Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture

Abstract The purpose of this paper is to present similarity solutions for laminar and turbulent fluid fracture. Fluid fracture is important for the transport of both magma and hydrothermal fluids. The similarity solutions assume a constant rate of fluid flow into the crack. The similarity equations are solved by an approximate method which produces results in good agreement with numerical solutions presented elsewhere. It is shown that the flow resistance of the fluid is more important than the fracture resistance of the solid for most geological problems. Turbulence can either increase or decrease any of the crack parameters, depending upon the Reynolds number. Crack roughness decreases the critical Reynolds number for the onset of turbulence. However, if at a given Reynolds number, the flow would be turbulent even for a smooth crack, then crack roughness has very little effect upon the crack parameters. The crack propagation rate is a weak function of fluid viscosity; thus, the low-viscosity precursors suggested by other workers are unlikely.

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