| Wed April 11th 2018 16:00 – 16:30 ZH286 | Seminar | Boundary layers in free surface flows Jonathan Tsang |
Details:Boundary layer theory has progressed far since Prandtl introduced the concept in 1905, but there has been no analytical work studying a boundary layer in a fluid of finite depth. This might occur in a current in a channel that experiences an abrupt increase in basal roughness, which would play a similar role to the blade in the classical Blasius problem. In the first part of this talk, we analyse the interaction between a basal boundary layer and a free surface, finding the conditions under which the coupling between the two phenomena may be neglected.We build on this to consider a current of a non-Newtonian fluid. Specifically, we consider the (I) rheology (Jop et al. 2006), widely used for granular flows, and show that these new equations also admit boundary layer solutions. These solutions match well with the results of discrete particle model (DPM) simulations. Finally, we present recent work at DAMTP, Cambridge, on granular fingering(Pouliquen 1997). Using a novel experimental protocol we attempt to trigger the fingering instability at particular widths in a controlled way, allowing us to test the predictions of linear stability analyses. We have also been able to produce the fingering instability in DPM simulations by choosing particular values for parameters such as the coecient of restitution and rolling resistance. | ||
