Abstract
Abstract
Highlights
Fluid systems involving the interactions between two layers driven by gravity arise widely in the natural world
Since these equations depend on η, it follows that the thickness profiles of the fluid layers both vary along the flow, differing qualitatively from the asymptotic form of layers produced by a constant flux (§ 3)
This study has established the general principles of the dynamics of two-layer fluid flows released on slopes
Summary
Fluid systems involving the interactions between two layers driven by gravity arise widely in the natural world. For an inclined substrate, Huppert (1982a) determined a different similarity solution describing the release of a fixed volume of fluid, showing that the front position instead grows as t1/3 In this case, the layer thickens towards a finite thickness at its front (forming a shock), differing qualitatively in essential form from a gravity current on a horizontal substrate. The analysis of two-layer axisymmetric gravity currents with equal densities over horizontal substrates has been considered, with the finding that it is possible for such flows to form interfacial shocks (Dauck et al 2019) Another group of related studies have analysed viscous instabilities of inclined two-layer films with a free surface (Loewenherz & Lawrence 1989; Loewenherz et al 1989; Balmforth, Craster & Toniolo 2003) and of viscous stratified flows on slight inclines (Kliakhandler & Sivashinsky 1997).
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