Bounds on poloidal kinetic energy in plane layer convection

A numerical method is presented which conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with earlier results. These bounds imply upper bounds for the poloidal energy which follow directly from the definitions of dissipation and energy. The same constraints used for computing upper bounds on the heat transport lead to improved bounds for the poloidal energy.