Oscillatory convective instability in a superfluid /sup 3/He-/sup 4/He mixture

The linear stability analysis of a superfluid mixture subject to a vertical temperature gradient is presented. The main result obtained in this paper is the existence of an oscillatory instability in a superfluid mixture heated only from below. The criteria for onset of oscillatory instability and the corresponding neutral frequencies in a superfluid region of the /sup 3/He-/sup 4/He phase diagram are treated. Depending on the magnitude of dissipation of superfluid motion, two different types of overstabilities exist. These have different physical origins. In the case of large dissipation of superfluid motion the oscillatory criterion and the neutral frequency are similar to those in a regular binary mixture with large abnormal thermal diffusion. In the case of small dissipation of superfluid motion a fundamentally new type of oscillatory convective instability is predicted. This instability is actually the undamped standing second-sound waves. We believe it should be possible to observe the predicted effect in the vicinity of the tricritical point.