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Local isotropy and the decay of turbulence in a stratified fluid

Published online by Cambridge University Press:  20 April 2006

A. E. Gargett ,
T. R. Osborn  and
P. W. Nasmyth
A. E. Gargett
Affiliation:
Institute of Ocean Sciences, Patricia Bay, P.O. Box 6000, Sidney, B.C., VSL 4B2, Canada
T. R. Osborn
Affiliation:
U.S. Naval Postgraduate School, Monterey, CA 93940, U.S.A.
P. W. Nasmyth
Affiliation:
Institute of Ocean Sciences, Patricia Bay
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Abstract

The validity of the assumption of local isotropy is investigated using measurements of three orthogonal components of the turbulent velocity fields associated with initially high-Reynolds-number geophysical turbulence. The turbulent fields, generated by various large-scale internal motions caused by tidal flows over an estuarine sill, decay under the influence of stable mean density gradients. With measurements from sensors mounted on a submersible, we examine the evolution of spectral shapes and of ratios of cross-stream to streamwise components, as well as the degree of high-wavenumber universality, for the observational range of the parameter I≡ ks/kb = lb/ls. This ratio is a measure of separation between the Kolmogoroff wavenumber ks≡ (ε/ν3)¼ ≡ 2π/ls typical of scales by which turbulent kinetic energy has been dissipated (at rate ε), and the buoyancy wavenumber kb ≡ (N3/ε)½ ≡ 2π/lb typical of scales at which the ambient stratification parameter N ≡ (−gρz/ρ0)½ becomes important. For values of I larger than ∼ 3000, inertial subranges are observed in all spectra, and the spectral ratio ϕ22/ϕ11 of cross-stream to streamwise spectral densities reaches the isotropic value of 4/3 for about a decade in wavenumber. As ks/kb decreases, inertial subranges vanish, but spectra of the cross-stream and streamwise components continue to satisfy isotropic relationships at dissipation wavenumbers. We provide a criterion for when ε may safely be estimated from a single measured component of the dissipation tensor, and also explore questions of appropriate low-wavenumber normalization for buoyancy-modified turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 231 - 280
Copyright
© 1984 Cambridge University Press

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