Dynamics of the Vortex Line Density in Superfluid Turbulence

A comprehensive experimental study of the intrinsic fluctuations associated with superfluid turbulence is presented. Fluctuations in the chemical potential and temperature difference for HeII thermal counterflow in a small diameter tube become extremely large at the TI/TII transition. The fluctuations in the fully developed TII state are smaller than 0.1%, in accord with computer simulations of fluctuations in homogeneous turbulence. Consistent measurements of the power spectra, power amplitude, relaxation time, and steady state vortex line density are reported. Our results are in substantial disagreement with previous measurements of fluctuations in superfluid turbulence. It is suggested that the major discrepancy is due to unexpectedly large amplitude fluctuations generated by macroscopic inhomogeneities in the vortex line density present in earlier experiments. Evidence from our own measurements of externally driven fluctuations support this interpretation. In addition to the dynamics of the intrinsic line density fluctuations, a study of the effects of externally driven quadratic, colored noise are reported. The findings of this study are that the turbulence states are postponed with respect to the steady state results at high frequency noise, while at low frequencies behavior quite different from the steady state results is observed.