Laminar flow of constant-flux released gravity currents: Friction factor-Reynolds number relationship

This study aims to provide a relationship for the friction factor, $C_{f}$, in terms of the Reynolds number, \textit{Re}, for two-dimensional constant-flux release gravity currents during viscous-buoyancy propagation phase. Motivation of this study was related to the pipeline disposal of high-concentration dredged fluid-mud. Such disposal operations form non-Newtonian gravity currents that propagate over the coastal seafloor. Our theoretical and experimental analysis resulted in $C_{f}$\textit{--Re} relationships for both Newtonian (e.g. saline solution) and power-law (e.g. non-Newtonian fluid mud) fluids. A large number of experiments were conducted with different concentrations of both fluid mud mixtures (Kaolinite clay mixed with tap water) and saline solutions in a laboratory tank [dimensions: 4.3$m$ x 0.25$m$ x 0.5$m$]. In the experiments, different depths of ambient fluid (tap water) were considered. To determine the experimental $C_{f}$ values for the viscous-buoyancy propagation phase, theoretical analysis was conducted to relate $C_{f}$ to the experimental measurables. Based upon experimental observations, $C_{f}$ is shown to relate to \textit{Re} of the gravity currents inversely for both Newtonian and power-law fluids. While Newtonian gravity currents revealed a single value of the constant of proportionality for the $C_{f}$\textit{--Re} relationship, power-law gravity currents revealed multiple values of the constant of proportionality that depends on the fluid-mud concentration.