Dissipation in quantum turbulence in superfluid ${}^4$He above 1K

Abstract

There are two commonly discussed forms of quantum turbulence in superfluid ${}^4$He above 1K: in one there is a random tangle of quantizes vortex lines, existing in the presence of a non-turbulent normal fluid; in the second there is a coupled turbulent motion of the two fluids, often exhibiting quasi-classical characteristics on scales larger than the separation between the quantized vortex lines in the superfluid component. The decay of vortex line density, $L$, in the former case is often described by the equation $dL/dt=-{\chi }_2(\kappa /2\pi )L^2$, where $\kappa$ is the quantum of circulation, and ${\chi }_2$ is a dimensionless parameter of order unity. The decay of total turbulent energy, $E$, in the second case is often characterized by an effective kinematic viscosity, ${\nu }^{\prime }$, such that $dE/dt=-{\nu }^{\prime }{\kappa }^2{L}^2$. We present new values of ${\chi }_2$ derived from numerical simulations and from experiment, which we compare with those derived from a theory developed by Vinen and Niemela. We summarise what is presently known about the values of ${\nu }^{\prime }$ from experiment, and we present a brief introductory discussion of the relationship between ${\chi }_2$ and ${\nu }^{\prime }$, leaving a more detailed discussion to a later paper.

11 pages, 12 figures