Inertial-diffusive range for a passive scalar advected by a white-in-time velocity field
Résumé
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-ξ (0 < ξ < 2), has an inertial-diffusive range with a spectrum propto k-3-ξ. 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.