Abstract
The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue 'Stokes at 200 (Part 1)'.
Highlights
Viscous gravity currents are abundant in nature and industry and their modelling began with Sir George Stokes’ equations for creeping flow
We show that the contact line where the flow depth vanishes is relatively insensitive to the opening angle and is well-described by a simple similarity solution, with a single virtual origin for any opening angle
This contribution has described the spreading of viscous fluid into an expanding channel using the equations of Stokes flow and the lubrication approximation
Summary
Viscous gravity currents are abundant in nature and industry and their modelling began with Sir George Stokes’ equations for creeping flow His ideas in this area have been applied to gravitationally-driven viscous flows in diverse fields including glass manufacture, lava flows, coating and printing processes, food manufacture and many biological settings [1]. There have been theoretical, numerical and experimental analyses of the flow behaviour upstream of surface piercing cylinders of various cross-sections [2, 10, 11, 12] These works have shown that there may be a dry zone (in which there is no fluid) downstream of the obstruction and there have been investigations into the location and extent of the dry zone in the regime that capillary forces play a dominant role [11]. We conclude with a brief discussion of the implications of our results in the context of lava flow barrier design and infer that the design of the downstream side of barriers has little influence on the extent of the fluid-free zone that is safely protected
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