Investigations of dynamic behaviors of lock-exchange turbidity currents down a slope based on direct numerical simulation

This study presents a two-dimensional (2D) direct numerical simulation (DNS) of the effects of bed slope and sediment settling on the dynamic behaviors of lock-exchange turbidity currents. The 2D DNS model is first validated against existing DNS solutions and experimental data. Afterwards, a series of numerical case studies on the effect of bed slope and sediment settling is conducted. Numerical solutions show three distinct stages of current evolution according to the behavior of the front velocity, i.e., a rapid acceleration stage due to the collapse of the dense water, followed by a second stage in which the characteristics vary with the bed slope, and finally, a deceleration stage. For a relatively steep bed (e.g., θ = 30°), the turbidity current continues to accelerate in the second stage with a reduced accelerating rate; for an intermediate bed (e.g., θ = 10°), the current appears to have a quasi-constant front velocity in the second stage; for a relatively mild slope (e.g., a flat bed), the current directly enters the final deceleration stage after the first acceleration stage. A higher settling velocity causes greater sediment settling, which reduces the driving force of the turbidity current and therefore the current front velocity. The water entrainment effect is most dominant at the very beginning of the current evolution due to the collapsing effect. Later, the water entrainment ratios drop rapidly due to the diminishing collapsing effect. Regarding the second and third stages, the bulk entrainment ratio appears to have a constant value of approximately 0.05. The absolute values of the energy components (potential energy, kinetic energy, dissipated energy, etc.) vary greatly with the bed slope and the settling velocity. The higher the bed slope is, the higher the amount of potential energy that can be converted during the turbidity current evolution. Nevertheless, when these energy components are normalized, the differences in the energy conversion patterns between the potential energy and kinetic energy are greatly reduced. Specifically, the normalized potential energy continuously decreases. The normalized kinetic energy tends to sharply increase first, then remain nearly constant, and finally decrease.