  The Turbidity current (TC), a ubiquitous fluid-particle coupled phenomenon in
the natural environment and engineering, can transport over long distances on
an inclined terrain due to the suspension mechanism. A large-eddy simulation
and discrete element method coupled model is employed to simulate the
particle-laden gravity currents over the inclined slope in order to investigate
the auto-suspension mechanism from a Lagrangian perspective. The particle
Reynolds number in our TC simulation is $0.01\sim0.1$ and the slope angle is
$1/20 \sim 1/5$. The influences of initial particle concentration and terrain
slope on the particle flow regimes, particle movement patterns, fluid-particle
interactions, energy budget and auto-suspension index are explored. The results
indicate that the auto-suspension particles predominantly appear near the
current head and their number increases and then decreases during the current
evolution, which is positively correlated with the coherent structures around
the head. When the turbidity current propagates downstream, the average
particle Reynolds number of the auto-suspension particles remains basically
unchanged, and is higher than that of other transported particles. The average
particle Reynolds number of the transported particles exhibits a negative
correlation with the Reynolds number of the current. Furthermore, the increase
in particle concentration will enhance the particle velocity, which allows the
turbidity current to advance faster and improves the perpendicular support,
thereby increasing the turbidity current auto-suspension capacity. Increasing
slope angle will result in a slightly larger front velocity, while the effect
of that on the total force is insignificant.
