Spatial distribution of vortices and metastable states in rotating He II

Accurate measurements of the attenuation of second sound in rotating rectangular cavities are reported. By driving different resonant modes of the cavity, we obtained information about the spatial distribution of vortices. The theory of stable and metastable states in deformed rotating cylinders is developed in the limit of many vortices, then tested by experiment in the high-velocity range. Metastability and hysteresis phenomena are observed in the whole investigated range of angular velocities ($\Omega \sim {10}^{-2\mathrm{}} \mathrm{to} 10$ ${\sec }^{-1\mathrm{}}$). At a given $\Omega$, the observed vortex number $N$ can fluctuate around the equilibrium value $N_0$: $\frac{\Delta N}{N_0}\lesssim 10\%$ for $\Omega \gtrsim 1$ ${\sec }^{-1\mathrm{}}$; $\frac{\Delta N}{N_0}\sim 1$ for $\Omega \lesssim {10}^{-1\mathrm{}}$ ${\sec }^{-1\mathrm{}}$. Primarily, thanks to a good temperature stabilization, we were able to distinguish and systematically reproduce three vortex states for any value of $\Omega$: the thermodynamic equilibrium $N_0$ state, and two limiting metastable states containing, respectively, the minimum number $N_1$ and the maximum number $N_2$ of vortices. In the high-velocity range, $\Delta N$ can be related to a variation of the thickness $d$ of the vortex-free strip occurring near the walls; $d$ varies between two extremal values $d_1$ and $d_2$, which turn out to be independent of the boundary geometry. The role of mechanical vibrations is discussed, and the hyrdodynamic predictions concerning the barrier energy are reconsidered in relation to these experiments. From the low-velocity results, it emerges that the experimental value of the critical angular velocity is in substantial disagreement with theory.