The total flow control equations and the characteristics of unsteady gradually varied flow in open channels

Most unsteady channel flows in nature and practical engineering appear as gradually varied ones, and in the free surface, the deformation conforms to the long wave hypothesis. One-dimensional total flow models were usually used to for the numerical simulation of long-term and long-distance reaches to describe the water movements, however, the models lack a clear relationship between the three-dimensional flow field and the total flow field. Moreover, few studies of the variations of the roughness coefficient against the time in unsteady flows were conducted. The following results are obtained through the theoretical analysis and the numerical simulations in this paper. (1) One-dimensional total flow control equations of the unsteady gradually varied flow in open channels are obtained directly from the mathematical model of the viscous fluid motion, and can both reflect the influence of the turbulence and provide an explicit expression of the energy slope term. These equations establish a direct connection between the descriptions of the three-dimensional flow fields and the one-dimensional total flows. (2) Synchronous prototype observation data and planar two-dimensional numerical simulation results are used to extract the one-dimensional total flow information and discuss the total flow characteristics. (3)The orders of magnitude for terms in the total flow motion equation are compared, and the variation of the roughness coefficient against the time is analyzed.