Estimating transverse mixing in open channels due to secondary current-induced shear dispersion

For transverse mixing problems in open channels, the effect of secondary currents on a tracer cloud is to disperse and mix the tracer in three dimensions more rapidly than would be the case if transverse turbulent diffusion were acting alone. Transverse mixing of this kind is difficult to simulate using two-dimensional depth-averaged mixing models which typically requires the specification of an equivalent dispersivity combining the effects of vertical shear dispersion and horizontal turbulent diffusion. In this paper, a two-dimensional vertically averaged and moment (VAM) equation technique for describing the transverse mixing mechanics of passive tracer vertical shear dispersion in approximately uniform curved open channel flow is detailed. An analytical expression is generated and compared to previous works in the literature describing the longitudinal development and asymptotic value of transverse dispersivity due to secondary current vertical shear dispersion. This expression is shown to describe the changing value of dispersivity even within the advective zone where traditional two-dimensional models cannot be applied. Distributions of depth-averaged concentration generated from numerical simulations of the VAM equations are compared to other higher fidelity computational results. The practical value of this VAM analysis framework is discussed relative to the potential for implementation in modern river modeling software packages.