Wave turbulence of a rotating array of quantized vortices in the $T \rightarrow 0$ temperature limit

etc15 Tracking Number 310

The dynamics of quantized vortices in the zero temperature limit $T \rightarrow 0$ is currently of great interest, particularly in the case of the Fermi superfluid $^3$He-B. Here we study wave turbulence, generated by the librating motion of a rotating cylindrical container filled with $^3$He-B, in the limit of vanishing viscous forces at temperatures $T \leq 0.2 T_{c}$. The polarization of the quantized vortices with respect to the axis of rotation is measured using non-invasive NMR techniques. We observe a decrease of the polarization when the librating motion is started, and a two-stage relaxation process when the modulation of the rotation velocity is stopped. The first relaxation process is associated with the dissipation of large-scale flow stored in inertial waves and the solid body rotation of the vortex array. From the decay of these energy reservoirs we determine the rate of energy dissipation of large-scale flow. The later second process is related to the relaxation of Kelvin waves on individual vortices. This process is monitored by the recovery of the polarization. The existence of a Kelvin wave cascade at the lowest temperatures is currently a central open question. We supply some evidence for the cascade.