On the dynamics of quasi-steady gravity currents flowing up a slope

Quasi-steady gravity currents propagating first on a horizontal and then up a sloping boundary are investigated by means of theoretical analysis and laboratory experiments. The bottom slope ranged from 0.18 to 1 and full- and partial-depth configurations were considered. The developed theoretical model, using the depth averaged momentum equation, provides new physical insight into the importance of the different forces that act on the current and accounts for the gravity component along the slope, whose effect increases with both the slope angle and the ratio of current to ambient fluid depths. The height of the current decreases linearly with up-slope distance and the spatial rate of decrease, expressed by the current shape parameter is determined from the theory, using the measured up slope distance at which the current stops. This current shape parameter is found to depend on the slope only and it is not dependent on the current to ambient fluid depths. It can then be used to calculate the current velocity and the up-slope distance reached by the current. It is shown that the front velocity of all performed experiments is predicted by the theory indicating that the theory remains valid up to a slope equal to 1