Spreading of Gravity Plumes on an Incline

Gravity plumes are buoyancy-driven underflows in a deep ambient fluid. We develop spreading laws for gravity plumes which propagate laterally as well as longitudinally on a uniform slope. Examples of such flows are turbidity currents in the ocean and ignimbrite flows in the atmosphere. Laboratory experiments with a large tank, employing saline density currents, coupled with dimensional analysis, have been used to develop simple expressions for spreading rates of three-dimensional flows on sloping beds. Characteristic length and time are determined by the flow discharge and the buoyancy flux at the inlet. By knowing the initial width of the flow, the spreading laws can be used to estimate the maximum width of the current at different times as well as the longitudinal spreading rate. Predictions for flows compare favorably against observations.