Role of thermal friction in relaxation of turbulent Bose-Einstein condensates

In recent experiments, the relaxation dynamics of highly oblate, turbulent Bose-Einstein condensates (BECs) was investigated by measuring the vortex decay rates in various sample conditions [Phys. Rev. A 90, 063627 (2014)] and, separately, the thermal friction coefficient $\ensuremath{\alpha}$ for vortex motion was measured from the long-time evolution of a corotating vortex pair in a BEC [Phys. Rev. A 92, 051601(R) (2015)]. We present a comparative analysis of the experimental results, and find that the vortex decay rate $\mathrm{\ensuremath{\Gamma}}$ is almost linearly proportional to $\ensuremath{\alpha}$. We perform numerical simulations of the time evolution of a turbulent BEC using a point-vortex model equipped with longitudinal friction and vortex-antivortex pair annihilation, and observe that the linear dependence of $\mathrm{\ensuremath{\Gamma}}$ on $\ensuremath{\alpha}$ is quantitatively accounted for in the dissipative point-vortex model. The numerical simulations reveal that thermal friction in the experiment was too strong to allow for the emergence of a vortex-clustered state out of decaying turbulence.