Bounds on the convective heat transport in a rotating layer

Previous bounds on the convective heat transport in a horizontal layer heated from below and rotating about a vertical axis have been improved through the use of separate energy balances for the poloidal and toroidal components of the velocity field. Because the additional constraint imposed for the solution of the variational problem for the extremalizing vector field leads to Euler-Lagrange equations which can no longer be solved analytically, numerical methods must be employed. A Galerkin scheme is introduced and the variational problem is solved in the case when stress-free conditions are assumed at the upper and lower boundaries. Results are presented as a function of the Rayleigh number and the rotation parameter for the Prandtl numbers P=7, 0.7, 0.1, and 0.025.