### Kenneth Miller, Professor

Partial Differential Equations, University of Chicago; PhD, 1975

### Awards

Excellence in Teaching Award, 2005

### Research: Fluid Dynamics

Vortices are the most significant features of fluid flows in many
situations. Ken Miller considers flows in which vortices are
concentrated in certain regions over long periods of time, and
for which the fluid is inviscid, i.e. viscous forces can be ignored.
In some recent papers the possible positioning of vortex patches in
equilibrium with flow past a cylinder or a sphere has been studied
and an investigation of the stability of such configurations has
been carried out. Another recent work is a study of solitary waves in
equilibrium with a point vortex. All of this research makes use of
extensive computations, although it is some sense complementary to
conventional "computational fluid dynamics." Other papers consider
more theoretical results of related interest.

### Selected Publications

- K. G. Miller, B. Fornberg, N. Flyer, B.C. Low, "Magnetic relaxation in the Solar Corona", Astrophysical Journal 690 (2009), 720-733
- A.R. Elcrat, B. Fornberg, K.G. Miller, "Steady axisymmertic vortex flows with swirl and shear", Journal of Fluid Mechanics, 613 (2008), 395-410
- A. R. Elcrat, K. G. Miller, "Free surface waves in equilibrium with a vortex", European Journal of Mechanics B/Fluids, 25 (2006), 255-266.
- A. R. Elcrat, B. Fornberg, K. G. Miller, "Stability of vortices in equilibrium with a cylinder", Journal of Fluid Mechanics, 544 (2005), 53-68
- A. R. Elcrat, K. G. Miller, "A monotone iteration for axisymmetric vortices with swirl," Differential and Integral Equations, 16 (2003), 949-968.
- A. R. Elcrat, K. G. Miller, "A monotone iteration for concentrated vortices," Nonlinear Analysis, 44 (2001), 777-789.