Transport of Sand Grains by Suspension: Experimental Validation of the Mixing Length Theory of Turbulence

Suspended sand grains in low-concentration flows are generally assumed to be supported by flow turbulence which, in turn, depends upon the basal shear stress. Recent research, however, has questioned the validity and continuing application of the underlying classic “mixing-length” theory of turbulence developed by Reynold’s, Prandtl, von Karman and others. Unfortunately, ever since the theory was developed over fifty years ago, it has not been technically possible to fully test its assumptions and predictions. Concerns are now being raised about discrepancies in bed shear stress estimates obtained from the three traditional approaches i.e. Law-of-the-Wall, Reynold’s stress decomposition and slope. Arising from these concerns, we attempt, in this paper, to re-examine and re-validate the key assumptions of the turbulence-suspension theory using detailed and unusually large fluctuating flow velocity dataset obtained from flume tank experiments instrumented with modern flow velocity sampling equipment.
Our results and data analysis show reasonable agreement in the bed shear stress estimates and that “mixing-length” theory produces a good estimate for the time-averaged velocity profile with depth. Thus, this widely used mathematical approximation of turbulent suspension remains supported by experimental evidence and can continue to be confidently utilized