Strong anisotropy of superfluid He4 counterflow turbulence

Abstract

We report on a combined theoretical and numerical study of counterflow turbulence in superfluid 4 He in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normal-fluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity.

Bathtub vortex in superfluid He4

“…Microscopically, this assumption does not hold. Recent studies [31][32][33][34] have shown that the normal fluid profile is nontrivially modulated by the presence of quantized vortices, through mutual friction on the scale of the intervortex distance. However, in the analysis below, we consider only the macroscopic vortex bundle structure that develops in the macroscopic steady normal flow; a study of the characteristic small-scale structures that emerge due to coupled dynamics remains future work to be dealt with.…”

Theory of anisotropic superfluid4He counterflow turbulence

“…Similar to [30], our approach to the problems of counterflow turbulence with the scales much larger than the intervortex distance [23,24,36] is based on the coarse-grained equations [14,24,36,37] of the incompressible superfluid turbulence. These equations, often called Hall–Vinen–Bekarevich–Khalatnikov equations (HVBK) [38,39], have a form of two Navier–Stokes equations (NSE) for the turbulent velocity fluctuations of the normal fluid and superfluid components unfalse(bold-italicr,tfalse) and usfalse(bold-italicr,tfalse) in the presence of space-homogeneous mean normal and superfluid velocities Un and Us normal∂usnormal∂t+false[false(us+Usfalse)⋅bold∇false]us−1ρsbold∇ps=νsnormalΔus+fns,1emfns≃Ω…”

“…Since all relevant fluid parameters [25] are strongly temperature-dependent, the statistical properties of such a counterflow are not universal. Instead, the statistics of the counterflow depends on the temperature and on the relative velocity bold-italicUns=Un−Us [24,26–30]. Recent flow visualization experiments [27,28,31–33] stimulated theoretical and numerical investigations of the energy spectra of the counterflow turbulence.…”

“…Recent flow visualization experiments [27,28,31–33] stimulated theoretical and numerical investigations of the energy spectra of the counterflow turbulence. It was shown [23,24,30,34,35] that besides the dependence on flow parameters, the energy spectra are sensitive to the angle with respect to the direction of the counterflow velocity. As a result, the energy spectra in the counterflow turbulence are anisotropic and strongly suppressed in the direction of Uns.…”

“…Although such a spectral anisotropy was predicted theoretically and confirmed numerically [29,30], the experimental investigations of the energy spectra for the time being are limited to the plane, orthogonal to the direction of the counterflow velocity [28,33], while the theory of counterflow turbulence [24] was developed assuming spectral isotropy. In this paper, we relax this assumption and offer a theoretical description of the spectral anisotropy of the energy spectra of the counterflow turbulence in superfluid 4 He.…”