Existence of a codimension-2 point at the threshold of binary-fluid convection between rigid, impermeable boundaries

Numerical calculation of the linear instability to oscillatory and stationary convection in binary-fluid mixtures between rigid, impermeable boundaries shows that the critical wave number and frequency of the oscillatory solution jump discontinuously as the threshold Rayleigh number is followed as a function of fluid parameters, contrary to a recent claim of B. J. A. Zielinska and H. R. Brand [Phys. Rev. A 35, 4349 (1987)]. A degenerate codimension-2 point is found only if the wave numbers of the onset solutions are constrained.