A dam-break driven by a moving source: a simple model for a powder snow avalanche

Billingham, John

Abstract

We study the two-dimensional, irrotational flow of an inviscid, incompressible fluid injected from a line source moving at constant speed along a horizontal boundary, into a second, immiscible, inviscid fluid of lower density. A semi-infinite, horizontal layer sustained by the moving source has previously been studied as a simple model for a powder snow avalanche, Caroll et al. (2012). We show that with fluids of unequal densities, in a frame of reference moving with the source, no steady solution exists, and formulate an initial/boundary value problem that allows us to study the evolution of the flow. After considering the limit of small density difference, we study the fully nonlinear initial/boundary value problem and find that the flow at the head of the layer is effectively a dam-break for the initial conditions that we have used. We study the dynamics of this in detail for small times using the method of matched asymptotic expansions. Finally, we solve the fully nonlinear free boundary problem numerically using an adaptive vortex blob method, after regularising the flow by modifying the initial interface to include a thin layer of the denser fluid that extends to infinity ahead of the source. We find that the disturbance of the interface in the linear theory develops into a dispersive shock in the fully nonlinear initial/boundary value problem and overturns. For sufficiently large Richardson number, overturning can also occur at the head of the layer.

Citation

Billingham, J. (2019). A dam-break driven by a moving source: a simple model for a powder snow avalanche. Journal of Fluid Mechanics, 870, 353-388. https://doi.org/10.1017/jfm.2019.273

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2019
• Online Publication Date: May 9, 2019
• Publication Date: Jul 10, 2019
• Deposit Date: Nov 9, 2018
• Publicly Available Date: Nov 10, 2019
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press (CUP)
• Peer Reviewed: Not Peer Reviewed
• Volume: 870
• Pages: 353-388
• DOI: https://doi.org/10.1017/jfm.2019.273
• Keywords: Avalanche; vortex sheet; vortex blob method; dam-break
• Public URL: https://nottingham-repository.worktribe.com/output/1238446
• Publisher URL: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/dam-break-driven-by-a-moving-source-a-simple-model-for-a-powder-snow-avalanche/84A634EF0E006138411F6DF7E35BC52C#