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Numerical study of vertical dispersion by stratified turbulence

Published online by Cambridge University Press:  17 July 2009

G. BRETHOUWER  and
E. LINDBORG
G. BRETHOUWER*
Affiliation:
Linné Flow Centre, Department of Mechanics, KTH, SE-100 44 Stockholm, Sweden
E. LINDBORG
Affiliation:
Linné Flow Centre, Department of Mechanics, KTH, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

Numerical simulations are carried out to investigate vertical fluid particle dispersion in uniformly stratified stationary turbulent flows. The results are compared with the analysis of Lindborg & Brethouwer (J. Fluid Mech., vol. 614, 2008, pp. 303–314), who derived long- and short-time relations for the mean square vertical displacement 〈δz〉 of fluid particles. Several direct numerical simulations (DNSs) with different degrees of stratification and different buoyancy Reynolds numbers are carried out to test the long-time relation 〈δz2〉 = 2ϵPt/N2. Here, ϵP is the mean dissipation of turbulent potential energy; N is the Brunt–Väisälä frequency; and t is time. The DNSs show good agreement with this relation, with a weak dependence on the buoyancy Reynolds number. Simulations with hyperviscosity are carried out to test the relation 〈δz2〉 = (1+πCPL)2ϵPt/N2, which should be valid for shorter time scales in the range N−1 ≪ t ≪ T, where T is the turbulent eddy turnover time. The results of the hyperviscosity simulations come closer to this prediction with CPL about 3 with increasing stratification. However, even in the simulation with the strongest stratification the growth of 〈δz2〉 is somewhat slower than linear in this regime. Based on the simulation results it is argued that the time scale determining the evolution of 〈δz2〉 is the eddy turnover time, T, rather than the buoyancy time scale N−1, as suggested in previous studies. The simulation results are also consistent with the prediction of Lindborg & Brethouwer (2008) that the nearly flat plateau of 〈δz2〉 observed at t ~ T should scale as 4EP/N2, where EP is the mean turbulent potential energy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 149 - 163
Copyright
Copyright © Cambridge University Press 2009

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