Vertical Distribution of Velocity and Shear Stress on the Stoss Side over Dunes
Year: 2025
Type: article
Abstract: Objective Dunes are shaped by the interaction between flow and sediment grains at the riverbed. The flow structures are influenced by bedforms and exhibit non-uniform characteristics due to changes in asymmetric features. Common formulas and predictors of flow structure are primarily based on the horizontal flow velocity over a flat bed and are described using length-averaged data of dunes. However, velocity over sand dunes continuously accelerates and decelerates along the stoss side, and the inherent relationship between the horizontal and vertical components is often neglected in velocity profile calculations. Experimental data and theoretical analysis are utilized to examine the variation characteristics of velocity and turbulent shear stress on the stoss side of dunes. Vertical distribution formulas for velocity and shear stress are derived, incorporating information on flow velocity's horizontal and vertical components. This study further reveals the effect of bedforms on flow characteristics and improves the calculation accuracy of velocity and turbulent shear stress over dunes.Methods The distributions of velocity and shear stress along the stoss side were quantitatively analyzed based on experimental data from flume studies with dunes. Statistical methods were employed to propose the concept of the flow velocity deviation angle. A sub-coordinate system near the riverbed was established based on dune geometry, and the relationship between the standard coordinate system and the sub-coordinate system was derived using coordinate rotation. Utilizing the vertical two-dimensional flow momentum equation and the Boussinesq hypothesis, theoretical derivations for the vertical distribution formulas of velocity and shear stress on the stoss side of dunes were developed. Experimental data from two published studies were utilized to validate the proposed formulas.Results and Discussions The variation characteristics of flow structure over dunes were influenced by both the stoss side angle and the horizontal distance along the stoss side. As the flow passed over the crest, velocity exhibited dynamic deceleration in the main flow area and acceleration near the bottom, causing a positive flow velocity deviation angle near the water surface. With decreasing relative water depth, the flow velocity deviation angle became negative, reaching its minimum at 0.1 times the relative water depth before returning to a positive value downstream along the stoss side. The distribution of the flow velocity deviation angle after the reattachment point followed an exponential function and was accurately described. The velocity vector variation with water depth was correlated with the velocity vector near the bottom of the stoss side through coordinate transformation. The probability distribution of fluctuating velocity, considering water particle interactions, aligned with a binormal distribution. The vertical distributions of velocity and turbulent shear stress on the stoss side of dunes were derived from the vertical two-dimensional dynamic flow equations, incorporating both horizontal and vertical flow velocity components. Validation results showed that the calculated values closely matched the measured flume data for both deep and shallow water depths, and the proposed velocity formula effectively captured velocity distribution characteristics influenced by velocity vector adjustments along the stoss side. The feedback effect of bedforms on flow structure was also evident in the distribution patterns of the momentum transfer coefficient and turbulent diffusion flux, which were well described by the established formulas and aligned with experimental observations. As flow progressed downstream along the stoss side, the vertical distribution of the momentum transfer coefficient exhibited a trend of monotonically increasing. The vertical velocity distribution over dunes continuously evolved from trough to crest, reflecting the complex characteristics of turbulent structure.Conclusions The results demonstrated that the established flow velocity deviation angle formula effectively captured the adjustment mechanisms of the flow velocity vector along the stoss side of dunes. Mathematical expressions describing the transformation relationships between standard and sub-coordinate systems were derived using coordinate rotation, and vertical distribution formulas for flow velocity and turbulent shear stress were derived, incorporating the dynamic characteristics of horizontal and vertical components of flow velocity. Comparison between experimental data and calculated values indicated that the proposed expressions effectively characterized the influence of sand dunes on the spatial distribution of flow velocity for both deep and shallow water depths. However, the influence of boundary layer separation over dunes was not fully considered when deriving the formulas for vertical velocity and turbulent shear stress distribution. Therefore, further research is necessary to investigate the adjustment mechanisms of turbulent structure and the spatial distribution characteristics of flow velocity resulting from boundary layer separation over dunes.
Authors: Qing FENG, Qianlu XIAO, Xiaohua ZHANG, Yanshuang ZHENG, Bin LI
Language: English
Subfield: Ecology
Field: Environmental Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7062826388
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