Dispersion in Oscillatory Flow Superimposed on Steady Flow in Open Channel

Abstract

ABSTRACTThe dispersion in an oscillatory flow superimposed on a steady flow is analyzed theoretically. On the assumption that for flow in an open channel with variable depth the transverse profile of the velocity is similar to that of steady flow, the mass conservation equation reduces to an eigenvalue problem. The distributions of concentration and dispersion coefficients are calculated numerically for the flows in channels with triangular and parabolic cross-sections. The dispersion coefficient is expressed as a function of two non-dimensional parameters, which are the ratio of the velocity of the steady flow to the amplitude of the oscillatory flow, and the ratio of the period of oscillation to the characteristic time scale of the cross-sectional turbulent mixing. It is found that the dispersion is determined by the combined effects of so-called shear effect and turbulent mixing in the transverse direction, and that the shear effect increases the dispersion coefficient whereas the transverse mixing dec...