研究了超流湍流氦非均匀逆流通道中的量子湍流问题。假设沿通道的逆流速度$V_{ns}^{x}(y)$在横向$y$上具有抛物线分布。这种说法对应于Khomenko等人最近的数值模拟[Phys. Rev. B \textbf{91}，180504（2015）]。作者报道了涡线密度（VLD）$\mathcal{L}(\mathbf{r},t)$的复杂行为，不同于$% \mathcal{L}\propto V_{ns}^{x}(y)^{2}$，它来自传统Vinen理论的简单直接的应用。很明显，维南理论应该通过考虑横向效应来改进，并且应该这样做的方式是文献中积极讨论的主题。本文讨论了VLD $\mathcal{L}(\mathbf{r},t)$的横向通量的几种可能机制，这些机制应包含在标准Vinen方程中，以充分描述非均匀量子湍流（QT）。结果表明，这些机制中最有效的是一个是有关的相位滑移现象。在现代化的Vinen方程中使用该通量修正了涡线密度分布异常的情况，并令人满意地描述了稳态和非稳态情况下的行为$\mathcal{L}(\mathbf{r},t)$。讨论了非均匀非定常量子湍流唯象Vinen理论的一般问题。
英文摘要：
The problem of quantum turbulence in a channel with an inhomogeneous counterflow of superfluid turbulent helium is studied. \ The counterflow velocity $V_{ns}^{x}(y)$ along the channel is supposed to have a parabolic profile in the transverse direction $y$. Such statement corresponds to the recent numerical simulation by Khomenko et al. [Phys. Rev. B \textbf{91}, 180504 (2015)]. The authors reported about a sophisticated behavior of the vortex line density (VLD) $\mathcal{L}(\mathbf{r},t)$, different from $% \mathcal{L}\propto V_{ns}^{x}(y)^{2}$, which follows from the naive, straightforward application of the conventional Vinen theory. It is clear, that Vinen theory should be refined by taking into account transverse effects and the way it ought to be done is the subject of active discussion in the literature. In the work we discuss several possible mechanisms of the transverse flux of VLD $\mathcal{L}(\mathbf{r},t)$ which should be incorporated in the standard Vinen equation to describe adequately the inhomogeneous quantum turbulence (QT). It is shown that the most effective among these mechanisms is the one that is related to the phase slippage phenomenon. The use of this flux in the modernized Vinen equation corrects the situation with an unusual distribution of the vortex line density, and satisfactory describes the behavior $\mathcal{L}(\mathbf{r},t)$ both in stationary and nonstationary situations. The general problem of the phenomenological Vinen theory in the case of nonuniform and nonstationary quantum turbulence is thoroughly discussed.
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…
The superfluid Reynolds number and the transition from potential flow to turbulence in superfluid $^4$He at mK temperatures
这篇评论发表在Phys.Rev.Lett上。144，155302（2015），M.T. Reeves，T.P. Billam，B.P. Anderson，and A.S. Bradley“Identifying a superfluid Reynolds number via dynamic similarity”，其中引入了一个新的超流雷诺数。这个定义被证明是有用的在一个小的速度间隔$Δv =(v-v_c)$以上的临界速度$v_c$在mK温度的超流氦中的振荡球观察到的湍流的有限寿命的数据分析。非常迅速的增加的寿命与超流雷诺数的增加相比，在经典的管流中观察到的“超瞬态”湍流。
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…
The coupled dynamics of quantum turbulence (QT) and normal-fluid turbulence (NFT) have been a central challenge in quantum hydrodynamics, since it is expected to cause the unsolved T2 state of QT. We numerically studied the coupled dynamics of the two turbulences in thermal counterflow. NFT is driven by external forces to control its turbulent intensity, and the fast multipole method accelerates the calculation of QT. We show that NFT enhances QT via mutual friction. The vortex line density $L$ of the QT satisfies the statistical law $L^{1/2} \approx γV_{ns}$ with the counterflow velocity $V_{…
We use particle tracking velocimetry to study Eulerian and Lagrangian second-order statistics of superfluid $^4$He grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov-1941 scaling and are almost isotropic. The Lagrangian second-order structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearly-classical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity o…
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。
