Oscillatory Convection in a Dilute HELIUM-3-SUPERFLUID HELIUM-4 Solution

Convective instabilities in a rectangular, unity aspect ratio Rayleigh-Benard cell with a solution of 1.46% ('3)He in superfluid ('4)He have been studied in The Prandtl number range of 0.045(, )<(, )(sigma)(, )<(, )0.15. The onset of stationary convection is much like that in a classical, one-component fluid. The oscillatory instability is studied by using an extremely sensitive local temperature probe. It is found that the total heat transport efficiency is suppressed by the oscillations in the entire range of Prandtl number we have studied. The local temperature probe indicates a striking difference in the oscillatory amplitude when the sense of rotation of the convective rolls is reversed. The magnitude of the convective velocity is deduced from both the initial slope of the Nusselt number near the onset of the stationary convection and the frequency of the oscillations. The temperature dependence of the convective velocity determined by these two methods agrees very well with each other. The observed behavior of the oscillatory frequency and onset condition support the theory of oscillatory convection for a classical, low-Prandtl-number, one-component fluid. It is found that the onset of oscillations can be treated analogously to a second-order phase transition. The oscillatory temperature amplitude is interpreted as closely related to the square of the order parameter. The first quantitative measurements of the relaxation of the oscillatory temperature amplitude have been made both above and below the onset. The relaxation is more accurately described by the solution of Landau's equation than by a simple exponential form. The relaxation time exhibits critical slowing down at the onset and shows an excellent symmetry around the onset.