Counterflow quantum turbulence of He-II in a square channel: Numerical analysis with nonuniform flows of the normal fluid

Abstract

We perform a numerical analysis of counterflow quantum turbulence of superfluid 4 He with nonuniform flows by using the vortex filament model. In recent visualization experiments nonuniform laminar flows of the normal fluid, namely, Hagen-Poiseuille flow and tail-flattened flow, have been observed. Tail-flattened flow is a novel laminar flow in which the outer part of the Hagen-Poiseuille flow becomes flat. In our simulation, the velocity field of the normal fluid is prescribed to be two nonuniform profiles. This work addresses a square channel to obtain important physics not revealed in the preceding numerical works. In the studies of the two profiles we analyze the statistics of the physical quantities. Under Hagen-Poiseuille flow, inhomogeneous quantum turbulence appears as a statistically steady state. The vortex tangle shows a characteristic space-time oscillation. Under tail-flattened flow, the nature of the quantum turbulence depends strongly on that flatness. Vortex line density increases significantly as the profile becomes flatter, being saturated above a certain flatness. The inhomogeneity is significantly reduced in comparison to the case of Hagen-Poiseuille flow. Investigating the behavior of quantized vortices reveals that tail-flattened flow is an intermediate state between Hagen-Poiseuille flow and uniform flow. In both profiles we obtain a characteristic inhomogeneity in the physical quantities, which suggests that a boundary layer of superfluid appears near a solid boundary. The vortex tangle produces a velocity field opposite to the applied superfluid flow, and, consequently, the superfluid flow becomes smaller than the applied one.PACS numbers: 67.25.dk, 67.25.dm

Numerical Studies of Quantum Turbulence

“…The studies [75,78,80] reviewed above confirmed the steady state condition Eq. (32) of Vinen's equation:…”

“…Yui and Tsubota studied counterflow quantum turbulence in a duct by performing numerical simulations [77,78]. The visualization experiment of thermal counterflow by Marakov et al showed that the normal fluid velocity distribution becomes a Poiseuille profile, a tail-flattened profile, and a turbulent profile [35], as explained above.…”

“…This study investigated a mean velocity profile in a superfluid boundary layer, motivated by numerical studies for spatially inhomogeneous thermal counterflow [74,75,78,91] and visualization experiments [35,93,94,95,96,97,98]. As a result, they found that the logarithmic velocity profile could appear in wall-bounded QT.…”

“…(79) and (80) To begin with, we comment on A 0 (t) in Eq. (78). A constant field for A(r, t), which is a zero-wave-number mode, satisfies both the compressible and the incompressible conditions.…”

Coupled motion of Xe clusters and quantum vortices in He nanodroplets

“…The shapes and dynamics of bare vortices with fixed boundary conditions can, in principle, be calculated using the BiotSavart law [30][31][32][33]. However, the implementation of this approach is not straightforward due to the additional acquired mass of the dopant atoms and a possible vorticity-dependence of the droplet shape.…”