Up, down, and round again: The circulating flow dynamics of flux-driven fractures

Abstract

Fluid-filled fracture propagation is a complex problem that is ubiquitous in geosciences, from controlling magma propagation beneath volcanoes to water transport in glaciers. Using scaled analog experiments, we characterized the internal flow inside a propagating flux-driven fracture and determined the relationship between flow and fracture evolution. Different flow conditions were created by varying the viscosity and flux (Q) of a Newtonian fluid injected into an elastic solid. Using particle image velocimetry, we measured the fluid velocity inside the propagating fracture and mapped the flow across the crack plane. We characterized the internal flow behavior with the Reynolds number (Re) and explored Re values spanning five orders of magnitude, representing very different internal force balances. The overall fracture tip propagation velocity is a simple linear function of Q, whereas the internal velocity, and Re, may be vastly different for a given Q. We identified four flow regimes—viscous, inertial, transitional, and turbulent—and produced viscous and inertial regimes experimentally. Both flow regimes exhibit a characteristic flow pattern of a high-velocity central jet that develops into two circulating vortices on either side. However, they exhibit the opposite behavior in response to changing Q: the jet length increases with Q in the inertial regime, yet decreases in the viscous regime. Spatially variable, circulating flow is vastly different from the common assumption of unidirectional fracture flow and has strong implications for the mixing efficiency and heat transfer processes in volcanic and glacial applications.