Journal of Fluid Mechanics



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


JESSE OTERO a1, LUBOMIRA A. DONTCHEVA a2, HANS JOHNSTON a3, RODNEY A. WORTHING a4, ALEXANDER KURGANOV a5, GUERGANA PETROVA a6 and CHARLES R. DOERING a3a7
a1 Department of Mathematics, Ohio State University, Columbus, OH 43210, USA
a2 Department of Computer Science & Engineering, University of Washington, Seattle, WA 98195-2350, USA
a3 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA
a4 Breasco LLC, Ann Arbor, MI 48197, USA
a5 Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
a6 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
a7 Michigan Center for Theoretical Physics, Ann Arbor, MI 48109-1120, USA

Article author query
otero j   [Google Scholar] 
dontcheva l   [Google Scholar] 
johnston h   [Google Scholar] 
worthing r   [Google Scholar] 
kurganov a   [Google Scholar] 
petrova g   [Google Scholar] 
doering c   [Google Scholar] 
 

Abstract

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 $Ra \,{=}\, 4\pi^2$ up to $Ra\,{=}\,10^4$. Over an intermediate range of increasing Rayleigh numbers, the simulations display the ‘classical’ heat transport $\hbox{\it Nu} \,{\sim}\, Ra$ scaling. As the Rayleigh number is increased beyond $Ra \,{=}\, 1255$, we observe a sharp crossover to a form fitted by $\hbox{\it Nu} \,{\approx}\, 0.0174 \times Ra^{0.9}$ 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: $\hbox{\it Nu} \,{\le}\, 0.0297 \times Ra$. 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.

(Received April 30 2003)
(Revised September 2 2003)



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