Passive Scalar: Scaling Exponents and Realizability

Details Passive Scalar: Scaling Exponents and Realizability Passive Scalar: Scaling Exponents and Realizability

1996-11-16

arxiv.org/abs/chao-dyn/9611007v2

Phys. Rev. Lett. 78 (1997) 4922-4925

Nonlinear Sciences

Chaotic Dynamics

Substantially revised to conform with published version. Revtex (4 pages) with 2 postscript figures. Send email to rhk@lanl.go

Scientific paper

10.1103/PhysRevLett.78.4922

An isotropic passive scalar field $T$ advected by a rapidly-varying velocity field is studied. The tail of the probability distribution $P(\theta,r)$ for the difference $\theta$ in $T$ across an inertial-range distance $r$ is found to be Gaussian. Scaling exponents of moments of $\theta$ increase as $\sqrt{n}$ or faster at large order $n$, if a mean dissipation conditioned on $\theta$ is a nondecreasing function of $|\theta|$. The $P(\theta,r)$ computed numerically under the so-called linear ansatz is found to be realizable. Some classes of gentle modifications of the linear ansatz are not realizable.

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