Hydrodynamics of Lock-exchange Turbidity Currents down a Slope Based on Direct Numerical Simulation

Turbidity currents play a vital role in various geophysical environments. However, until now, few studies have taken into the effects of both suspended particle and slope on its evolution, which requires a precise information of the spatio-temporal flow field. Hence, this study presents high-resolution and two-dimensional direct numerical simulations (DNS) of lock-exchange turbidity currents down a slope. By analyzing front velocity, water entrainment, and energy budget, the factors that affect the driving force, thus the development of the turbidity current, are detailedly investigated. The front velocity history exhibits three distinct stages over time, i.e., a short acceleration stage, a quasi-constant stage, and a deceleration stage. The calculation of the entrainment ratio shows that the mixing due to the collapse of the dense fluid is much stronger than that due to the Kelvin-Helmholtz instabilities and turbulent billows. For a turbidity current down a slope, the entrainment volume of ambient water decreases as the particle size increases, which is contrary to the situation of the turbidity current on a flat bed. This is because the increase effect of the larger front velocity exceeds the decrease effect of the stronger stratification to the entrainment volume of ambient water. However, the change of the particle size has little effect on the entrainment ratio. The analysis of the energy budget exhibits that the potential energy is rapidly converted into the kinetic energy in the initial time period. Later then, most of the energy is dissipated. The increase of the slope angle leads to a more rapid energy transition process from the potential energy to the kinetic and the dissipated energy.