Complex convective structures in three-dimensional binary fluid convection in a porous medium

Abstract

Three-dimensional convection in a binary mixture in a porous medium heated from below is studied. For negative separation ratios steady spatially localized convection patterns are expected. Such patterns, localized in two dimensions, are computed in square domains with periodic boundary conditions and three different aspect ratios. Numerical continuation is used to examine their growth as the Rayleigh number varies and to study their interaction with their images under periodic replication once they reach the size of the domain. In relatively small domains with six critical wavelengths on a side three different structures are found, two with four arms extended either along the principal axes or the diagonals and one with eight arms. As these states are followed as a function of the Rayleigh number all succeed in growing so as to ultimately fill the domain thereby generating an extended convection pattern. In contrast, in larger domains, with 12 or 18 critical wavelengths on a side, the solution branches undergo much more complex behavior but appear to fail to generate spatially extended states. In each case both D4- and D2-symmetric structures are computed.