Laminar bottom gravity currents: friction factor–Reynolds number relationship

Abstract

ABSTRACTThis study elucidates a relationship between the Fanning friction factor and the Reynolds number for the laminar propagation of constant-flux gravity currents. The particular motivation for this study was related to the pipeline disposal of dredged fluid-mud where non-Newtonian bottom gravity currents form. The power-law rheology model, which has been shown to model fluid-mud rheology well, was incorporated in the theoretical analysis. The proposed Fanning friction factor–Reynolds number relationship includes a proportionality constant (henceforth, the shape factor) that considers the shape of the current. For non-Newtonian fluid-mud gravity currents, a relationship for the shape factor was developed through laboratory experiments. Different potential applications of the developed friction factor–Reynolds number relationship are discussed. In this regard, a new viscous propagation model was developed and evaluated through comparisons with laboratory experimental data for fluid-mud gravity currents. The approach presented in this manuscript can be extended for currents of different fluids propagating over smooth and rough bottoms.