Internal waves, fossil turbulence, and composite ocean microstructure spectra

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 ] 5 N 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):7 N 2 k −1 for the saturated vertical shear spectrum and 0.7 (∂ T̄/∂ z)² k⁻¹ for the saturated temperature gradient spectrum. Both composite spectra exhibit a transition between k −1 and k 0 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 ≡ ( ∇T)²/( ∇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 C̄ are distributed as a very intermittent lognormal, with variance σ²ln C̄ = 5.4 , also indicating extreme undersampling of the turbulence and mixing.