E3S Web of Conferences 415, 01014 (2023)
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https://doi.org/10.1051/e3sconf/202341501014

Formation of dry granular fronts and watery tails in debris flows
Xiannan Meng1, Chris G. Johnson2, and John M.N.T. Gray2
1Centre for Ports and Maritime Safety, Dalian Maritime University, Dalian, 116026, P R China
2Department of Mathematics and Manchester Centre for Nonlinear Dynamics, University of Manchester, Oxford Road, Manchester

M13 9PL, UK

Abstract. Debris flows are particle-fluid mixtures that pose a significant hazard to many communities
throughout the world. Bouldery debris flows are often characterized by a deep dry granular flow front, which
is followed by a progressively thinner and increasingly watery tail. The formation of highly destructive
bouldery wave fronts is usually attributed to particle-size segregation. However, the moving-bed flume
experiments of Davies (N. Z. J. Hydrol., vol. 29, 1990, pp. 18-46) show that discrete surges with dry fronts
and watery tails also form in monodisperse particle-fluid mixtures. These observations motivate thedevelopment of a new depth-averaged mixture theory for debris flows, which explicitly takes account of thediffering granular and phreatic surfaces, velocity shear, and relative motion between grains and fluid toexplain these phenomena. This poster presents the theory of Meng et al. (J. Fluid Mech., vol. 943, 2022,
A19), which consists of four coupled conservation laws that describe the spatial and temporal evolution ofthe grain and water thicknesses and depth-averaged velocities. This system enables travelling wave solutions
to be constructed that consist of (i) a large amplitude dry flow front that smoothly transitions to (ii) an undersaturated body, (iii) an oversaturated region and then (iv) a pure water tail. It is shown that these solutions
are in good quantitative agreement with Davies' experiments at high bed speeds and slope inclinations. At
lower bed speeds and inclinations, the theory produces travelling wave solutions that connect to a steadyuniform upstream flow, and may or may not have a bulbous flow front, consistent with Davies' observations.

1 Introduction
One of the most destructive parts of a debris flow is theinitial surge or front, which is usually deeper, drier andricher in boulders and other large debris, than the rest of
the flow. Following the passage of this front, many
debris flows wane and transition to a fluid-saturated tail,with suspended sediment that is finer-grained than thefront [3]. It is common for successive surges, withsimilar boulder-rich fronts, to follow the first.
Since water and fluid-saturated grains usuallyexperience less friction than dry grains, it would benatural to suppose that the grains would be left at theback of the flow, with the faster-moving water travellingin front – and indeed several multi-phase debris flow
models predict this, in contradiction to observations.
Another mechanism must therefore be responsible forthe formation of dry granular fronts in debris flows.
The laboratory experiments of Davies [1] show thata simple mixture of monodisperse grains and waterflowing down an inclined plane develops a pronounced
dry granular front, followed by a thinner watery tail asshown schematically in Figure 1. These experiments
demonstrate that the dry front forms even in a very
simplified analogue flow, in which particle size
segregation is not present.

Fig. 1. Schematic diagram of a debris flow front, based on asolution of the two-phase model of Meng et al. [2]. The grains
lie below the red line in the region partially filled with
schematic grains. The phreatic (water) surface is shown witha blue line and the water saturated region is shaded blue. The
green arrow indicates the recirculation of grains, with the lightgrey ones being sheared towards the front and darker grey
ones moving back relative to it.

2 Modelling of Meng et al. (2022)
Motivated by the experimental results of Davies, Menget al. [2] derive a two-phase depth-integrated flow
model, in which grains and water satisfy separate mass© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 01014 (2023)
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https://doi.org/10.1051/e3sconf/202341501014

Fig. 2. Plot of the granular free surface (red) and water free surface (blue), predicted by the Meng et al. [2] model for parameterscorresponding to an experiment of Davies [1]. Circles in the top panel indicate the granular free surface measured in experiments.
Green lines in the bottom panel indicate particle paths predicted by the model, which are in qualitative agreement with the experiment.

and momentum equations. They demonstrate that thatvelocity shear plays an essential role in the formation ofdry fronts. When the flow is under saturated, thecomposition of the flow varies vertically, with thevolume fraction of water near the free surface less thanthat in the bulk of the flow. Velocity shear thentransports the grains near the surface faster than thedepth-averaged velocity, towards the flow front. Meng
et al. [2] demonstrate a travelling wave solution inwhich a bulbous dry granular front is followed by aflowing body with a mixture of grains and water, andfinally a streamflow of water, matching both theexperimental observations of Davies [1] anddescriptions of natural debris flows in the field [3](figure 1).
Solutions of the Meng et al. [2] model accurately
reproduce the shape of the bulbous flow in theexperiments of Davies [1] (figure 2, top panel), andadditionally capture the recirculation observed byDavies, where grains at the surface approach the flow
front, are buried, carried back through the flow near its
base, and rise in the body of the flow to be carried
towards the front once more (figure 2, bottom panel).
This transport by velocity shear is extremely
effective at carrying grains to the front of the flow andforming a dry flow front, even when the water is moremobile than the grains. That is, even when water islocally percolating downslope through the granularmatrix, the depth-averaged speed of grains may
nonetheless be faster than that of the water in an undersaturated flow, due to the fastest-flowing layer at theflow surface being predominantly granular.

3 Conclusion
A characteristic feature of bouldery debris flows is the
spontaneous development of a dry granular front, thepresence of which significantly increases the thickness
and thereby the hazard posed by such flows. Meng et al.
[2] showed that velocity shear is essential to theformation of this dry front. The overwhelming majorityof current depth-integrated debris flow models assume aplug-flow velocity profile (that is, no velocity shear),and in doing so, are unable to properly capture thephysical mechanisms leading to the formation of the dry
region at the debris-flow front.
The research was supported by the European-Commission
Marie Skłodowska-Curie Individual Fellowships (IF) scheme(792967), the Royal Society (WM150058), the EPSRC(EP/M022447/1) and NERC (NE/X00029X/1).

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2

T.R.H. Davies, N. Z. J. Hydrol. 29, 18-46 (1990)
X. Meng, C.G. Johnson and J.M.N.T. Gray, J.
Fluid Mech. 943, A19 (2022)
T. C. Pierson, in Hillslope Processes (ed.
A.D.Abrahams) pp 269-296, Allen and Unwin.