Numerical investigation of the flow properties of He II

Abstract

In the framework of the reconnecting vortex-tangle model, flow properties of He II were studied numerically. The Crank-Nicolson method was used to calculate the motion of quantized $^{4}\mathrm{He}$ vortices, assuming smooth walls in infinitely long channels, applying periodic boundary conditions in the direction of the flow, and with friction coefficients \ensuremath{\alpha}=0.1 and \ensuremath{\alpha}'=0. Flow channels with square and circular cross sections and infinitely wide slits were studied. The superfluid velocity profile was assumed to be flat; the normal-component velocity profile was either flat or parabolic. Special interest was paid to the time-averaged line-length density and the average mutual-friction force density as functions of the difference between the average normal-fluid velocity and the externally applied superfluid velocity. The influence of the periodicity length on the calculated flow properties was determined. The results were compared with experiment.