3-DIMENSIONAL CONVECTION IN A CUBIC BOX OF FLUID-SATURATED POROUS MATERIAL

Calculations of finite amplitude convection in cubic boxes containing fluid-saturated porous material are reported for Rayleigh numbers R as large as 150. Steady two- or three-dimensional convection can always be forced by appropriate choice of initial conditions. Randomly chosen initial conditions will result in either two- or three-dimensional convection. Although there is a non-uniqueness associated with initial conditions which makes possible either two- or three-dimensional convection, the non-uniqueness is limited in the sense that only one two-dimensional or one three-dimensional solution appears to be realizable. Two-dimensional flows have larger Nusselt numbers than three-dimensional flows for R ≲ 97; the opposite is true for R ≳ 97. © 1979, Cambridge University Press. All rights reserved.