Limits on Turbulent Transport: Charles Doering, University of Michigan

Mathematical bounds on mass, momentum and heat transport for solutions of the incompressible Navier-Stokes and Boussinesq equations are reviewed. In some cases the scaling indicated by the bounds is (nearly) saturated by turbulent flows, but in some cases---most notably turbulent Rayleigh-Benard convection---there remains a large gap between experiments and the rigorous heat transport limits. We discuss some current research exploring these issues further.