On the governing equations for horizontal and vertical coupling of one- and two-dimensional open channel flow models

One-dimensional (1D) models of open-channel flow are efficient for simulating in-channel hydrodynamics over long reaches and time periods, but cannot accurately simulate overbank flows that require two-dimensional (2D) models. The derivation and discussion of the behaviour of the coupling terms for horizontal and vertical coupling of the governing equations of 1D and 2D flow are presented here for the first time. Transfer terms for mass and momentum are introduced. Also, for the first time, the quantification of these transfer terms for the case of an experimental meandering channel with overbank flow is presented. For both coupling methods and relatively high overbank flow depth, the advective momentum transfer exceeded the diffusive momentum transfer. The diffusive momentum transfer has similar magnitude between both coupling approaches. The advective momentum transfer was one order of magnitude higher for the horizontal-coupling approach than for the vertical-coupling approach.