Abstract
Chaotic behaviour in numerical experiments can be demonstrated by tracking narrow periodic windows within the chaotic regime. Their presence guarantees that of the associated bifurcation structure, so the existence of these windows can be exploited in order to determine whether chaos is a property of the partial differential equations or created by discretization. If the bifurcation structure is robust individual bifurcations of codimension one converge at a rate consistent with the accuracy of the numerical scheme. Codimension-two bifurcations may be much more sensitive to truncation errors. This procedure is applied to thermosolutal convection in order to confirm the presence of chaos caused by a heteroclinic bifurcation with eigenvalues satisfying Shil'nikov's criterion.