Friction slope in depth-averaged flow

Due to the manner in which the friction slope S-f is calculated, many two-dimensional (2D) depth-averaged models include only bottom friction. Specifically, 2D depth-averaged models that assume vertical channel sidewalls and utilize free-slip boundary conditions do not account for the friction due to the channel sidewalls. The principal intent of this paper is to inform modelers of this largely neglected issue, establish the validity of the aforementioned statement, and introduce a strategy for alleviating the problem. First, the relevant equations are presented. Based on these equations, the problem is clearly explained and interpreted. Further illustration is provided by analyzing a backwater profile in a straight rectangular channel. The one-dimensional (1D) and 2D computed results are compared with Lansford and Mitchell's experimental data. The 2D numerical solution does not coincide with the experimental data unless the 2D friction slope equation is modified to account for sidewall friction.