Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2007-03-25
J. Fluid Mech. 583, pp. 189-198 (2007)
Nonlinear Sciences
Chaotic Dynamics
10 pages, 1 figure, submitted to Journal of Fluid Mechanics
Scientific paper
10.1017/S0022112007006520
The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the spectrum, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is in the injection mechanism, the advecting velocity here being statistically homogeneous and isotropic. Our main results can be summarized as follows. 1) For a very large velocity integral scale, a pure scaling behaviour in the distance between the two points emerges only if their separation is much smaller than their distance from the point source. 2) The value we have found for the scaling exponent suggests the existence of a direct cascade, in spite of the fact that here the forcing integral scale is formally set to zero. 3) The combined effect of a finite inertial-range extension and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that we have quantified and discussed.
Afonso Marco Martins
Celani Antonio
Mazzino Andrea
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