Laminar, turbulent, or doubly turbulent?

Abstract

Heat is transferred in superfluid 4 He via a process known as thermal counterflow. It has been known for many years that above a critical heat current the superfluid component in this counterflow becomes turbulent. It has been suspected that the normal-fluid component may become turbulent as well, but experimental verification is difficult without a technique for visualizing the flow. Here we report a series of visualization studies on the normal-fluid component in a thermal counterflow performed by imaging the motion of seeded metastable helium molecules using a laser-induced-fluorescence technique. We present evidence that the flow of the normal fluid is indeed turbulent at relatively large velocities. Thermal counterflow in which both components are turbulent presents us with a theoretically challenging type of turbulent behavior that is new to physics. DOI: 10.1103/PhysRevLett.105.045301 PACS numbers: 67.25.dk, 29.40.Gx, 47.27.Ài The superfluid phase of liquid 4 He exhibits two-fluid behavior [1]: a normal fluid, carrying all the thermal energy, coexists with a superfluid component. The proportion of superfluid falls from unity to zero as the temperature T rises from zero to the transition [1]. In a thermal counterflow, the normal-fluid velocity v n is related to the heat flux q by q ¼ STv n ;( 1) where is the total density and S is the entropy per unit mass [1]. Above a certain critical heat flux, superflow is known to become turbulent. This quantum turbulence takes the form of a disorganized tangle of quantized vortex lines [2,3]. A mutual friction force between the two fluids arises through the interaction between the quantized vortices and the normal fluid [4]. This type of quantum turbulence is maintained by the relative motion of the two fluids, through processes that are reasonably well understood [2,3]. Features in the observed relation between vortex density and heat flux suggest that the normal fluid may also become turbulent, and mutual friction has been shown theoretically to induce an instability in the laminar flow of the normal fluid [5]. Satisfactory evidence for such normalfluid turbulence can come only from a visualization of the normal-fluid flow. Techniques for such visualization have recently started to be developed. Turbulence in both fluids has been observed in other types of flow in liquid helium [6], such as that behind a moving grid [7]. But in those cases the two fluids are not forced to have any relative motion and behave like a single classical fluid, exhibiting a Kolmogorov energy spectrum [1]. Simultaneous turbulence in both fluids in a counterflow must be different, and it would be a type of turbulence that is new to physics. Past experiments on the visualization of thermal counterflow have used micron-sized tracer particles formed from polymer spheres or solid hydrogen, and they have been based on either particle image velocimetry [8] or particle tracking techniques [9]. The particle image velocimetry data obtained at large heat fluxes are hard to interpret since micron-s...

Effect of vortex line distribution in superfluid plane Poiseuille flow instability

“…However, they assumed a constant parabolic velocity profile for the normal fluid. In reality as shown in Barenghi (2010) and Guo et al (2010) both profiles may be a function of z and Re. In approximating the mutual friction with (1.3) we have in fact approximated curl of U s with κl, to represent the vorticity of the superfluid averaged over several quantized vortex lines.…”

“…However further experiments are required to make it clear whether the state is 'laminar, turbulent or doubly turbulent?' as Barenghi (2010) suggests in a review on this work. Guo et al (2010) in their conclusion point to a possibility of both superfluid and normal fluid becoming turbulent and velocity profiles being flattened.…”

“…The pressure gradient is chosen such that Re dP/dx = −2, as in the case of classical 720 R1-3 fluid (Barenghi, Donnelly & Vinen 1983;Donnelly 1991;Bergström 2008). Since U s is assumed inviscid, the superfluid velocity is constant across the channel width.…”