Quantum turbulence in superfluids with wall-clamped normal component

Abstract

In Fermi superfluids, such as superfluid 3 He, the viscous normal component can be considered to be stationary with respect to the container. The normal component interacts with the superfluid component via mutual friction, which damps the motion of quantized vortex lines and eventually couples the superfluid component to the container. With decreasing temperature and mutual friction, the internal dynamics of the superfluid component becomes more important compared with the damping and coupling effects from the normal component. As a result profound changes in superfluid dynamics are observed: the temperature-dependent transition from laminar to turbulent vortex motion and the decoupling from the reference frame of the container at even lower temperatures.superfluid Reynolds number | vortex tension | vortex front | rotating flow | pipe flow I n this paper, we consider the motion of quantized vortices in superfluids, where the normal component is clamped to the walls of the container; that is, it is stationary in a reference frame moving with the wall. This situation can be experimentally realized in superfluid 3 He. In such systems, turbulent motion can occur only in the superfluid component and thus, in principle, is easier to analyze. Here the role of the normal fluid is twofold: first, it provides friction in the superfluid motion, which is mediated by quantized vortices and works over a wide range of length scales. Second, it provides a coupling to the container walls, which acts uniformly over the whole volume of the superfluid. This situation is quite unlike classical turbulence, where viscous dissipation operates only at the small Kolmogorov scale and coupling to the walls is provided by thin boundary layers.As a result, a variety of new phenomena is observed in experiments and numerical simulations as a function of temperature. These phenomena are controlled by the normal-fluid density. At the highest temperatures, turbulent motion is suppressed completely. When the temperature decreases, a sharp transition to turbulence is seen. The transition can be characterized by a superfluid Reynolds number, which is composed of the internal friction parameters of the superfluid and is independent of velocity. When turbulence is triggered by a localized perturbation of the laminar flow, the critical value of the Reynolds number is found to scale with the strength of the perturbation.When the temperature decreases further, friction from the normal component rapidly vanishes. The overall dissipation rate in quantum turbulence remains nevertheless finite, owing to the contribution from the turbulent energy cascade, and reaches a temperatureindependent value in the zero-temperature limit. This zero-temperature dissipation can be characterized by an effective viscosity or friction. It is found, however, that coupling to the walls is not essentially improved by the turbulence and can potentially become very small. At the lowest temperatures the concept of a single effective friction breaks down; for the proper descriptio...

Introduction to quantum turbulence

“…Temperature thus plays an analogous role to that of the Reynolds number in classical turbulence (27). This type of quantum turbulence is discussed in the article by Eltsov et al (59).…”

Breaking the superfluid speed limit in a fermionic condensate

“…Related effects are seen in rotating superfluid 3 He-B where at very low temperatures the lack of normal fluid disconnects the superfluid from the rotating container [17][18][19] . This scenario is shown schematically in panel g of Fig.…”

Investigation of properties of superfluid He4 turbulence using a hot-wire signal

“…Following lead (ii), a mechanism explaining the influence of the hot-wire signal to quantum intervortex distance in the outerflow is as follows: in a mechanically driven quantum turbulence, the mutual friction between the normal and superfluid components couples their turbulent fluctuations: u n (r, t) ≈ u s (r, t) at all scales larger than the intervortex scale δ. The resulting turbulent energy spectra of the mechanically driven quantum turbulence for the scales much greater than δ are close to those of the classical hydrodynamic turbulence [2,3,[26][27][28][29][30]. However, u n (r, t) and u s (r, t) decouple at scales of the order of δ.…”