2D Advective-Diffusive Transport of Dissolved Oxygen in Channels

Abstract

A two-dimensional (2D) theoretical analysis of the dissolved-oxygen (DO) concentration in rectangular channels is performed. It was assumed that the dissolved-oxygen concentration was affected by constant longitudinal advection, constant transverse diffusion, consumption by dissolved biochemical oxygen demand (BOD) and reaeration. The solution obtained presents the same behavior as conservative constituents and first-order decay constituents when expressed in the nondimensional form given by the ratio between the concentration and the cross-sectional concentration for the corresponding cross section. An order-of-magnitude analysis of the constants involved suggests that the location of maximum DO deficit for a bank discharge occurs in a region of the channel where the dissolved oxygen is almost completely mixed across the transverse direction. In this case, both one-dimensional (1D) and 2D dissolved oxygen models yield similar values for the location and value of the critical DO deficit. This solution may be useful as a first estimate of what happens in real situations as well as to provide a way to assess the performance of algorithms that numerically solve the DO transport equation.