Asymptotic analysis for the propagation and arresting process of a finite dry granular mass down a rough incline
Journal
Journal of Fluid Mechanics
Journal Volume
806
Pages
234-253
Date Issued
2016
Author(s)
Lee, K.-L.
Abstract
This work presents an asymptotic analysis for the propagation and arresting process of a two-dimensional finite granular mass down a rough incline in a shallow configuration. Bulk shear stress and arresting mechanism are formulated according to the coherence length model that considers momentum transport at a length scale over which grains are spatially correlated. A Bagnold-like streamwise velocity and a non-zero transverse velocity are solved and integrated into a surface kinematic condition to give an advection-diffusion equation for the bulk surface profile, h(x,t), that is solved using the matched asymptotic method. These flow solutions are further employed to determine composite solutions for a flow-front trajectory and a local coherence length, l(x,t), which reveals smooth growth of h(x,t) and l(x,t) from zero at the propagating front with l(x,t)
Type
journal article