Standing jumps in shallow granular flows down smooth inclines

Abstract

The shapes of standing jumps formed in shallow granular flows down an inclined smooth-based chute are analysed in detail, by varying both the slope and mass discharge. Laboratory tests and analytic jump solutions highlight two important transitions. First, for dense flows at high mass discharge, we observe a transition between steep jumps and more diffuse jumps. The traditional shallow-water equation offers a valid prediction for the thickness of the steep water-like jumps. Diffuse frictional jumps require a more general equation accounting for the forces acting inside the jump volume. Second, moving from dense to dilute flows produces another transition between incompressible and compressible jumps. The observed jump height decrease may be reproduced for a more dilute incoming flow by including experimentally measured density variation in the jump equation. Finally, we briefly discuss the likely relevance to avalanche protection dam design that currently utilises traditional shock equations for incompressible frictionless fluids.

Unsteady flows and inhomogeneous packing in damp granular heap flows

“…For the unsteady flows with θ > 30 • , deposition is only possible via the upslope traveling jump, where particles flow along the slope to the traveling jump and are deposited on the face of the jump. Previous studies of dry granular flows in a chute indicate that a minimum base incline angle and a downstream obstacle are required for the formation of the jump [41,42,44], as mentioned previously. Here, increased θ due to cohesion and the presence of the downstream bounding walls satisfy these two conditions, respectively.…”

GEODAR Data and the Flow Regimes of Snow Avalanches

“…In several CDR flows, MTI plots show triangular shaped features at specific ranges (Figure h). We interpret these features as standing waves or shocks (Gray et al, ; Faug et al, ) or even jets (Hákonardóttir et al, ), perhaps initiated by obstructions and terrain features such as changing roughness, slope (Hopfinger, ), or narrowing width of the couloir. Standing shocks occur when the flow is supercritical; that is, the Froude number is greater than 1, so that their existence is dependent on flow height and velocity.…”

Dry granular avalanche impact force on a rigid wall of semi-infinite height

“…In the momentum equation, assuming that the jump volume shrinks into a singular surface ( ∼ 0) yields S = 0. In other words, the volume and surface forces acting over the finite length of the jump are neglected here, though a recent experimental study dedicated to standing jumps formed in granular flows revealed the importance of those forces under certain circumstances when the jumps become diffuse [4]. This crucial assumption will be further discussed while concluding the present paper.…”

“…The density of the granular fluid is ρ P φ, where ρ P is the particle density. A detailed discussion on considering values of k and β slightly different from 1 (either upstream or downstream the shock) is given in [1,4] and some other references therein. In the momentum equation, assuming that the jump volume shrinks into a singular surface ( ∼ 0) yields S = 0.…”

“…The integral forms of mass and momentum conservation equations across the compressible jump are given by the following relations (see more detail in [4]):…”