Anomalous scaling of a randomly advected passive scalar

Solenoidal advection in [ital d] dimensions may induce inertial-range behavior [l angle][vert bar][ital T]([bold x],[ital t])[minus][ital T]([bold x]+[bold r],[ital t])[vert bar][sup [ital n]][r angle][proportional to][ital r][sup [zeta][ital n]([ital T])] of a passive scalar field [ital T]([bold x]...

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Bibliographic Details
Published in:Physical review letters 1994-02, Vol.72 (7), p.1016-1019
Main Author: Kraichnan, RH
Format: Article
Language:English
Subjects:
665000 - Physics of Condensed Matter- (1992-)
ADVECTION
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFUSION
FLUID FLOW
MANY-BODY PROBLEM
MASS TRANSFER
MOLECULES
MOMENT OF INERTIA
RANDOMNESS
SCALARS
SCALING LAWS
TURBULENT FLOW
TWO-BODY PROBLEM
VELOCITY
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Summary:Solenoidal advection in [ital d] dimensions may induce inertial-range behavior [l angle][vert bar][ital T]([bold x],[ital t])[minus][ital T]([bold x]+[bold r],[ital t])[vert bar][sup [ital n]][r angle][proportional to][ital r][sup [zeta][ital n]([ital T])] of a passive scalar field [ital T]([bold x],[ital t]). If the velocity field changes very rapidly in time, the [zeta][sub [ital n]]([ital T]) are determined by the two-particle eddy-diffusion coefficient [eta]([ital r])[proportional to][ital r][sup [zeta]([eta])]. An approximation to the molecular-diffusion terms yields [zeta][sub [ital n]]([ital T])=1/2 [radical]2[ital nd][2[minus][zeta]([eta])]+[alpha][sup 2] [minus]1/2[alpha] where [alpha]=[ital d]+[zeta]([eta])[minus]2. As [ital n][r arrow][infinity], [zeta][sub [ital n]]([ital T])[proportional to] [radical][ital nd] .
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.72.1016