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W. G. Pritchard Lab Seminar: 4:30-5:30 PM, 320 Whitmore Laboratory

	            **Monday May 2, 2005**
	
High Rayleigh number convection in a fluid saturated porous layer

Charles Doering

Dept of Mathematics
University of Michigan

Abstract:

Thermal convection and fluid mechanics in a porous medium are relevant to 
a variety of phenomena ranging from groundwater flow and geothermal 
energy transport to the effectiveness of fiberglass insulation.  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=4 pi^2 up to Ra=10^4.  Over an intermediate range of increasing
Ra, the simulations display the `classical' (jargon to be explained) heat 
transport 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 are 
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. This is joint work with J. Otero, L. 
Dontcheva, H. Johnston, R. Worthing, A. Kurganov and G. Petrova; it is the 
content of a paper published in Journal of Fluid Mechanics (2004).

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