We propose a different type of Landau instability in trapped Bose-Einstein condensates by a helically moving environment. In the presence of quantized vortices, the instability can cause spontaneous radiation and amplification of Kelvin waves. This study gives a microscopic understanding of the Donnelly-Glaberson instability which was known as a hydrodynamic instability in superfluid helium.
The Donnelly-Glaberson instability can be a powerful tool for observing the dispersion relation of Kelvin waves, vortex reconnections, and quantum turbulence in atomic Bose-Einstein condensates.
Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
研究了由Gross-Pitaevskii方程驱动的量子化超流涡旋中Kelvin波的统计性质。没有人为的强迫或耗散。准确跟踪涡流位置。这一过程直接使我们能够获得凯文波占据数谱。从初始条件下的长时间积分和整体平均获得的数值数据支持[L 'vov和Nazarenko，JETP Lett 91，428（2010）]中提出的谱。惯性范围内的开尔文波模式被发现是高斯弱湍流预测所预期的。最后研究了开尔文波谱的耗散范围。在这个范围内观察到强烈的非高斯波动。
One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a self-consistent model based on the three-dimensional Gross-Pitaevskii (GP) equation to explore theoretically and numerically the attractive interaction between particles and quantised vortices at very low temperature. Particles are described as localised potentials depleting the superfl…
Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging, which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small-amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simpified model that provides an analytical approximation developed for nearly parallel vortice…
Development of experimental techniques to study superfluid dynamics, in particular, application of nanomechanical oscillators to drive vortex lines, enables potential observation of the Kelvin-wave cascade on quantized vortices. One of the first questions which then arises in analysis of the experimental results is the relation between the energy flux in the cascade and the amplitude of the Kelvin waves. We provide such relation based on the L'vov-Nazarenko picture of the cascade. Remarkably, the amplitude of the waves depends on the energy flux extermely weakly, as power one tenth.
We study inelastic interactions of particles with quantized vortices in superfluids by using a semi-classical matter wave theory that is analogous to the Landau two-fluid equations, but allows for the vortex dynamics. The research is motivated by recent experiments on xenon doped helium nanodroplets that show clustering of the impurities along the vortex cores. We numerically simulate the dynamics of trapping and interactions of xenon atoms by quantized vortices in superfluid helium and the obtained results can be extended to scattering of other impurities by quantized vortices. Different ener…
Comment on "Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation"
我们评论Van Gorder的论文[“Motion of a helical vortex filament in superfluid ${}^4$ He under the extrinsic form of the local induction approximation”，Phys. Fluids 25，085101（2013）]。我们指出，平行于涡旋的正常流体分量的流动往往会导致Donnelly-Glaberson不稳定性，从而引起Kelvin波的放大。我们解释了为什么与局部非线性方程的比较是不合理的，并指出，忽略在$x$方向的运动是不合理的开尔文波与任意波长和振幅。在一般情况下，正确的方程也被导出。
