Critical dynamics at a Hopf bifurcation to oscillatory Rayleigh-Bénard convection

The steady-state and dynamic properties of the transition to oscillatory convection in a low-Prandtl-number fluid, dilute ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, are presented. Critical slowing down is observed and characterized by a phenomenological Landau-Hopf equation in analogy with equilibrium mean-field critical phenomena. In contrast to the onset of classical time-independent Rayleigh-Bénard convection, where appreciable rounding is typically observed, there is no measurable rounding at the oscillatory onset down to a reduced Rayleigh number of 3×${10}^{\mathrm{-}4}$. Possible reasons for this are discussed. Different functional singularities are observed for the rms amplitudes of the fundamental and first harmonic spectral components of the oscillation. Finally, the Prandtl-number dependence of the parameters of the dynamics is presented.