High-Rayleigh-number convection in a fluid-saturated porous layer

The Darcy-Boussinesq equations at infinite Darcy-Prandtl number are used to study convection and heat transport In a basic model of porous-medium convection over a broad range of Rayleigh number Ra. High-resolution direct numerical simulations are performed to explore the modes of convection and measure the heat transport, i.e. the Nusselt number Nu, from onset at Ra = 4pi(2) up to Ra = 10(4). Over an intermediate range of increasing Rayleigh numbers, the simulations display the 'classical' heat transport Nu similar to Ra scaling. As the Rayleigh number is increased beyond Ra = 1255, we observe a sharp crossover to a form fitted by Nu approximate to 0.0174 x Ra-0.9 over nearly a decade up to the highest Ra. New rigorous upper bounds on the high-Rayleigh number heat transport are derived, quantitatively improving the most recent available results. The upper bounds are of the classical scaling form with an explicit prefactor: Nu less than or equal to 0.0297 x Ra. The bounds are compared directly to the results of the simulations. We also report various dynamical transitions for intermediate values of Ra, including hysteretic effects observed in the simulations as the Rayleigh number is decreased from 1255 back down to onset.