The background method is a widely used technique to bound mean properties of turbulent
flows rigorously. This work reviews recent advances in the theoretical formulation and …

In most results concerning bounds on the heat transport in the Rayleigh-B\'{e} nard
convection problem no-slip boundary conditions for the velocity field are assumed …

Rigorous upper limits on the vertical heat transport in two-dimensional Rayleigh-Bénard
convection between stress-free isothermal boundaries are derived from the Boussinesq …

Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard
convection Page 1 J. Fluid Mech. (2006), vol. 560, pp. 229–241. c 2006 Cambridge University …

We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh–
Bénard convection between free-slip boundaries. We focus on the ability of the convection to …

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 …

We derive a formula for the Péclet number (Pe) by estimating the relative strengths of
various terms of the momentum equation. Using direct numerical simulations in three …

We consider Rayleigh–Bénard convection as modelled by the Boussinesq equations in the
infinite-Prandtl-number limit. We are interested in the scaling of the average upward heat …

An alternative computational procedure for numerically solving a class of variational
problems arising from rigorous upper-bound analysis of forced-dissipative infinite …

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-
scale quantities, eg, Péclet number Pe, Nusselt number Nu, and rms value of the …