Fabian Waleffe

Fabian Waleffe's main research focus has been on `Exact Coherent States', how to calculate them and how they control turbulent flows.

Exact coherent states are particular steady, traveling wave or periodic solutions of the governing partial differential equations (Navier-Stokes, Boussinesq) in physically realistic wall-bounded domains. These solutions are generally unstable, strongly nonlinear and 3D (for Navier-Stokes). They are remarkably similar to coherent structures observed in turbulent flows, hence the name `exact coherent states' since these are actual solutions of the equations as opposed to the coherent structures that come and go and interact in complex ways within turbulent flows. Examples of such coherent structures are the thermals and plumes in Rayleigh-Benard convection and the streaks and quasi-streamwise vortices in the near wall region of turbulent shear flows. Finding such complex unstable solutions requires insight from physics and experiments and special numerical algorithms. These solutions typically develop small scale structures as the (non-dimensional) viscosity and diffusivity go to zero and do not tend to solutions of the corresponding inviscid equations.

Waleffe
Fabian
MIT
1989
Professor
Research Interests: 
Coherent structures, Computational methods, Fluid dynamics
email: 
waleffe at math dot wisc dot edu
person_type: 
Faculty
web_site: 
http://math.wisc.edu/~waleffe