Three-Dimensional Coupled Dynamics of the Two-Fluid Model in Superfluid He4 : Deformed Velocity Profile of Normal Fluid in Thermal Counterflow

Abstract

The coupled dynamics of the two-fluid model of superfluid ^{4}He is numerically studied for quantum turbulence of the thermal counterflow in a square channel. We combine the vortex filament model of the superfluid and the Navier-Stokes equations of normal fluid. Simulations of the coupled dynamics show that the velocity profile of the normal fluid is deformed significantly by superfluid turbulence as the vortices become dense. This result is consistent with recently performed visualization experiments. We introduce a dimensionless parameter that characterizes the deformation of the velocity profile.

Fully Coupled Two-Fluid Dynamics in Superfluid He4 : Anomalous Anisotropic Velocity Fluctuations in Counterflow

“…The result is qualitatively consistent with the one-ring simulation [41]. The normalfluid vortex structure smaller than the mean spacing of the filaments was not examined in the preceding simulation [45].…”

“…However, the model does not describe the dynamics of quantized vortices although it is essential for QT. The other method is to employ the VFM for the superfluid coupled with the HVBK equations for the normal fluid [41][42][43][44][45]. Kivotides et al performed simulation of a propagating quantized-vortex ring and indicated that two vortex rings of the normal fluid are produced around the quantized vortex [41].…”

“…Kivotides et al performed simulation of a propagating quantized-vortex ring and indicated that two vortex rings of the normal fluid are produced around the quantized vortex [41]. Yui et al examined the laminar normal fluid in the counterflow QT, and confirmed the deformation of the velocity profile caused by coarse-grained mutual friction [45].…”

“…L (r) denotes the filaments in the local subvolume Ω (r) at the position r. The size of Ω determines the coupling length scale (See Supplements). In the study, we employ the local coupling condition 3 > Ω , i.e., the mutual friction F ns only affects the normal fluid at the position of the vortex filaments in contrast to a preceding study [45]. We use the incompressible condition ∇ · v n = 0 as a closure.…”

Dissipation in quantum turbulence in superfluid He4 above 1 K

“…The experiments [8] use wider channels; in practice the velocity profile of the normal fluid differs generally from the Poiseuille form [8]; and in practice the vortex lines in the superfluid component are likely to suffer drag or pinning at the solid boundaries. Simulations that take account of these differences are starting to be practicable [22], and could eventually allow more satisfactory comparison with experiment.…”