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

Original · EN

In Taylor's theory, the longitudinal dispersion in turbulent pipe flows approaches, on long timescales, a diffusive behavior with a constant diffusivity Kₗ, that depends 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 Kₗ(Re) depending on the different turbulent cascades in two-dimensional turbulence. We also explore numerically the Kₗ(Re) dependence in turbulent channel flows with smooth and rough walls using a lattice Boltzmann method.