On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $α(T) \ll 1$, responsible for the cutoff. The curve $\ln L(\ln α)$ is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wavenumber regions. Excellent agreement with recent experiment by Walmsley {\it et al.} [arXiv:0710.1033]--in which $L(T)$ has been measured down to $T \sim 0.08 $K--implies that the scenario of low-temperature superfluid turbulence is now experimentally validated, and allows to quantify the Kelvin-wave cascade spectrum.
Scale Separation Scheme for Simulating Superfluid Turbulence: Kelvin-Wave Cascade
开尔文波的柯尔莫哥洛夫型级联-涡线上的扭曲波-在低温下超流湍流的松弛中起着关键作用。本文提出了一种模拟单涡线上Kelvin波叶栅的有效数值格式。这个想法很可能是一个全面的模拟超流湍流的不同制度的推广。利用新的方案，我们能够明确地解决级联谱指数，从而解决最近的模拟[1]和最近发展的解析理论[2]之间的争议。[1]W.F. Vinen，M. Tsubota和A. Mitani，Phys. Rev. Lett. 91，135301（2003）。[2]E. V. Kozik和B. V. Svistunov，物理学评论快报。92，035301（2004）中所述。
Theoretical considerations are made of superfluid turbulence in the Kelvin wave cascade regime at low temperatures (T < 1K) and length scales of the order or smaller than the intervortical distance. The energy spectrum is shown to be in accord with the Kolmogorov scaling. The vortex line decay equation is shown to have an underlying Hamiltonian framework. Effects of spatial intermittency (exhibited in laboratory experiments) on superfluid turbulence are incorporated via the fractal nature of the vortex lines, for length scales of the order or smaller than the intervortical distance. The spatia…
Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a non-zero mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi two-dimensional system exhibiting a…
Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
研究了由Gross-Pitaevskii方程驱动的量子化超流涡旋中Kelvin波的统计性质。没有人为的强迫或耗散。准确跟踪涡流位置。这一过程直接使我们能够获得凯文波占据数谱。从初始条件下的长时间积分和整体平均获得的数值数据支持[L 'vov和Nazarenko，JETP Lett 91，428（2010）]中提出的谱。惯性范围内的开尔文波模式被发现是高斯弱湍流预测所预期的。最后研究了开尔文波谱的耗散范围。在这个范围内观察到强烈的非高斯波动。
In quantum electrodynamics, the zero-charge effect originates from the logarithmic dependence of the coupling constant in the action of the electromagnetic field on the ratio of the ultraviolet and infrared energy cutoffs. An analogue of this effect in Weyl superfluid $^3$He-A is the logarithmic divergence of the bending energy of the orbital anisotropy axis at low temperatures, where temperature plays the role of the infrared cutoff and the vector of the orbital anisotropy plays the role of the vector potential of the synthetic electromagnetic field for Weyl fermions. We calculate numerically…
Development of experimental techniques to study superfluid dynamics, in particular, application of nanomechanical oscillators to drive vortex lines, enables potential observation of the Kelvin-wave cascade on quantized vortices. One of the first questions which then arises in analysis of the experimental results is the relation between the energy flux in the cascade and the amplitude of the Kelvin waves. We provide such relation based on the L'vov-Nazarenko picture of the cascade. Remarkably, the amplitude of the waves depends on the energy flux extermely weakly, as power one tenth.
We discuss the energy and vorticity spectra of turbulent superfluid $^4$He in all the temperature range from $T=0$ up to the phase transition "$λ$ point", $T_λ\simeq 2.17\,$K. Contrary to classical developed turbulence in which there are only two typical scales, i.e. the energy injection $L$ and the dissipation scales $η$, here the quantization of vorticity introduces two additional scales, i.e the vortex core radius $a_0$ and the mean vortex spacing $\ell$. We present these spectra for the super- and normal-fluid components in the entire range of scales from $L$ to $a_0$ including the cross-o…
We report a detailed analysis of the energy spectra, second- and high-order structure functions of velocity differences in superfluid $^4$He counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the one-dimensional energy spectrum $E_{xz} (k_y)$ (averaged over the $xz$-plane, parallel to the channel wall), directly measured as a function of the wall-normal wave-vector $k_y$, gives more detailed information on the energy distribution over scales than the corresponding second-order structure function $S_{2}(δ_y)$. In particular, we discover two intervals …
We present a comprehensive statistical study of free decay of the quantized vortex tangle in superfluid $^4$He at low and ultra-low temperatures, $0\leqslant T \leqslant 1.1\,$K. Using high resolution vortex filament simulations with full Biot-Savart vortex dynamics, we show that for ultra-low temperatures $T\lesssim 0.5 \,$K, when the mutual friction parameters $α\simeq α' < 10^{-5}$, the vortex reconnections excite Kelvin waves with wave lengths $λ$ of the order of the inter-vortex distance $\ell$. These excitations cascade down to the resolution scale $Δξ$ which in our simulations is of the…
We report on the analysis of the root mean square curvature as a function of the numerical resolution for a single reconnection of two quantized vortex rings in superfluid helium. We find a similar scaling relation as reported in the case of decaying thermal counterflow simulations by L. Kondaurova et al. There the scaling was related to the existence of a Kelvin-wave cascade which was suggested to support the L'vov-Nazarenko spectrum. Here we provide an alternative explanation that does not involve the Kelvin-wave cascade but is due to the sharp cusp generated by a reconnection event in a sit…
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…
