Yes / For overbank flows in meandering channels, the flow direction along a meander varies and is affected by floodplain vegetation. This study proposes a model for predicting the depth-averaged two-dimensional flow direction (depth-averaged flow angle) along a meander in smooth and vegetated meandering compound channels. Laboratory experiments were performed in smooth and vegetated channels. Measurements show that the height of the secondary current cell in the main channel is increased by dense floodplain vegetation comparing with that in a non-vegetated channel. A method of determining the height of the cell is proposed. At the middle section between the apex and exit sections, where the secondary current cell is absent, the depth-averaged flow angle is independent of the height of the cell. Beyond the middle section, a new secondary current cell is formed, and the flow angle is highly dependent on the height of the cell. The proposed model is thoroughly verified using the flume experimental and field observed data. Good agreement is obtained between predictions and measurements, indicating that the proposed model is capable of accurately predicting the depth-averaged flow angle along a meander in smooth and vegetated meandering compound channels. / National Key Research and Development Program of China (No. 2016YFC0402302), and the National Natural Science Foundation of China (Nos. 51709022, 51609160 and 51539007)

Yes / The Prandtl second kind of secondary current occurs in any narrow channel flow causing velocity dip in the flow velocity distribution by introducing the anisotropic turbulence into the flow. Here, a study was conducted to explain the occurrence of the secondary current in the outer region of flow velocity distribution using a universal expression. Started from the basic Navier-Stokes equation, the velocity profile derivation was accomplished in a universal way for both smooth and rough open channel flows. However, the outcome of the derived theoretical equation shows that the smooth and rough bed flows give different boundary conditions due to the different formation of log law for smooth and rough bed cases in the inner region of velocity distribution. Detailed comparison with a wide range of different measurement results from literatures (from smooth, rough and field measured data) evidences the capability of the proposed law to represent flow under all bed roughness conditions.

Yes / Turbulence-induced secondary currents are commonly present in straight natural as well as artificial open channels without bed forms. Different structures of cellular secondary currents can be seen in open-channel flows due to various bed configurations. In our study, mathematical models of turbulence-induced secondary currents in the vertical and transverse directions within a straight open rectangular channel with alternate rough and smooth longitudinal bed strips are proposed. The proposed models are derived using appropriate theoretical and mathematical analysis. Most of the previous models of secondary currents in the literature are proposed empirically and without proper mathematical derivations. The effects of fluid viscosity and eddy diffusivity are included in the present study to make it more practical. Initially, the governing equation for vertical secondary flow velocity is derived from continuity and the Reynolds-Averaged Navier Stokes equations. Then, the proposed problem is divided into two sub-considerations, corresponding to the base flow and perturbed flow. Finally, these sub-problems are analytically solved using method of variables separation with suitable boundary conditions. Different models to consider two different types of bed-roughness configurations (i.e. equal and unequal lengths of smooth and rough longitudinal bed strips) are obtained. Apart from velocity formulations, models of the stream function are proposed for these two types of bed configurations. All proposed models are validated using existing experimental data for the various bed configurations in open-channel flows and satisfactory results have been obtained. These present models are also compared with empirical models from the literature and they are found to be more effective in representing both types of bed-roughness configurations. The effects of bed configuration on the streamlines of settling velocity are also investigated. Results show that laterally-skewed secondary cells (which occurs due to unequal smooth and rough bed strips), have significant effects on the closed ω-streamlines in terms of shape and location of the centre of these streamlines. More precisely, it is found that the area of the downflow zone proportionally increases with the length of rough-bed strips.

Yes / The flow in the main channel of a meandering compound channel does not occur in the ridge direction because of the effect of the upstream floodplain flows. This study proposes a model for estimating the flow direction in the depth-averaged two-dimensional domain (depth-averaged flow angles) between the entrance and the apex sections. Detailed velocity measurements were performed in the region between the meander entrance section and apex section in a large-scale meandering compound channel. The vertical size of the secondary current cell is highly related to the depth-averaged flow angle; thus, the means of the local flow angles above the secondary current cell and within the cell are separately discussed. The experimental measurements indicate that the mean local flow angle above the cell is equal to the section angle, whereas the mean local flow angle within the cell is equal to zero. The proposed model is validated using published data from five sources. Good agreement is obtained between the predictions and measurements, indicating that the proposed model can accurately estimate the depth-averaged flow direction in the meandering compound channels. Finally, the limitations and application ranges of the model are discussed. / National Key Research and Development Program of China (No. 2016YFC0402302), the National Natural Science Foundation of China (Nos. 51539007 and 51609160)