Fig. 1

Problem setup and configuration. a Particle-laden fluid. b Ambient stratified fluid. c Solid region. H and L denote the height and length of the ramp, L _d is the horizontal length of the domain, h ₀ and L _l denote the height and horizontal length of the lock, and m is the slope. ρ ₁ is the bulk density of the lock, ρ _T is the initial density at the top of the ambient, ρ _B is the initial density at the bottom of the ambient, and ρ _A is the initial density in the ambient at half-lock depth