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Evolution of scalar spectra with the decay of turbulence in a stratified fluid

Published online by Cambridge University Press:  20 April 2006

A. E. Gargett
A. E. Gargett
Affiliation:
Institute of Ocean Sciences, 9860 West Saanich Road, Sidney, B.C., Canada V8L 4B2
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Abstract

Temperature measurements taken in association with the velocity measurements described by Gargett, Osborn & Nasmyth (1984) are examined. With careful noise removal the temperature dissipation spectrum is fully resolved and χ, the dissipation rate of temperature-fluctuation variance, is determined directly. With directly measured values of χ and ε, the turbulent-kinetic-energy dissipation rate per unit mass, the observed temperature spectra are non-dimensionalized by Oboukov–Corrsin–Batchelor scaling. Shapes and levels of the resulting non-dimensional spectra are then examined as functions of the degree of isotropy (measured) in the underlying velocity field. Two limiting cases are identified: Class A, associated with isotropic velocity fields; and Class B, associated with velocity fields which are anisotropic (owing to buoyancy forces repressing vertical relative to horizontal dimensions of energy-containing ‘eddies’). The present observations suggest that the Corrsin–Oboukov–Batchelor theory does not provide a universal description of the spectrum of temperature fluctuations in water. Class A scalar spectra have neither $k^{-\frac{5}{3}}$ nor k−1 subranges: a Batchelor-spectrum fit to the high-wavenumber roll-off region yields a value of 12 for the ‘universal’ constant q. In striking contrast, the buoyancy-affected Class B spectra exhibit a clear $k^{-\frac{5}{3}}$ subrange, an approach to a k−1 subrange, and a value of q ∼ 4 which is in rough agreement with most previous estimates. Previous oceanic and atmospheric measurements are re-examined in the light of the present results. It is suggested that these previous results are also affected by vertical scale limitation. Reasons underlying the discrepancies between theories and observations are discussed: these may be different in the two classes presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 379 - 407
Copyright
© 1985 Cambridge University Press

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