Superfluid transition in He-4 in gravity and heat flow

When He-4 in a normal fluid state near the superfluid transition is cooled from the bottom below the transition, a superfluid region appears at the bottom and slowly expands in the upward direction. We performed simulations for this case in one dimension fixing the temperature T-b at the bottom and the heat flux at the top Q. We find densely distributed phase slip centers rapidly oscillating in time in the expanding superfluid region. Their role is to produce a temperature gradient compensating the transition temperature gradient (dT(lambda)(p)/dp)rho g in gravity and to produce a constant negative reduced temperature T-Tx(p) with small fluctuations superposed. The superfluid velocity multiplied by the correlation length is found to be violently fluctuating around h/root 3m.