Dynamies of turbuleni helium II, limits of the Vinen model (Archives of Mechanics - Test, 1997)
The dynamics of superfiuid helium is considered within the framework of the Vinen model. According to Vinen equation, counterfiow (the relative velocity of the two helium components) gives rise to quantum turbulence. The mutual friction force, exerted on the vortex tangle by the normal component, couples it with the superfiuid component. The system of 3 ordinary equations is numerically solved to calculate the characteristic entrainment time in which the counterflow ceases. For the typical velocities of order 1 cm/s, the entrainment time is found to be much smaller 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 coupling the two components. Unfortunately the Vinen model applied to spin-up turned out to be inconsistent; the vortex line density calculated from the superfluid component vorticity was found to be much larger than that predicted by the Vinen equation.