Georgia Institute of Technology College of Sciences

Hot fluid expands. Expansion makes a fluid ``parcel'' lighter, causing it to rise. Cold, dense patches of fluid sink. And there we have the thermally induced motion of a fluid sitting on a hot plate... A longstanding open problem in applied analysis is the scaling of the Nusselt number (with respect to the Rayleigh number or, equivalently, system height) in thermal convection. The goal is a fundamental understanding of the effect of buoyancy-induced convection on heat transport in chaotic systems. The commonly held belief that the Nusselt number scales like (Ra)^(1/3) has eluded analytical proof for decades. We will describe the nature of the questions involved, the way that they can be framed (and reframed) mathematically, and the partial successes so far, including a recent preprint by Otto and Seis and a work in progress by the same authors