http://www.me.unm.edu/~kalmoth/
Joint work with Peter Vorobieff (UNM).
Earlier work on stagnation flows was done with Patrick Weidman (UC Boulder), and I have made some progress on applications of Weierstrass elliptic functions to the problem of two-fluid flows. See my vita for more information.
Jeffery Hamel flows are two-dimensional fluid flows from a point source inside a wedge. They have been one of the most fundamental solutions in fluid dynamics since their discovery in the beginning of the 20th century. For the outflow (fluid moving out of the wedge on average) they show a non-trivial structure of bifurcations and coexistence of solutions: for a given Reynolds number, there are infinitely many possible solutions. Thus, there is an important question of solution selection. Previous studies were devoted exclusively to theoretical studies, but the outflow boundary conditions are highly problematic to take into account consistently. Surprisingly, there have been almost no consistent experimental studies of Jeffery Hamel Flows.
We have used the technique of Particle Image Velocimetry to visualize the flows in a wedge. We have shown that the bifurcation values given by the Jeffery-Hamel flows are indeed observed in Nature, but the bifurcation structure is completely different than that obtained from the theory. Here is a picture of experimental velocity profiles, from our article in Phys. Rev. Lett (2006).
We have also demonstrated the existence of periodically spaced vortices (inlog r) as was predicted by Tutty (1996). Here is a picture of a two-vortex solution.
This work was partially supported by Department of Energy grant DE-FG02-04ER46119 and Petroleum Research Foundation grant PRF:40218-AC9.