Two timescales for longitudinal dispersion in a laminar open-channel flow

At small dimensionless timescales T(= tD / H-2), where t is the time, H is the depth of the channel and D is the molecular diffusion coefficient, the mean transverse concentration along the longitudinal direction is not in a Gaussian distribution and the transverse concentration distribution is nonuniform. However, previous studies found different dimensionless timescales in the early stage, which is not verified experimentally due to the demanding experimental requirements. In this letter, a stochastic method is employed to simulate the early stage of the longitudinal transport when the Peclet number is large. It is shown that the timescale for the transverse distribution to approach uniformity is T = 0.5, which is also the timescale for the dimensionless temporal longitudinal dispersion coefficient to reach its asymptotic value, the timescale for the longitudinal distribution to approach a Gaussian distribution is T = 1.0, which is also the timescale for the dimensionless history mean longitudinal dispersion coefficient to reach its asymptotic value.