard, R. T. & Millard, R. C. 1970 Comparison between observed and simulated wind-generated inertial oscillations. Deep-Sea Res. 17, 813–821.Google Scholar
Pollard, R. T., Rhines, P. B. & Thompson, R. 1973 The deepening of the wind-mixed layer. Geophys. Fluid Dyn. 3, 381–404.Google Scholar
Smith, R. 1973 Evolution of inertial frequency oscillations. J. Fluid Mech. 60, 383–389.Google Scholar
Tolstoy, I. 1973 Infrasonic fluctuation spectra in the atmosphere. Geophys. J. Roy. Astr. Soc. 34, 343–363.Google Scholar
Tolstoy, I. & Miller, C. D. 1975 Ionospheric fluctuations due to turbulent wind layers. J. Atmos. Terr. Phys. 37, 1125–1132.Google Scholar
Townsend, A. A. 1965 Excitation of internal waves by a turbulent boundary layer. J. Fluid Mech. 22, 241–252.Google Scholar
Townsend, A. A. 1966 Internal waves produced by a convective layer. J. Fluid Mech. 24, 307–319.Google Scholar
Townsend, A. A. 1968 Excitation of internal waves in a stably-stratified atmosphere with considerable wind-shear. J. Fluid Mech. 32, 145–171.Google Scholar
Watson, G. N. 1966 A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge University Press.
Webster, F. 1968 Observations of inertial-period motions in the deep sea. Rev. Geophys. 6, 473–490.Google Scholar