A time-varying diffusivity model for shear dispersion in oscillatory channel flow

Abstract

An analysis is presented of the shear dispersion in turbulent channel flow forced by a purely oscillatory pressure gradient. The flow is described by an algebraic eddy viscosity model in which the instantaneous flow and viscosity are inter-dependent. Both eddy viscosity and eddy diffusivity contain a second-harmonic time-varying component. The effective transport equation is derived using a two-time-scale perturbation analysis, which also yields a closed-form expression for the dispersion coefficient. Numerical results demonstrate that, in this problem, the time-varying component of the eddy diffusivity can have a finite effect on the dispersion coefficient, which can be as much as a 30% difference from that obtained from a time-invariant eddy viscosity model.