Method of Moments for Estimating Two-Dimensional Laminar Dispersion in Curved Channels

Natural streams are characterized by complicated channel geometry features like bends, curvature and meanders. The increasing interest in studying how a stream transports and disperses a pollutant is responsible for development of models which try to find a dispersion coefficient depending on the bulk flow and channel geometry parameters.

This article studies the dispersion of a solute in a shallow curved channel. Assuming vertical mixing, the steady, two-dimensional velocity profile for laminar flow in a curved channel is used to derive the longitudinal dispersion coefficient. First, an analytic expression is derived for small curvature ratio by solving an eigenvalue problem with discrete spectrum of eigenvalues. This is complemented by a complete numerical model which has no constraints on the curvature ratio and the longitudinal diffusion coefficient is derived for wider ranges of parameters involved. Due to the asymmetric velocity profile whose maximum value is towards the inner bend, the dispersion coefficient is found to be increased. For large Peclet numbers Pe, say 1000, and for a fixed curvature ratio, (ratio of the width of the channel to its radius of curvature), say 0.5, the dispersion coefficient is 3.6 times that in a straight channel. The mean concentration profiles show that the effect of curvature is to delay the approach to normality. The results are of vital importance in understanding the transport of pollutants in shallow coastal waters.