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

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.

Nautilus magazine 's July 2014 issue is devoted to Turbulence.

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