Combined Logarithmic and Linear Law for Double-Averaged Flow Velocity Profiles over Two-Dimensional Fixed Dunes

Since the existence of dunes in fluvial channels significantly alters near-bed flow structures, the related velocity profile is complex and different from that over a plane bed. To understand its average characteristics over a dune length, velocity distribution is analyzed preferably in a spatiotemporal or double-averaging manner. In this study, turbulent flow velocities over two-dimensional fixed dunes with smooth and rough surfaces are measured using particle image velocimetry (PIV). The data analysis shows that the double-averaged velocity profile generally comprises two layers, the first being linear near the bed and the second being logarithmic away from the bed. The two-layer velocity profile can be described using a unified formula, which is proposed by combining the linear and logarithmic laws in a power-sum fashion. The new formula is finally validated using the experimental data.

As a prevalent bedform in fluvial and coastal environments, dunes have been a subject of research for decades. To appreciate the average characteristics of the flow over a dune-covered bed, it would be better to perform a proper average of measurements of flow fields in both time and space domains. Such an effort was made in the present study. With the measured data, we are able to develop a new approach for unifying the velocity distribution from the dune trough to the free water surface. This is done by combining logarithmic and linear laws in a power-sum form. Although conducting fine-scale field measurements of flows over dunes is still not easy at present, the formula proposed in this paper would be of great significance in estimating dune-affected flow velocity distributions, and thus helpful for understanding flow resistance, sediment transport, and river and coastal management.