Appreciating how the heat flux in convection scales with the Rayleigh number (Ra) continues to be a central challenge with manifold applications in nature. Here I’ll discuss the use of the so-called `background' technique for producing an upper bound on this heat flux in the hope that this bound captures the correct turbulent scaling with Ra. The novelty of this work is to adopt a more sophisticated background field than previously in order to incorporate more dynamical information from the Boussinesq equations. I will discuss how the subsequent results compare with a complementary `wall-to-wall’ approach and, time-permitting, what happens when even more dynamical information is built in. This is joint work with Zijing Ding (now of Harbin Institute of Technology).
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