Transport in a slowly perturbed convective cell flow

We study transport properties in a simple model of two-dimensional roll convection under a slow periodic (period of order 1/ε≫1) perturbation. The problem is considered in terms of conservation of the adiabatic invariant. It is shown that the adiabatic invariant is well conserved in the system. It results in almost regular dynamics on large time scales (of order ∼ε −3 ln ε) and hence, fast transport. We study both generic systems and an example having some symmetry.