Self-organization in H4 e near the superfluid transition in heat flow and gravity

We investigate the nonlinear dynamics of H4 e slightly below the superfluid transition by integrating model F equations in three dimensions. When a superfluid is heated from above under gravity, a vortex tangle and sheetlike phase slips both appear near the bottom plate. Then a self-organized superfluid containing high-density vortices and phase slips grows upward, where high-amplitude second sounds are emitted from the self-organized to the ordinary superfluid region. A phase slip sheet often changes into a vortex aggregate and vice versa. The thermal resistance due to these defects produces a constant temperature gradient equal to the gradient of the pressure-dependent transition temperature Tλ (p). In this self-organized region, the temperature deviation T- Tλ (p) consists of a negative constant determined by the heat flux Q and time-dependent fluctuations. Its time average is calculated to be 155 nK for Q=11.2 erg/ cm2 s in good agreement with the experiment.