Applied Maths Seminar: Duncan Sutherland -- Numerics, Fluid Dynamics

Our own Duncan Sutherland will present the Applied Math Seminar tomorrow.  

We’ll 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.