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Register a new userReconnections of quantized vortex rings in superfluid $^4$He at very low temperatures
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Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii $R$ in superfluid $^4$He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value $500{rm ,cm}^{-2} R^{-1}$ independent of the injected density. This is due to collisions between rings causing piling-up of many other vortex rings. Both observations are in quantitative agreement with our theory.
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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.
There are two commonly discussed forms of quantum turbulence in superfluid $^4$He above 1K: in one there is a random tangle of quantizes vortex lines, existing in the presence of a non-turbulent normal fluid; in the second there is a coupled turbulent motion of the two fluids, often exhibiting quasi-classical characteristics on scales larger than the separation between the quantized vortex lines in the superfluid component. The decay of vortex line density, $L$, in the former case is often described by the equation $dL/dt=-chi_2 (kappa/2pi)L^2$, where $kappa$ is the quantum of circulation, and $chi_2$ is a dimensionless parameter of order unity. The decay of total turbulent energy, $E$, in the second case is often characterized by an effective kinematic viscosity, $ u$, such that $dE/dt=- u kappa^2 L^2$. We present new values of $chi_2$ derived from numerical simulations and from experiment, which we compare with those derived from a theory developed by Vinen and Niemela. We summarise what is presently known about the values of $ u$ from experiment, and we present a brief introductory discussion of the relationship between $chi_2$ and $ u$, leaving a more detailed discussion to a later paper.
The transition to turbulence in the boundary flow of superfluid $^4$He is investigated using a vortex--free vibrating wire. At high wire vibration velocities, we found that stable alternating flow around the wire enters a turbulent phase triggered by free vortex rings. Numerical simulations of vortex dynamics demonstrate that vortex rings can attach to the surface of an oscillating obstacle and expand unstably due to the boundary flow of the superfluid, forming turbulence. Experimental investigations indicate that the turbulent phase continues even after stopping the injection of vortex rings, which is also confirmed by the simulations.
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 of the flow, we verify a set of relations that connect various second-order statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the two-way bridge relations between Eulerian energy spectra and second-order structure functions to reconstruct the energy spectrum from the known second-order velocity structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the Eulerian-Lagrangian bridge differs from the measured Lagrangian spectrum in the quasi-classical range which calls for further investigation.
We have measured the temperature dependence of the time of flight of helium excimer molecules He2* in superfluid 4He and find that the molecules behave ballistically below 100mK and exhibit Brownian motion above 200 mK. In the intermediate temperature range the transport cannot be described by either of the models.
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