A 2‐D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient

Abstract

The longitudinal dispersion coefficient, DL, is a fundamental parameter of longitudinal solute transport models: the advection‐dispersion (AD) model and various deadzone models. Since DL cannot be measured directly, and since its calibration using tracer test data is quite expensive and not always available, researchers have developed various methods, theoretical or empirical, for estimating DL by easier available cross‐sectional hydraulic measurements (i.e., the transverse velocity profile, etc.). However, for known and unknown reasons, DL cannot be satisfactorily predicted using these theoretical/empirical formulae. Either there is very large prediction error for theoretical methods, or there is a lack of generality for the empirical formulae. Here, numerical experiments using Mike21, a software package that implements one of the most rigorous two‐dimensional hydrodynamic and solute transport equations, for longitudinal solute transport in hypothetical streams, are presented. An analysis of the evolution of simulated solute clouds indicates that the two fundamental assumptions in Fischer's longitudinal transport analysis may be not reasonable. The transverse solute concentration distribution, and hence the longitudinal transport appears to be controlled by a dimensionless number , where Q is the average volumetric flowrate, Dt is a cross‐sectional average transverse dispersion coefficient, and W is channel flow width. A simple empirical relationship may be established. Analysis and a revision of Fischer's theoretical formula suggest that ɛ influences the efficiency of transverse mixing and hence has restraining effect on longitudinal spreading. The findings presented here would improve and expand our understanding of longitudinal solute transport in open channel flow.