Forces on stationary particles in near-bed turbulent flows

In natural flows, bed sediment particles are entrained and moved by the fluctuating forces, such as lift and drag, exerted by the overlying flow on the particles. To develop a better understanding of these forces and the relation of the forces to the local flow, the downstream and vertical components of force on near-bed fixed particles and of fluid velocity above or in front of them were measured synchronously at turbulence-resolving frequencies (200 or 500 Hz) in a laboratory flume. Measurements were made for a spherical test particle fixed at various heights above a smooth bed, above a smooth bed downstream of a downstream-facing step, and in a gravel bed of similarly sized particles as well as for a cubical test particle and 7 natural particles above a smooth bed. Horizontal force was well correlated with downstream velocity and not correlated with vertical velocity or vertical momentum flux. The standard drag formula worked well to predict the horizontal force, but the required value of the drag coefficient was significantly higher than generally used to model bed load motion. For the spheres, cubes, and natural particles, average drag coefficients were found to be 0.76, 1.36, and 0.91, respectively. For comparison, the drag coefficient for a sphere settling in still water at similar particle Reynolds numbers is only about 0.4. The variability of the horizontal force relative to its mean was strongly increased by the presence of the step and the gravel bed. Peak deviations were about 30% of the mean force for the sphere over the smooth bed, about twice the mean with the step, and 4 times it for the sphere protruding roughly half its diameter above the gravel bed. Vertical force correlated poorly with downstream velocity, vertical velocity, and vertical momentum flux whether measured over or ahead of the test particle. Typical formulas for shear-induced lift based on Bernoulli's principle poorly predict the vertical forces on near-bed particles. The measurements suggest that particle-scale pressure variations associated with turbulence are significant in the particle momentum balance.