Dynamies of turbuleni helium II - limits of the Vinen model 635 Z. TUREK, Applieation of the Fourier eosine series to the approximation of solutions to initial non-Diriehlet boundary value problems

Abstract

T HE DYNAMICS of superfiuid helium is considered within the framework of the Vinen model. According to Vinen equation, counterfi ow (the relative velocity of the two helium components) gives rise to quantum turbulence. The mutual fr iction force , exerted on t he vortex tangle by the normal component, couples it with t he superfiui d component. The system of 3 ordin ary equations is numerically solved to calculate t he characteristic entrainment t ime in which the counterfl ow ceases. For t he typical velocities of order 1 cmjs, t he entrain ment t ime is found to be much small er than the vorticity diffusion time for the length scale of 1 cm. It suggests that in the typical spin-up experiments the quantum turbulence plays a key role coup ling t he two components. Unfortunately t he Vinen model appli ed to spin-up turned out to be inconsistent; the vortex line density calculated from the superfluid component vorticity was fou nd to be m uch larger than that predicted by t he Vinen equation.