Reynolds-mediated scale effects on the modeling of turbidity currents

Field observations of turbidity currents are rare due to the unpredictable nature of these flows. To understand the flow and sedimentation mechanisms of turbidity currents, researchers have depended on modeling at a small scale, either through laboratory experiments or numerical simulations. The problem of scaling associated with the modeling of turbidity currents has been recognized, but has not been explored adequately. Scale physical modeling of fixed-bed open channel flow considers Froude similarity alone by ensuring rough turbulent flow in the model. In case of a mobile bed model, the Shields' number is also typically matched. Non-dimensionalization of the governing equations of turbidity currents lead to two controlling dimensionless numbers, namely, the densimentric Froude number (textbf{Fr}) and the Reynolds number (textbf{Re}). Following observations are made from the analysis of the non-dimensional governing equations and boundary conditions: (i) scale-invariant results can be obtained for a conservative density current flowing over a rough boundary by satisfying the densimetric Froude similarity alone; (ii) in case of purely depositional flows, the Reynolds-mediated scale effects appear in the bottom boundary condition of the flow velocity and concentration but the effects of Reynolds number may not be strong; (iii) The Reynolds effect becomes more significant for mixed erosional and depositional turbidity currents as it appears in the entrainment rate of sediment as well. Numerical simulations of turbidity currents are conducted by imposing the densimetric Froude similarity as well as the combined densimetric Froude and Reynolds similarities at different scales. The simulation results confirm that satisfying the densimetric Froude similarity alone can produce scale-invariable results for conservative density currents over rough bed, but not for turbidity currents. Perfect matches of results at different scales can occur for turbidity currents only when combined densimetric Froude and Reynolds similarities are satisfied.