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Internal waves, fossil turbulence, and composite ocean microstructure spectra

Published online by Cambridge University Press:  21 April 2006

Carl H. Gibson
Carl H. Gibson
Affiliation:
Departments of Applied Mechanics and Engineering Sciences, and Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
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Abstract

Composite vertical shear spectra of Gargett et al. (1981) and composite vertical temperature-gradient spectra of Gregg (1977) are compared with the fossil-turbulence model of Gibson (1980–6). Both the shear and temperature-gradient spectra show high-wavenumber microstructure bumps which are identified by Gargett et al. (1981) and Gregg (1980) as due to turbulence in the fluid at the time of measurement. However, using γ [ges ] 5N as the criterion for turbulence to exist in a stratified fluid, where γ is the rate of strain and N is the Brunt-Väisälä frequency, the largest-scale fluctuations of the microstructure bumps may actually be remnants of previous turbulence persisting in fluid that is no longer turbulent at these scales: such fluctuations are termed fossil vorticity turbulence (a class of internal waves) and fossil temperature turbulence respectively. Both composite spectra exhibit k−1 subranges which are identified by their low amplitudes as subsaturated (two-three)-dimensional internal waves and resulting temperature fine structure by comparison with saturated three-dimensional internal-wave subranges proposed by Gibson (1980):7N2k−1 for the saturated vertical shear spectrum and $0.7 (\partial \overline{T}/\partial z)^2 k^{-1}$ for the saturated temperature gradient spectrum. Both composite spectra exhibit a transition between k−1 and k0 subranges at wavelengths of 6–14 metres: possibly a fossil remnant of previous overturning turbulence which produced 3–7 m thick partially mixed layers. Dissipation rates ε and χ and Cox numbers $C \equiv (\overline{{\boldmath \nabla}T})^2/(\overline{{\boldmath \nabla}T})^2$ of the turbulence required by this assumption are much larger than the measured values, suggesting that the turbulence process has been undersampled. Fossil overturning scales up to about 10 m are indicated by the Gregg (1977) data. Average (150 m) C values $\overline{C}$ are distributed as a very intermittent lognormal, with variance $\sigma^2_{\ln \overline{C}} = 5.4$, also indicating extreme undersampling of the turbulence and mixing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 168 , July 1986 , pp. 89 - 117
Copyright
© 1986 Cambridge University Press

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