Journal of Fluid Mechanics

Internal waves, fossil turbulence, and composite ocean microstructure spectra

Carl H.  Gibson a1
a1 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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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 [gt-or-equal, slanted] 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.

(Published Online April 21 2006)
(Received January 4 1984)
(Revised December 9 1985)