**Investigation of Gravity-Driven Infiltration Instabilities in Smooth and
Rough Fractures Using a Pairwise-Force Smoothed Particle Hydrodynamics
Model**

E Shigorina and AM Tartakovsky and J Kordilla, VADOSE ZONE JOURNAL, 18, 180159 (2019).

DOI: 10.2136/vzj2018.08.0159

This work investigates small-scale infiltration dynamics in smooth and
rough single fractures using a three-dimensional multiphase pairwise-
force smoothed particle hydrodynamics (PF-SPH) model. Gravity-driven
infiltration instabilities in fractures under unsaturated conditions can
significantly influence the arrival time of tracers or contaminants, and
the rapid and localized recharge dynamics in fractured-porous aquifer
systems. Here, we study the influence of roughness and injection rate on
fluid flow modes and flow velocity. Three types of fractures are
considered with different degrees of roughness, including a smooth
fracture. Both the rough and smooth fractures exhibit flow
instabilities, fingering, and intermittent flow regimes for low
infiltration rates. In agreement with theoretical predictions, a flat
fluid front is achieved when the flux q supplied to a fracture is larger
than the gravitationally driven saturated flux **q > k rho g/mu cos(phi),
where k is the intrinsic permeability of the fracture, rho is a density,
mu is the viscosity, and phi is the fracture inclination angle measured
from the vertical direction**. To characterize the flow instability, we
calculate standard deviations of velocity along the fracture width. For
the considered infiltration rates, we find that an increase in roughness
decreases the flow velocity and increases the standard deviation of
velocity. This is caused by a higher likelihood of flow discontinuities
in the form of fingering and/or snapping rivulets. To validate our
unsaturated flow simulations in fractures, we estimate the scaling of
specific discharge with normalized finger velocity, compute the
relationship between fingertip length and scaled finger velocity, and
find good agreement with experimental results.

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