Turbulent open-channel flows over mobile granular low-tortuosity beds: velocity distribution and friction factor

Open channel flows over granular mobile beds are affected by the nature and intensity of hyporheic/surface mass and momentum exchanges. Near-bed surface mean flow and turbulence find an equilibrium with the flow in the hyporheic region and with the type and amount of granular material transported in equilibrium conditions. The processes involved in these adaptive process are not well known. This work addresses this knowledge gap and it is aimed at describing the effect of the hydraulic conductivity on the friction factor and on the parameters of the log-law that is thought to constitute a valid model for the turbulent flow in the overlapping region of fully developed hydraulically rough boundary layers over mobile cohesionless beds. To fulfil the objectives, experimental tests performed in high conductivity beds (mono-sized glass sphere beads) are compared with the existing database of low conductivity beds of Ferreira et al. (2012), keeping constant the range of values of porosity, Shields parameters and roughness Reynolds numbers. The hydraulic conductivity is varied by changing the tortuosity (and the dimensions of the pore paths) and not the porosity.

A new database of instantaneous velocities was acquired with Particle Image Velocimetry (PIV) and processed to gather time-averaged velocities and space-time (double-averaged) quantities, namely velocities, Reynolds stresses and form-induced stresses. The hydraulic conductivity was measured for both types of bed.

The parameters of log-law obtained from high conductivity are compared with low conductivity of existing database, for mobile and immobile bed conditions. The main finding can be summarized as follows.

i. Hydraulic conductivity does not affect the location of the zero plane of the log-law, the thickness of the region above the crests where the flow is determined by roughness.

ii. Increasing the hydraulic conductivity does not appear to decrease the value of bed roughness parameters such as the roughness heigh.

iii. Higher hydraulic conductivity is associated to a structural change: the same near-bed velocity can be achieved with lower shear stress in the inner region. A lower friction factor, (u_*/U)², is thus registered.

iv. Flows over high conductivity beds appear drag-reducing even if roughness parameters do not change appreciably.

This work was partially funded by FEDER, program COMPETE, and national funds through the Portuguese Foundation for Science and Technology (FCT) project ASHES - PTDC/ECI-EGC/29835/2017