Wake vortex behind an airplane shows the disordered small scales characteristic of turbulent flows together with a large scale coherent structure, the vortex. Credit: NASA Langley

Professor Department of Engineering Physics

Coordinator AMEP Program

Associate Editor Physics of Fluids

I am an Applied Mathematician at the University of Wisconsin, Madison, with a joint appointment between the Department of Mathematics and the Department of Engineering Physics.

## Research Interests

Much of my research has been related to the fundamental problem of turbulence in fluid flows and its relation to Exact Coherent States.

I have developed a Self-Sustaining Process theory for shear flows that has provided an *ab initio* method to discover families of 3D traveling wave solutions of the
Navier-Stokes equations in all canonical shear flows (plane Couette, Poiseuille and pipe flows with velocity, stress or mixed boundary conditions). The traveling wave solutions appear to constitute the unstable `backbone' of turbulent shear flows. My other research activities focus on geophysical flows and computational methods for solving partial differential equations.

Here is a beautiful visualization of a geophysical turbulent flow: the Gulf Stream and eddies in the western North Atlantic Ocean:

Credit: NASA Scientific Visualization Studio