Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Abstract

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3 He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with a modified Kelvin-Helmholtz theory.Instabilities in the shear flow between two layers of fluids [1] belong to a class of interfacial hydrodynamics which is attributed to many natural phenomena. Examples are wave generation by wind blowing over water [2], the flapping of a sail or flag in the wind [3,4], and even flow in granular beds [5]. In the hydrodynamics of inviscid and incompressible fluids the transition from calm to wavy interfaces is known as the Kelvin-Helmholtz (KH) instability [6,2]. Since Lord Kelvin's treatise in 1871, difficulties have plagued its description in ordinary fluids, which are viscous and dissipative. They also display a shear-flow instability, but its correspondence with that in the ideal limit is not straightforward. The tangential velocity discontinuity in the shear-flow instability is created by a vortex sheet. In a viscous fluid a planar vortex sheet is not a stable equilibrium state and not a solution of the hydrodynamic equations [7].Superfluids provide a close variation of the ideal inviscid limit considered by Lord Kelvin and thus an environment where the KH theory can be tested. The initial state is a non-dissipative vortex sheet -the interface between two superfluids brought into a state of relative shear flow. So far the only experimentally accessible case where this can be studied in stationary conditions, is the interface between 3 He-A and 3 He-B [8], where the order parameter changes symmetry and magnitude, but is continuous on the scale of the superfluid coherence length ξ ∼ 10 nm. We discuss an experiment, where the two phases slide with respect to each other in a rotating cryostat:3 He-A performs solid-body-like rotation while 3 He-B is in the vortex-free state and thus stationary in the laboratory frame. While increasing the rotation velocity Ω, we record the events when the AB phase boundary becomes unstable -when some circulation from the A-phase crosses the AB interface and vortex lines are introduced into the initially vortex-free B phase. On increasing the rotation further, the instability occurs repeatedly. Such a succession of instability events can be understood as a spin-up of 3 He-B by rotating 3 He-A. Our experimental setup is shown in Fig. 1. The AB boundary is forced against a magnetic barrier in a smooth-walled quartz container, by cooling the sample below T AB at constant pressure in a rotating refrigerator. The number of vortices in both phases is indepe...

Topological Fermi arcs in superfluid3He

“…This is important for the development of the Kelvin-Helmholtz instability of the moving AB interface observed in Ref. 34 We considered the simplest most symmetric realizations of the A-A and A-B interfaces. The problem for future investigations is whether the Fermi arc survives or not, if the symmetry of the interface is violated.…”

Microkelvin Thermometry with Bose–Einstein Condensates of Magnons and Applications to Studies of the AB Interface in Superfluid $$^3$$ 3 He

“…In this situation it is not clear how such remnants would affect the behavior of the texture on the B-phase side. On the other hand, it is known that a moving AB interface can lead to the creation of defects in the B phase, both spin-mass [55] and regular [56] vortices.…”

Quantum swapping of immiscible Bose-Einstein condensates as an alternative to the Rayleigh-Taylor instability

“…Recently there has been much interest in the quantum hydrodynamics and nonlinear responce of two-component BECs [1][2][3][4][5][6][7][8][9] and, in particular, in the development of quasihydrodynamic instabilities at the interface separating the immiscible components [10][11][12][13][14][15][16]. Among these phenomena, the quantum Rayleigh-Taylor instability (RTI) is, probably, one of the most representative and fascinating [12,16].…”