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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: [email protected]
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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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References

Adzhemyan, L. Ts., Antonov, N. V., Mazzino, A., Muratore-Ginanneschi, P. & Runov, A. V. 2001 Pressure and intermittency in passive vector turbulence. Europhys. Lett. 55, 801–806.CrossRefGoogle Scholar
Antonov, N. V., Honkonen, Y., Mazzino, A. & Muratore-Ginanneschi, P. 2000 Manifestation of anisotropy persistence in the hierarchies of magnetohydrodynamical scaling exponents. Phys. Rev. E 62, R5891–R5894.CrossRefGoogle ScholarPubMed
Bensoussan, A., Lions, J.-L. & Papanicolaou, G. 1978 Asymptotic Analysis for Periodic Structures. North-Holland.Google Scholar
Biedenharn, L. C., Louck, J. D. & Carruthers, P. A. 1981 Angular Momentum in Quantum Physics: Theory and Application. Addison-Wesley.Google Scholar
Biferale, L., Crisanti, A., Vergassola, M. & Vulpiani, A. 1995 Eddy diffusivities in scalar transport. Phys. Fluids 7, 2725–2734.CrossRefGoogle Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44 (1), 427–451.CrossRefGoogle Scholar
Boi, S., Afonso, M. M. & Mazzino, A. 2015 Anomalous diffusion of inertial particles in random parallel flows: theory and numerics face to face. J. Stat. Mech. Theory Exp. 2015 (10), P10023.Google Scholar
Castiglione, P., Crisanti, A., Mazzino, A., Vergassola, M. & Vulpiani, A. 1998 Resonant enhanced diffusion in time-dependent flow. J. Phys. A 31, 7197–7210.CrossRefGoogle Scholar
Castiglione, P., Mazzino, A., Muratore-Ginanneschi, P. & Vulpiani, A. 1999 On strong anomalous diffusion. Physica D 134, 75–93.CrossRefGoogle Scholar
Cencini, M., Mazzino, A., Musacchio, S. & Vulpiani, A. 2006 Large-scale effects on meso-scale modeling for scalar transport. Physica D 220, 146–156.CrossRefGoogle Scholar
Crisanti, A., Falcioni, M., Paladin, G. & Vulpiani, A. 1991 Lagrangian chaos: transport, mixing and diffusion in fluids. Nuovo Cimento 14 (12), 1–80.Google Scholar
Dubrulle, B. & Frisch, U. 1991 Eddy viscosity of parity-invariant flow. Phys. Rev. A 43, 5355–5364.CrossRefGoogle ScholarPubMed
Falkovich, G., Gawedzki, K. & Vergassola, M. 2001 Particles and fields influid turbulence. Rev. Mod. Phys. 73, 913–975.CrossRefGoogle Scholar
Frisch, U. 1987 Lecture on turbulence and lattice gas hydrodynamics. In Lecture Notes, NCAR-GTP Summer School June 1987 (ed. Herring, J. R. & McWilliams, J. C.), pp. 219–371. World Scientific.Google Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Fung, J. C. H., Hunt, J. C. R., Malik, N. A. & Perkins, R. J. 1992 Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid Mech. 236, 281–318.CrossRefGoogle Scholar
Gama, S., Vergassola, M. & Frisch, U. 1994 Negative eddy viscosity in isotropically forced two-dimensional flow: linear and nonlinear dynamics. J. Fluid Mech. 260, 95–126.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Kaneda, Y., Ishihara, T. & Gotoh, K. 1999 Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. Phys. Fluids 11, 2154–2166.CrossRefGoogle Scholar
Lacorata, G., Mazzino, A. & Rizza, U. 2008 3D chaotic model for sub-grid turbulent dispersion in large eddy simulations. J. Atmos. Sci. 65, 2389–2401.CrossRefGoogle Scholar
Majda, A. J. & Kramer, P. R. 1999 Simplified models for turbulent diffusion: theory, numerical modelling, and physical phenomena. Phys. Rep. 314, 237–574.CrossRefGoogle Scholar
Mauri, R. 2003 Heat and mass transport in nonhomogeneous random velocity fields. Phys. Rev. E 68, 066306.CrossRefGoogle ScholarPubMed
Mazzino, A. 1997 Effective correlation times in turbulent scalar transport. Phys. Rev. E 56, 5500–5510.CrossRefGoogle Scholar
Mazzino, A., Musacchio, S. & Vulpiani, A. 2005 Multiple-scale analysis and renormalization for preasymptotic scalar transport. Phys. Rev. E 71, 011113.CrossRefGoogle ScholarPubMed
Mazzino, A. & Vergassola, M. 1997 Interference between turbulent and molecular diffusion. Europhys. Lett. 37, 535–540.CrossRefGoogle Scholar
Pavliotis, G. A. & Kramer, P. R. 2002 Homogenized transport by a spatiotemporal mean flow with small-scale periodic fluctuations. In Proceedings of the 4th International Conference on Dynamical Systems and Differential Equations, pp. 1–8.Google Scholar
Pavliotis, G. A. & Stuart, A. M. 2007 Multiscale Methods: Averaging and Homogenization. Springer.Google Scholar
Vergassola, M. & Avellaneda, M. 1997 Scalar transport in compressible flow. Physica D 106, 148–166.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 73, 203–240.CrossRefGoogle Scholar