High Rayleigh Number Convection in a Fluid Saturated Porous Layer

Thermal convection and fluid mechanics in a porous medium is relevant to a variety of phenomena ranging from groundwater flow and geothermal energy transport, to the effectiveness of fiberglass insulation, to the occurance of avalanches on snow covered mountainsides.  In the research described here, the most basic model (the Darcy-Boussinesq equations at infinite Darcy-Prandtl number) is used to study convection and heat transport over a broad range of heating levels as measured by the nondimensional Rayleigh number Ra.  High resolution direct numerical simulations are performed to explore the modes of convection and measure the heat transport as quantified by the Nusselt number Nu, the enhancement factor of total (conductive plus convective) heat flux over pure conduction alone.  We present simulation results from onset at Ra = 4π2 up to Ra = 104. Over an intermediate range of increasing Rayleigh numbers, the simulations display the `classical' (jargon to be explained) heat transport Nu ~ Ra scaling.  As the Rayleigh number is increased beyond Ra = 1255 we observe a sharp crossover to a form fit by Nu ≈ .0174 Ra.9 over nearly a decade up to the highest Ra accessible.  Rigorous upper bounds on the high Rayleigh number heat transport have also been derived: they of the classical scaling form with an explicit prefactor, Nu ≤ .0297 Ra.   The bounds are compared directly to the results of the simulations, as well as to real laboratory experiments.  We also report various dynamical transitions in the simulations for intermediate values of Ra, including hysteresis and multistability observed in the simulations as the Rayleigh number is decreased from 1255 back down to onset.  This is joint work with Jesse Otero, Lubomira A. Dontcheva, Hans Johnston, Rodney A. Worthing, Alexander Kurganov and Guergana Petrova, and is the content of a paper published in Journal of Fluid Mechanics (2004).

Charles Doering

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