The time evolution equation for advective heat transport as a constraint for optimal bounds in Rayleigh-B\'enard convection.

Upper bounds on the heat transport and other quantities of interest in Rayleigh-B\'enard convection are derived in previous work from constraints resulting from the equations of time evolution for kinetic energy, the root mean square of temperature, and the temperature averaged over horizontal planes. Here, we investigate the effect of a new constraint derived from the time evolution equation for the advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.