Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

A theoretical and experimental investigation of the propagation of free-surface, channelized viscous gravity currents is conducted to examine the combined effects of fluid rheology, boundary geometry and channel inclination. The fluid is characterized by a power-law constitutive equation with behaviour index n. The channel cross section is limited by a rigid boundary of height parametrized by k and has a longitudinal variation described by the constant b ≥ 0. The cases k >=< 1 are associated with wide, triangular and narrow cross sections. For b>0, the cases k ≷ 1 describe widening channels and squeezing fractures; b=0 implies a constant cross-sectional channel. For a volume of released fluid varying with time like tα, scalings for current length and thickness are obtained in self-similar forms for horizontal and inclined channels/fractures. The speed, thickness and aspect ratio of the current jointly depend on the total current volume (α), the fluid rheological behaviour (n), and the transversal (k) and longitudinal (b) geometry of the channel. The asymptotic validity of the solutions is limited to certain ranges of parameters. Experimental validation was performed with different fluids and channel cross sections; experimental results for current radius and profile were found to be in close agreement with the self-similar solutions at intermediate and late times.