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Vertical dispersion by stratified turbulence

Published online by Cambridge University Press:  16 October 2008

E. LINDBORG  and
G. BRETHOUWER
E. LINDBORG
Affiliation:
Linné Flow Centre, Department of Mechanics, KTH, SE-100 44 Stockholm, Sweden
G. BRETHOUWER
Affiliation:
Linné Flow Centre, Department of Mechanics, KTH, SE-100 44 Stockholm, Sweden
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Abstract

We derive a relation for the growth of the mean square of vertical displacements, δz, of fluid particles of stratified turbulence. In the case of freely decaying turbulence, we find that for large times 〈δz2〉 goes to a constant value 2(EP(0) + aE(0))/N2, where EP(0) and E(0) are the initial mean potential and total turbulent energy per unit mass, respectively, a < 1 and N is the Brunt–Väisälä frequency. In the case of stationary turbulence, we find that 〈δz2〉 = 〈δb2〉/N2 + 2εPt/N2, where εP is the mean dissipation of turbulent potential energy per unit mass and 〈δb2〉 is the Lagrangian structure function of normalized buoyancy fluctuations. The first term is the same as that obtained in the case of adiabatic fluid particle dispersion. This term goes to the finite limit 4EP/N2 as t → ∞. Assuming that the second term represents irreversible mixing, we show that the Osborn & Cox model for vertical diffusion is retained. In the case where the motion is dominated by a turbulent cascade with an eddy turnover time T ≫ N−1, rather than linear gravity waves, we suggest that there is a range of time scales, t, between N−1 and T, where 〈δb2〉 = 2πCPLεPt, where CPL is a constant of the order of unity. This means that for such motion the ratio between the adiabatic and the diabatic mean-square displacement is universal and equal to πCPL in this range. Comparing this result with observations, we make the estimate CPL ≈ 3.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 614 , 10 November 2008 , pp. 303 - 314
Copyright
Copyright © Cambridge University Press 2008

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References

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