Multiple-scale analysis and renormalization for pre-asymptotic scalar transport

Abstract

Pre-asymptotic transport of a scalar quantity passively advected by a velocity field formed by a large-scale component superimposed to a small-scale fluctuation is investigated both analytically and by means of numerical simulations. Exploiting the multiple-scale expansion one arrives at a Fokker--Planck equation which describes the pre-asymptotic scalar dynamics. Such equation is associated to a Langevin equation involving a multiplicative noise and an effective (compressible) drift. For the general case, no explicit expression for both the effective drift and the effective diffusivity (actually a tensorial field) can be obtained. We discuss an approximation under which an explicit expression for the diffusivity (and thus for the drift) can be obtained. Its expression permits to highlight the important fact that the diffusivity explicitly depends on the large-scale advecting velocity. Finally, the robustness of the aforementioned approximation is checked numerically by means of direct numerical simulations.

revtex4, 12 twocolumn pages, 3 eps figures

References in corpus (2)

• Eddy diffusivities in scalar transport
• Scalar transport in compressible flow

Cited by in corpus (10)

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• Anomalous diffusion for inertial particles under gravity in parallel flows
• Coarse-grained description of a passive scalar
• Combined role of molecular diffusion, mean streaming and helicity in the eddy diffusivity of short-correlated random flows
• Generalization of Taylor's formula to particles of arbitrary inertia
• Settling velocity of quasi-neutrally-buoyant inertial particles
• Eddy diffusivity of quasi-neutrally-buoyant inertial particles