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arXiv:cond-mat/0111343 · Physical Review Letters

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

R. Blaauwgeers, V. B. Eltsov, Georg Eska, Antti Finne, R. P. Haley, M. Krusius, J. J. Ruohio, L. Skrbek, Григорий Ефимович Воловик

Published Sep 20, 2002• 182 citations
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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 3He 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 the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.

DOI
10.1103/physrevlett.89.155301

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We theoretically study the instability of helical shear flows, in which one fluid component flows along the vortex core of the other, in phase-separated two-component Bose-Einstein condensates at zero temperature. The helical shear flows are hydrodynamically classified into two regimes: (1) a helical vortex sheet, where the vorticity is localized on the cylindrical interface and the stability is described by an effective theory for ripple modes, and (2) a core-flow vortex with the vorticity distributed in the vicinity of the vortex core, where the instability phenomena are dominated only by the vortex-characteristic modes (Kelvin and varicose modes). The helical shear-flow instability shows remarkable competition among different types of instabilities in the crossover regime between the two regimes.
We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single-component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counterflowing channels, we seed a line of quantized vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behavior of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantized vortices. From this we demonstrate a straightforward method to measure the effective viscosity of a turbulent quantum fluid in a system with a moderate number of vortices, within the range of current experimental capabilities.
We investigate the Kelvin-Helmholtz instability of counter-rotating annular Fermi superfluids using time-dependent superfluid density functional theory. When the two initially separated superflows merge, a necklace of quantized vortices forms at their interface and subsequently becomes unstable. We extract mode-resolved instability growth rates and study their dependence on relative flow velocity, interaction strength, and temperature across the strongly interacting unitary regime and the weakly attractive BCS regime. In the unitary gas and moderate BCS regimes, the growth rates remain qualitatively consistent with the point-vortex model, though systematically at or above its predictions, with no significant dependence on interaction strength or temperature up to approximately 0.3Tc0.3 T_c0.3Tc​. Deeper in the BCS regime, the dynamics change qualitatively: boundary-generated antivortices proliferate faster than the Kelvin-Helmholtz instability itself, destroying the initial vortex necklace before the instability can fully develop. These results provide a microscopic benchmark for Kelvin-Helmholtz dynamics in fermionic superfluids and help constrain possible explanations of the existing experiment-theory discrepancy.
Interfacial hydrodynamic instabilities in multicomponent superfluids provide a versatile platform to explore nonequilibrium quantum dynamics beyond classical fluid analogues. We study dynamical interfacial instabilities in a quasi-two-dimensional three-component Bose-Einstein condensate confined in a harmonic trap, where rotation is applied selectively to the intermediate component to generate controlled relative motion at two interfaces. This selective rotation protocol enables the independent tuning of shear and counterflow across the inner and outer boundaries, allowing direct control over the nature and strength of the resulting instability mechanisms. Three regimes are examined: Kelvin-Helmholtz instability in the strongly immiscible limit, counter-superflow instability in the partially miscible regime, and a parameter window where both unstable mechanisms are present. The onset condition for the Kelvin-Helmholtz instability is derived using a hydrodynamic pressure-balance approach, and the subsequent nonlinear evolution is obtained from time-dependent Gross-Pitaevskii simulations. A Bogoliubov-de Gennes analysis is performed to identify the dominant unstable modes excited during the dynamical evolution of the system. The conniving features of the collective excitations and their spatial structures have been consistent with the density modulations observed during the dynamics. The results demonstrate that the presence of two interfaces and tunable intercomponent interactions in a three-component condensate modifies the instability mechanisms relative to binary mixtures and provides a controlled parameter regime to study multicomponent quantum hydrodynamics.
We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number WeWeWe, clarifying the microscopic aspects unique to the quantum fluid system. For We≲1We \lesssim 1We≲1, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to WeWeWe. When We≳1We \gtrsim 1We≳1 in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.