The $Re$-number dependence of the longitudinal dispersion in a turbulent channel flow

Abstract

In Taylor's theory, the longitudinal dispersion in turbulent pipe flows approaches, on long timescales, a diffusive behavior with a constant diffusivity $K_L$, that depends \emph{empirically} on the Reynolds number $Re$. We show that the dependence on $Re$ can be determined from the turbulent energy spectrum. By using the intimate connection between the friction factor and longitudinal dispersion in wall-bounded turbulence, we predict different asymptotic scaling laws of $K_L(Re)$ depending on the different turbulent cascades in two-dimensional turbulence. We also explore numerically the $K_L(Re)$ dependence in turbulent channel flows with smooth and rough walls using a lattice Boltzmann method.

References in corpus (5)

• Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar
• Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory
• Anomalous Scaling in the N-Point Functions of Passive Scalar
• Macroscopic effects of the spectral structure in turbulent flows
• The friction factor of two-dimensional rough-boundary turbulent soap film flows