Long-term dispersion in unsteady skewed free surface flow

Abstract

An analysis of two-dimensional horizontal plane shear dispersion in steady, periodic, almost-periodic and randomly forced skewed free surface flow is presented. A two-time scale perturbation analysis of the advection-diffusion equation is used to derive the two-dimensional advection-dispersion equation and the horizontal dispersion coefficient tensor. For combinations of steady, periodic and almost-periodic flow, the time dependent dispersion coefficient tensor contains steady terms and periodic terms at frequencies associated with the forcing frequencies and their sums and differences. For combinations of steady, periodic, almost-periodic and stationary random forcings, the expected value dispersion coefficient tensor contains terms associated with the steady forcings and terms associated with the unsteady forcings represented by the spectral density functions of the unsteady forcings. Estimates of the magnitude of the expected value dispersion coefficient tensor are presented for representative estuarine and continental shelf conditions.