Gravity Currents from Instantaneous Sources Down a Slope

Abstract

Gravity currents from instantaneous sources down a slope were modeled with classic thermal theory, which has formed the basis for many subsequent studies. Considering entrainment of ambient fluid and conservation of total buoyancy, thermal theory predicted the height, length, and velocity of the gravity current head. In this study, the problem with direct numerical simulations was re-investigated, and the results compared with thermal theory. The predictions based on thermal theory are shown to be appropriate only for the acceleration phase, not for the entire gravity current motion. In particular, for the current head forms on a 10° slope produced from an instantaneous buoyancy source, the contained buoyancy in the head is approximately 58% of the total buoyancy at most and is not conserved during the motion as assumed in thermal theory. In the deceleration phase, the height and aspect ratio of the head and the buoyancy contained within it may all decrease with downslope distance. Thermal theory relies on the increase in the mass of the current head through entrainment as the major mechanism for deceleration and, therefore, tends to underpredict the front velocity in the deceleration phase.