# Suspended load and bed-load transport of particle-laden gravity currents: the role of particle–bed interaction

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## Abstract

The development of particle-enriched regions (bed-load) at the base of particle-laden gravity currents has been widely observed, yet the controls and relative partitioning of material into the bed-load is poorly understood. We examine particle-laden gravity currents whose initial mixture (particle and fluid) density is greater than the ambient fluid, but whose interstitial fluid density is less than the ambient fluid (such as occurs in pyroclastic flows produced during volcanic eruptions or when sediment-enriched river discharge enters the ocean, generating hyperpycnal turbidity currents). A multifluid numerical approach is employed to assess suspended load and bed-load transport in particle-laden gravity currents under varying boundary conditions. Particle-laden flows that traverse denser fluid (such as pyroclastic flows crossing water) have *leaky* boundaries that provide the conceptual framework to study suspended load in isolation from bed-load transport. We develop leaky and saltation boundary conditions to study the influence of flow substrate on the development of bed-load. Flows with saltating boundaries develop particle–enriched basal layers (bed-load) where momentum transfer is primarily a result of particle–particle collisions. The grain size distribution is more homogeneous in the bed-load and the saltation boundaries increase the run-out distance and residence time of particles in the flow by as much as 25% over leaky boundary conditions. Transport over a leaky substrate removes particles that reach the bottom boundary and only the suspended load remains. Particle transport to the boundary is proportional to the settling velocity of particles, and flow dilution results in shear and buoyancy instabilities at the upper interface of these flows. These instabilities entrain ambient fluid, and the continued dilution ultimately results in these currents becoming less dense than the ambient fluid. A unifying concept is energy dissipation due to particle–boundary interaction: leaky boundaries dissipate energy more efficiently at the boundary than their saltating counterparts and have smaller run-out distance.

### Keywords

Particle-laden gravity current Multiphase flow Pyroclastic flows Bed-load### List of Symbols

- \({}^mc_{i}\)
instantaneous velocity of

*m*th phase [m/s]- \({}^mc_{i}\)
fluctuating velocity of

*m*th phase [m/s]- \(C_{1\mu}\)
constant in fluid turbulence model (0.09)

- \(C_{1\varepsilon}\)
constant in fluid turbulence model (1.44)

- \(C_{2\varepsilon}\)
constant in fluid turbulence model (1.92)

- \(C_{3\varepsilon}\)
constant in fluid turbulence model (1.22)

- \(C_{\rm D}^{S}\)
drag coefficient

- \({}^mc_{\rm p}\)
heat capacity [J/kg K]

^{p}*d*particle diameter [m] (1.0 × 10

^{−4}m and 0.01 m)*e*restitution coefficient (0.65)

- \({}^me_{ij}\)
strain rate [s

^{−1}]*F*_{c}coefficient of friction (0.62)

*g*_{i}gravitational acceleration [m/s

^{2}] (9.81 m/s^{2})*g*_{0}radial distribution function

- \(H_{gp}\)
interphase heat transfer [W/m

^{3}]*H*_{1}hindrance coefficient in particle–particle drag (0.3)

- \({}^mI_{i}\)
interphase momentum transfer [kg/m

^{3}s]- \({}^pI_{\rm 2D}\)
second invariant of rate of strain tensor [s

^{−2}]^{1}*k*fluctuating kinetic energy of the gas phase [m

^{2}/s^{2}]^{m}*P*pressure [Pa]

^{m}*q*thermal heat flux [J/m

^{2}s]*R*_{km}ratio thermal conductivities

^{m}*T*thermal temperature [K]

- \({}^{m}U_i \)
average velocity [m/s]

^{m}αvolume fraction of

*m*th phase- \({}^{m}\varepsilon \)
dissipation rate of fluctuating kinetic energy [m

^{2}/s^{3}]^{p}κgranular conductivity [J s /m

^{3}]^{p}θgranular temperature [m

^{2}/s^{2}]- \({}^{m}\mu\)
dynamic viscosity [Pa s]

^{m}λbulk viscosity [Pa s]

- \({}^{p}\varphi\)
angle of internal friction (32°)

- Π
turbulence exchange terms

^{m}ρdensity of

*m*th phase [kg/m^{3}]- σ
_{k} gas turbulence constant (1.0)

- \(\sigma _{\varepsilon}\)
gas turbulence constant (1.3)

- \({}^{m}\tau _{ij} \)
stress tensor [Pa]

- Preceding superscripts
*m*= 1, 2, 3 (1 is gas phase, and 2 and 3 are particle phases)*p*= 2 and 3 (particle phases)- Subscripts
*i*,*j*= 1, 2 (indices for spatial direction)

### PACS

91.40.Zz 91.45.Wa 91.50.Jc## Preview

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