The granular Blasius problem

Tsang, JMF and Dalziel, SB and Vriend, N. M. (2019) The granular Blasius problem. Journal of Fluid Mechanics, 872. pp. 784-817. ISSN 0022-1120, ESSN: 1469-7645 DOI https://doi.org/10.1017/jfm.2019.357

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Abstract

© 2019 Cambridge University Press. We consider the steady flow of a granular current over a uniformly sloped surface that is smooth upstream (allowing slip for x < 0) but rough downstream (imposing a no-slip condition on x > 0), with a sharp transition at x = 0. This problem is similar to the classical Blasius problem, which considers the growth of a boundary layer over a flat plate in a Newtonian fluid that is subject to a similar step change in boundary conditions. Our discrete particle model simulations show that a comparable boundary-layer phenomenon occurs for the granular problem: The effects of basal roughness are initially localised at the base but gradually spread throughout the depth of the current. A rheological model can be used to investigate the changing internal velocity profile. The boundary layer is a region of high shear rate and therefore high inertial number I; its dynamics is governed by the asymptotic behaviour of the granular rheology for high values of the inertial number. The μ(I) rheology (Jop et al., Nature, vol. 441 (7094), 2006, pp. 727-730) asserts that dμ/dI = O(1=I2) as I → but current experimental evidence is insufficient to confirm this. We show that this rheology does not admit a self-similar boundary layer, but that there exist generalisations of the μ(I) rheology, with different dependencies of μ(I) on I, for which such self-similar solutions do exist. These solutions show good quantitative agreement with the results of our discrete particle model simulations.

Item Type:	Article
Uncontrolled Keywords:	NILAREP; IA76
Subjects:	02 - Geodynamics, Geophysics and Tectonics
Divisions:	02 - Geodynamics, Geophysics and Tectonics
Journal or Publication Title:	Journal of Fluid Mechanics
Volume:	872
Page Range:	pp. 784-817
Identification Number:	https://doi.org/10.1017/jfm.2019.357
Depositing User:	Sarah Humbert
Date Deposited:	06 May 2020 16:36
Last Modified:	06 May 2020 16:36
URI:	http://eprints.esc.cam.ac.uk/id/eprint/4728

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