Experimental observation of a codimension-two bifurcation in a binary fluid mixture

Abstract

Heat-transport measurements in a normal-fluid $^{3}\mathrm{\ensuremath{-}}^{4}$He mixture contained in a porous medium and heated from below show a bifurcation to steady or oscillatory flow, depending on the mean temperature. With increasing Rayleigh number R the oscillatory state is entered via a forward Hopf bifurcation with frequency ${\mathrm{\ensuremath{\omega}}}_{\mathrm{c}}$>0. As the stationary bifurcation is approached by change of the mean temperature, ${\mathrm{\ensuremath{\omega}}}_{\mathrm{c}}$ vanishes. With increasing R, the oscillatory state terminates with vanishing frequency and finite amplitude in a hysteretic bifurcation to a steady state. Those observations agree with recent theoretical predictions.