Convection is an ubiquitous phenomenon which occurs in the atmosphere, theoceans, the interior of the Earth, and in numerous engineering applications.Convection has also served as a paradigm for pattern forming systems because theflow can organize itself into rolls or polygonal structures. It is not known howthe large scales of convection are organized once the flow has become turbulent. This project intends to study the large scale patterns which persist in theturbulent regime. Convection in a plane layer will be simulated within theBoussinesq approximation. Quantities extracted from the computations willinclude the Nusselt number, the Reynolds number, and the spectral distributionsof heat transport and kinetic energy. The equations of motion are solved with a spectral method. The velocity field isdecomposed into poloidal and toroidal scalars in order to automatically obtain adivergence free velocity field. The spectral decomposition uses Fourier modesand Chebychev polynomials.