Shallow free-surface Stokes flow around a corner

Edward Hinton*, Andrew J Hogg, Herbert Huppert

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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,thedetachmentpointiswellapproximated 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.
Original languageEnglish
Number of pages11
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Early online date8 Jun 2020
DOIs
Publication statusPublished - 26 Jun 2020

Keywords

  • viscous flows
  • gravity currents
  • lava flows

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