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Register a new userOn the investigation of properties of superfluid $^4$He turbulence using a hot-wire signal
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We report hot-wire measurements performed in two very different, co- and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.
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We obtain the von Karman-Howarth relation for the stochastically forced three-dimensional Hall-Vinen-Bekharvich-Khalatnikov (3D HVBK) model of superfluid turbulence in Helium ($^4$He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analyitcal studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P(gamma)$, of the ratio $gamma$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P(gamma) sim gamma^3$, for $gamma ll 1$, and $P(gamma) sim gamma^{-3}$, for $gamma gg 1$. Furthermore, we show that the PDF $P(theta)$, of the angle $theta$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P(theta)sim theta$ for $theta ll theta_*$ and $P(theta)sim theta^{-4}$ for $theta_* ll theta ll 1$, where $theta_*$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, and the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid Helium $^4$He, so our results are of direct relevance to superfluid turbulence in this system.
The results of experimental and theoretical studies of the parametric decay instability of capillary waves on the surface of superfluid helium He-II are reported. It is demonstrated that in a system of turbulent capillary waves low-frequency waves are generated along with the direct Kolmogorov-Zakharov cascade of capillary turbulence. The effects of low-frequency damping and the discreteness of the wave spectrum are discussed.
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.
We study numerically nonuniform quantum turbulence of coflow in a square channel by the vortex filament model. Coflow means that superfluid velocity $bm{v}_s$ and normal fluid velocity $bm{v}_n$ flow in the same direction. Quantum turbulence for thermal counterflow has been long studied theoretically and experimentally. In recent years, experiments of coflow are performed to observe different features from thermal counterflow. By supposing that $bm{v}_s$ is uniform and $bm{v}_n$ takes the Hagen-Poiseiulle profile, our simulation finds that quantized vortices are distributed inhomogeneously. Vortices like to accumulate on the surface of a cylinder with $bm{v}_s simeq bm{v}_n$. Consequently, the vortex configuration becomes degenerate from three-dimensional to two-dimensional.
We develop an analytic theory of strong anisotropy of the energy spectra in the thermally-driven turbulent counterflow of superfluid He-4. The key ingredients of the theory are the three-dimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energy-rate equation, which is fully supported by the numerical solution. The two-dimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiment, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a near-classical non-universal cascade-dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters. This article is a part of the theme issue Scaling the turbulence edifice.
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