Dynamics of vortex lines density and heat transfer processes in superfluid helium
Институт теплофизики им. С.С. Кутателадзе СО РАН, пр. Ак. Лаврентьева, 1, г. Новосибирск, 630090, Россия
Novosibirsk State University, 2 Pirogova Str., Novosibirsk 630090 Russia
Received August 24, 2017
In this paper we analyze three types of equations for dynamics of vortex lines density. It is shown that the Vinen equation is more correct gives the values of the vortex tangle development time in the case of constant counterflow than other alternative equations. In the framework of the system of equations of hydrodynamics superfluid turbulence obtained at the phenomenological approach, it was obtained the boiling times of helium as function from the density of the heat flux by using alternative equations of dynamics for vortex lines dencity. Unlike experiments in which different dependences of boiling time tboilfrom density of the heat flux Q (tboil ∝ Qn, −4 ≤ n ≤ −2) are observed, in this case we get only a power dependence with the order n = −4. It is obtained the distribution of velocity of the normal component along the channel, the time dependence temperature near the heater. A comparison is made with the numerical results obtained earlier in the literature.
PACS: 67.25.dk Vortices and turbulence; PACS: 47.37.+q Q Hydrodynamic aspects of superfluidity; quantum fluids; PACS: 03.75.Kk Dynamic properties of conden-sates; Collective and hydrodynamic excitations, superfluid flow.