Analytical Froude number solution for reservoir density inflows

This research presents a theoretical Froude number model at the incipient plunging point for a gravity current advancing into a sloping ambient reservoir. The analysis is based on the balance of potential energy, kinetic energy and energy losses. The Froude number at the incipient plunging point attracted attention in recent years. There are two opinions: either the Froude number is considered a constant, whereas others find it as variable in a wide range, depending on the bottom slope and the sediment concentration. The theoretical solution presented herein resolves the problem by stating that the Froude number is the function of bottom slope, relative thickness of the density current and the friction coefficient. Moreover, this theoretical analysis unifies all previous researches culminating in a general solution of the problem.