STOCHASTIC-THEORY FOR IRREGULAR STREAM MODELING .2. SOLUTE TRANSPORT

A stochastic theory is developed for longitudinal dispersion in natura l streams. Irregular variations in river width and bed elevation are c onveniently represented as one-dimensional random fields. Longitudinal solute migration is described by a one-dimensional stochastic solute transport equation. When boundary variations are small and statistical ly homogeneous, the stochastic transport equation is solved in closed- form using a stochastic spectral technique. The results show that larg e scale longitudinal transport can be represented as a gradient disper sion process described by an effective longitudinal dispersion coeffic ient. The effective coefficient reflects longitudinal mixing due to fl ow variation both within the river cross section and along the Bow and can be considerably greater than that of corresponding uniform channe ls. The discrepancy between uniform channels and natural rivers increa ses as the variances of river width and bed elevation increase, especi ally when the mean flow Froude number is high.