Inertial-diffusive range for a passive scalar advected by a white-in-time velocity field

U. Frisch; A. Wirth

doi:10.1209/epl/i1996-00170-7

All issues

Volume 35 / No 9 (September III 1996)

Europhys. Lett., 35 9 (1996) 683-688

Abstract

Issue		Europhys. Lett. Volume 35, Number 9, September III 1996


Page(s)		683 - 688
Section		Classical areas of phenomenology
DOI		https://doi.org/10.1209/epl/i1996-00170-7
Published online		01 September 2002

Europhys. Lett., 35 (9), pp. 683-688 (1996)

Inertial-diffusive range for a passive scalar advected by a white-in-time velocity field

U. Frisch and A. Wirth

CNRS, Observatoire de Nice - B.P. 229, 06304 Nice Cedex 4, France

Received: 24 June 1996
Accepted: 9 August 1996

Abstract

It is shown analytically and by Monte Carlo simulations that a passive scalar with finite diffusivity, advected by a white-in-time velocity field with a power law spectrum $\propto k^{-1-\xi}$ ( $0<\xi<2$ ), has an inertial-diffusive range with a spectrum $\propto k^{-3-\xi}$ . This is the analog of the Batchelor-Howells-Townsend (J. Fluid Mech., 5 (1959) 134) phenomenological derivation of the $k^{-17/3}$ law for low-Schmidt-number passive-scalar dynamics in ordinary turbulence.

PACS: 47.27.Qb – Turbulent diffusion

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