Two mathematical models for the simulation of the dynamics of sheetflow are presented, an analytical and a numerical one. In the analytical model the theory of Bagnold (1954) is implemented: a constant ratio between shear stress and normal stresses is assumed. In the numerical model the motion of each layer of grains is considered separately; each layer exists of a rigid rectangular structure of spherical grains. Grain- grain interaction between the successive layers occurs in two ways: on one hand viscous interaction forces, comparable with squeezing forces in lubrication problems and on the other hand direct contact with elastic response when the distance between the grains becomes less than .01 of the grain diameter. When the relative motion of adjacent layers results into compression or dilatation, a resistant force analogous to the Darcy law is assumed.The numerical model has been combined with the turbulent boundary layer model of Bakker and v. Kesteren (1984). Results of computations are compared with measurements of Bagnold (1954) and Horikawa et al (1982). The analytical model predicted the concentration in the sheet flow layer and the intrusion depth rather well, where the numerical model gave reasonable results with respect to the velocity pattern above the sheetflow layer. It is concluded, that up to now the more sophisticated assumptions of the numerical model do not lead as yet to higher accuracy with respect to the intrusion depth of the sheet flow, probably because the separation between sheet flow and the turbulent boundary layer above has been assumed too smooth.
Analytical model of the time developing turbulent boundary layer
