WALL TO WALL OPTIMAL TRANSPORT
Charles R. Doering
Session: Transport and mixing 1
Session starts: Wednesday 26 August, 13:30
Presentation starts: 14:15
Room: Room I
Charles R. Doering (University of Michigan)
The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of the kinetic energy or a fixed value of the enstrophy (the mean square rate of strain in this situation). The optimizing flows realize upper limits on convective transport in this scenario. We interpret the results in the context of buoyancy-driven Rayleigh–Bénard convection problems that satisfy the flow intensity constraints, enabling us to investigate how optimal transport scalings compare with upper bounds on Nu expressed as a function of the Rayleigh number Ra.