Mutual-friction-driven turbulent statistics in the hydrodynamic regime of superfluid ^{3}He-B.

Abstract

It is well known that the turbulence that evolves from the tangles of vortices in quantum fluids at scales larger than the typical quantized vortex spacing ℓ has a close resemblance with classical turbulence. The temperature-dependent mutual friction parameter α(T) drives the turbulent statistics in the hydrodynamic regime of quantum fluids that involves a self-similar cascade of energy. From a simple theoretical analysis, here we show that superfluid ^{3}He-B in the presence of mutual damping exhibits a k^{-5/3} Kolmogorov energy spectrum in the entire inertial range ℓ<r<L at temperature T≲0.2T_{c}, while at T≳0.2T_{c} dissipation begins to dominate larger eddies exhibiting a k^{-3} spectrum toward the energy pumping scale L. At T≈0.35T_{c}, eddies of all size, being highly affected by damping, exhibit a k^{-3} spectrum in the entire inertial range. The consistency of this result with the predictions of recent direct numerical simulations indicates that the present theoretical framework is applicable in quantifying the hydrodynamic regime of quantum turbulence.