A Mathematical Model of Two-Dimensional Vertical Flow Based on the Dual Approach

The mathematical model of two-dimensional vertical flow is commonly constructed using the classic average method by taking the integral from the right to the left riverbank of the three-dimensional Reynolds averaged Navier–Stokes equations. Hence, average quantities obtained from this approach are not generalized in comparison to ones estimated by the dual approach. This paper presents a dual approach to establish the two-dimensional vertical flow equations. The setup model will be more complex than the classic one because the integration can be done locally several times. In this paper, the author performed twice integrals: (i) the first integration is from the right riverbank to the intermediate vertical surface layer between the right bank and the left bank, and then (ii) the second integration is from the right bank to the left bank. The improved two-dimensional vertical flow model received from this dual approach allows the calculation of flow characteristics more accurate than the classical method. In other words, it provides some flexible parameters to adjust based on the field or experimental data.