Lava spreading during volcanic eruptions on the condition of partial slip along the underlying surface. (English. Russian original) Zbl 1325.76061
Fluid Dyn. 50, No. 2, 203-214 (2015); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2015, No. 2, 27-40 (2015).
Summary: In the axisymmetric approximation the problem of spreading lava as an incompressible constant-viscosity liquid over a flat horizontal surface is solved. Instead of the classical no-slip condition, a condition of partial lava slip along the underlying surface is used: at the surface the velocity is assumed to be a power function of friction. In the thin-layer approximation, for the problem of slow liquid spreading an asymptotic self-similar solution is constructed on the assumptions of partial slip along the underlying surface and a power time dependence of the flow rate. The same problem is solved in the complete formulation numerically. It is shown that the numerical and asymptotic solutions are in good agreement. It is established that with account for the slip effect the lava propagation velocity may be substantially higher than for the no-slip condition.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 86A60 | Geological problems |
Keywords:
viscous liquid spreading; thin-layer approximation; partial slip; self-similar solution; lava flowsReferences:
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