Longitudinal dispersion coefficient in ice-covered rivers

Abstract

ABSTRACTThe focus of this paper is on the ice-cover effects on the longitudinal dispersion coefficient in rivers. The dispersion coefficients due to either the vertical or transverse velocity shear are calculated using Elder’s or Fisher’s triple integral equation, respectively, based on the assumptions of a parabolic cross section and a vertical logarithmic velocity distribution in both the riverbed and the ice-cover zones. The results show that in ice-covered natural rivers, where the aspect ratio is usually larger than 10, the dispersion coefficient due to the transverse velocity shear is 50 times greater than that due to the vertical velocity shear. An analytical formula for longitudinal dispersion coefficient is further developed by the simplification of Fischer’s triple integral equation, and it is validated against field tracer tests with discrepancy between observations and predictions less than 150%. Comparing the proposed formula to the most widely-used Fischer’s formula demonstrates that for wide and shallow rivers the presence of ice-cover will lead to about a three-fold increase in the magnitude of the longitudinal dispersion.