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Point-source scalar turbulence

Published online by Cambridge University Press:  04 July 2007

ANTONIO CELANI ,
MARCO MARTINS AFONSO  and
ANDREA MAZZINO
ANTONIO CELANI
Affiliation:
CNRS, INLN, 1361 Route des Lucioles, 06560 Valbonne, France
MARCO MARTINS AFONSO
Affiliation:
Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel
ANDREA MAZZINO
Affiliation:
Department of Physics –University of Genova & CNISM and INFN – Genova Section, via Dodecaneso 33, 16146 Genova, Italy
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Abstract

The statistics of a passive scalar randomly emitted from a point source is investigated analytically for the Kraichnan ensemble. Attention is focused on the two-point equal-time scalar correlation function, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is the injection mechanism, the advecting velocity being here statistically homogeneous and isotropic. The main question we address is on the possible existence of an inertial range of scales and a consequent scaling behaviour. The question arises from the observation that for a point source the injection scale is formally zero and the standard cascade mechanism cannot thus be taken for granted. We find from first principles that an intrinsic integral scale, whose value depends on the distance from the source, emerges as a result of sweeping effects. For separations smaller than this integral scale a standard forward cascade occurs. This is characterized by a Kolmogorov–Obukhov power-law behaviour as in the homogeneous case, except that the dissipation rate is also dependent on the distance from the source. Finally, we also find that the combined effect of a finite inertial-range extent and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that are here quantified and discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 189 - 198
Copyright
Copyright © Cambridge University Press 2007

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