Advection models of longitudinal dispersion in rivers

Abstract

A derivation is presented of a general cross-section averaged model of longitudinal dispersion, which is based on the notion of the advection of tracer particles. Particle displacement length and particle travel time are conceived as stochastic variables, and a joint probability density function is introduced to arrive at an integral advection model for the cross-section averaged concentration. Starting from this model special advection models known from the literature are obtained in a consistent way. These models, in which only the travel time is a stochastic variable, predict skewed tracer concentration contributions of the kind observed in the field, but satisfy the condition of approach to Gaussian behaviour for large spreading times. A relationship between the particle displacement length and the longitudinal dispersion coefficient is derived. The application of advection models to non-uniform rivers and the relationship with the dead-zone model are outlined.