Energy relations of density-current flows: an experimental investigation*

Three series of density-current experiments were performed in a 5.76 m flume. In the first series, the flume was horizontal, and in the second and third, it was inclined with a positive slope and negative slope, respectively. Energy relations during successive stages of density-current movement were computed from observed data, which showed an appreciable frictional energy dissipation. The computed friction factors of our experimental density-flows were compared to the friction factors for pipe flows (Moody diagram), and while the calculated friction factor increases with increasing Reynold's number within the range of our experiments (Re 2 × 10³?2 × 10⁴), it is concluded that with increasing Reynold's number above about 5 × 10⁴ the friction factor decreases. For natural turbidity currents, the Moody diagram gives a reasonable estimate of the friction factor between the current and sediment bed. The value of the friction factor for the interface between the current and overlying water was found to be about 0.2 times the friction factor for the current and flume. However, due to errors inherent in measuring the depth of the current, a value of 0.4 would be more reasonable for density-currents in our range of Reynold's number. Friction tends to decrease the value of the dimensionless coefficient in Keulegan's law of saline front and to decrease the thickness of the flow. In contrast, the presence of a slope in the direction of flow tends to compensate the effect of friction. The angle θ^c that provides the potential energy to exactly offset the energy losses incurred during movement by the density-currents in our experiments has a calculated value of 31′. An empirical formula φ= 0.935θ—0·57 relating friction, in terms of the hydraulic gradient φ, to the slope angle θ was obtained. Since the thickness of the current can be computed from the relationship between φ and θ, we estimated the thickness of naturally occurring density-currents in Swiss lakes. The results suggest the applicability of our experimental results to small turbidity currents in nature. Our analysis further indicates that large turbidity currents have a small φ and can be expected to flow very long distances on a flat abyssal plain.