Abstract

The effect of the boundary condition imposed on the underlying surface on the propagation of lava flows is studied in the case in which the non-Newtonian properties of the medium should be taken into account. The problem of lava spreading over a plane horizontal plane is solved. The no-slip condition on the underlying surface is replaced by the partial slip condition. The lava is modeled as a power-law fluid. The flow is assumed to be axisymmetric. In the thin layer approximation the problem reduces to the solution of one nonlinear partial differential second-order equation with an additional integral condition. In the case of the power-law time dependence of the lava flow rate a self-similar solution is obtained; however, it exists only under some constraints on the problem parameters. The non-self-similar solution is considered numerically. It is shown that the lava propagation velocity can be considerably higher, when the slip is taken into account.

中文翻译：

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下表面部分滑移条件下熔岩作为非牛顿流体的扩散

摘要

在应考虑介质的非牛顿特性的情况下，研究了施加在下表面上的边界条件对熔岩流传播的影响。解决了熔岩在水平面上扩散的问题。基础表面上的无滑移条件被部分滑移条件代替。熔岩被模拟为幂律流体。假定流动是轴对称的。在薄层近似中，问题简化为一个带有附加积分条件的非线性偏微分二阶方程的解。在熔岩流的幂律时间相关性的情况下，获得了自相似解。但是，它仅在问题参数的某些约束下存在。非自相似解在数值上被考虑。