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

• Published in: Journal of fluid mechanics Vol. 500; pp. 263 - 281
• Main Authors: OTERO, JESSE, DONTCHEVA, LUBOMIRA A., JOHNSTON, HANS, WORTHING, RODNEY A., KURGANOV, ALEXANDER, PETROVA, GUERGANA, DOERING, CHARLES R.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.02.2004
• Subjects: Convection; Convection and heat transfer; Exact sciences and technology; Flows through porous media; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Heat transport; Nonhomogeneous flows; Physics; Turbulent flows, convection, and heat transfer; Porous medium flow; Nusselt number; Digital simulation; Natural convection; Modelling; Rayleigh number; Heat transfer
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112003007298

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.