CO-SYMMETRY BREAKDOWN IN PROBLEMS OF THERMAL-CONVECTION IN POROUS-MEDIUM

We investigate two-dimensional thermal convection of saturating incomp ressible fluid in a horizontal cylinder filled with porous medium. The temperature distribution on the boundaries is time-independent and co rresponds to the heating from below. At supercritical parameter values the problem has infinite number of stationary solutions for arbitrary shape of the region. This degeneracy is connected with the so-called co-symmetry property: the existence of the vector field which is ortho gonal to the considered one. Non-coincidence of zeroes of these two fi elds leads generally speaking, to the degeneracy of the solutions. To destroy the degeneracy we add weak fluid seeping of the fluid through the boundaries either in vertical or in the horizontal direction. The breakdown of the family of the stationary solutions at high supercriti cal values of the Rayleigh number is studied in detail with the help o f the corresponding normal form. Several limit cycles with the twisted leading manifolds appear as a result of the family destruction. To in vestigate the dynamical behavior the finite-dimensional models of the convection which maintain the breakdown of co-symmetry, are constructe d on the base of the Galerkin approximation. The same scenario of the transition to chaos which seems to be connected with the co-symmetry b reakdown, is recovered for both kinds of seeping. The quasi-periodic s olution branches from the limit cycle. The further increase of the Pec let number leads to mode-locking, which is followed by the appearance of the homoclinic surface formed by the unstable manifold of the saddl e periodic orbit; destruction of the latter surface leaves in the phas e space the object with torus-like shape and non-integer fractal dimen sion.