Our own Duncan Sutherland will present the Applied Math Seminar tomorrow. Well also take him to lunch before his talk. Please meet at the 6th floor elevators at 12noon if interested. Looking forward to seeing you all there! Title: Numerical study of vortex generation in bounded flows with no-slip and partial slip boundary conditions Abstract: The problem of a dipole rebounding from a rigid wall in a viscous fluid has been very well studied using a variety of numerical techniques. Recently, Romain Nguyen van yen, Kai Schneider and Marie Farge (Phys. Rev. Lett. 106, 184502 (2011)) used a volume penalisation method to investigate the energy dissipation over the rebound as the viscosity approaches zero. The penalisation method approximates a no-slip boundary condition and intrinsically introduces some non-zero slip length at the boundary, which also vanishes as the viscosity approaches zero. The results of Nguyen van yen et. al. surprisingly indicate that energy dissipating structures persist in the vanishing viscosity limit. We consider the problem of a dipole incident on a rigid wall with a Navier slip boundary condition, which reduces to the standard no-slip boundary condition in the case of zero slip length. We find no energy dissipating structures for any fixed slip length, but we recover the results of Nguyen van yen et. al. in the case where the slip length is proportional to the viscosity. Hence it appears that the observation of Nguyen van yen et. al. is an artifact of their numerical method. We then proceed to study the vorticity generation at the rigid wall in more detail. In any bounded domain the walls act as a source of enstrophy which constantly injects small scale vortices into the flow. To do this we study the number and location of the critical points, either minima, maxima, or saddles of the streamfunction and vorticity. We will discuss the techniques for identifying and classifying the fixed points, as well as some of the difficulties of interpretation that the boundaries present. Results showing the motion of critical points in time and the variation in the number of critical points over the simulation for bounded geometries will also be presented.