Abstract
Convection in a fluid-saturated porous layer at high Rayleigh numbers is briefly reviewed. When a saturated porous layer is subjected to bottom heating, steady convection sets in with the increase of the Rayleigh number R beyond the critical value. If the porous layer has an infinite horizontal extent, the critical value is R = 4π2= 40. Further increase of the Rayleigh number transforms steady convection to a time-dependent or oscillatory state. In a two-dimensional square the transition from steady to oscillatory state takes place at R = 390. The first oscillatory convection characterized by the oscillation of average heat flux (Nusselt number) exhibits a simply periodic state. The frequency at the onset of the oscillation is about 83 in a diffustion time. The oscillation frequency in general increases with the Rayleigh number. The flow and temperature fields possess center-symmetric patterns. At the Rayleigh number somewhere between 800 and 1000 the convective state becomes chaotic with a broad band noise in a spectral power diagram of the Nusselt number oscillation. The flow and temperature patterns at the chaotic state no longer possess the center-symmetry. The physical mechanism responsible for the oscillation is identified as a thermal boundary layer instability.
It has been also established that oscillatory condition exists in a three-dimensional space. The onset of oscillation takes place at R = 575. The first oscillatory state is simply periodic with the frequency 170. At R = 650 the convection becomes a more complex state with at least two fundamental frequencies. Key words: natural convection, porous medium, heat transfer, oscillatory convection, chaotic convection
