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.
|Number of pages||11|
|Journal||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Early online date||8 Jun 2020|
|Publication status||Published - 26 Jun 2020|
- viscous ﬂows
- gravity currents
- lava ﬂows