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Explicit expressions for eddy-diffusivity fields and effective large-scale advection in turbulent transport

Published online by Cambridge University Press:  19 April 2016

S. Boi ,
A. Mazzino  and
G. Lacorata
S. Boi
Affiliation:
Department of Chemical, Civil and Environmental Engineering (DICCA), University of Genova, 16145 Genova, Italy INFN, Genova Section, 16146 Genova, Italy
A. Mazzino*
Affiliation:
Department of Chemical, Civil and Environmental Engineering (DICCA), University of Genova, 16145 Genova, Italy INFN, Genova Section, 16146 Genova, Italy CINFAI Consortium, Genova Section, 16145 Genova, Italy
G. Lacorata
Affiliation:
Istituto di Scienze dell’Atmosfera e del Clima, Consiglio Nazionale delle Ricerche, Lecce, Italy
*
†Email address for correspondence: andrea.mazzino@unige.it
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Abstract

Large-scale transport is investigated in terms of new explicit expressions for eddy diffusivities and effective advection obtained from asymptotic perturbative methods. The carrier flow is formed by a large-scale component plus a small-scale contribution mimicking a turbulent flow. The scalar dynamics is observed in its pre-asymptotic regimes (i.e. on scales comparable to those of the large-scale velocity). The resulting eddy diffusivity is thus a tensor field which explicitly depends on the large-scale velocity. Small-scale interactions also cause the emergence of an effective large-scale (compressible) advection field which, as a result of the present study however, turns out to be of negligible importance. Two issues are addressed by means of Lagrangian simulations: quantifying the possible deterioration of the eddy-diffusivity/effective advection description by reducing to zero the spectral gap separating the large-scale velocity component from the small-scale component; comparing the accuracy of our closure against other simple, reasonable, options. Answering these questions is important in view of possible applications of our closure to tracer dispersion in environmental flows.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 524 - 548
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Copyright
© 2016 Cambridge University Press 

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