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Register a new userInteraction and decay of Kelvin waves in the Gross-Pitaevskii model
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By solving numerically the governing Gross-Pitaevskii equation, we study the dynamics of Kelvin waves on a superfluid vortex. After determining the dispersion relation, we monitor the turbulent decay of Kelvin waves with energy initially concentrated at large length scales. At intermediate length scales, we find that the decay is consistent with scaling predictions of theoretical models. Finally we report the unexpected presence of large-length scale phonons in the system.
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We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross-Pitaevskii equation. By utilizing the pseudo-vorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems.
The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinens decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in Helium II is observed. The topology of the tangle is then studied showing that linked rings may appear during the decay. The tracking also allows for determining the statistics of small-scales quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.
We experimentally investigate internal coastal Kelvin waves in a two-layer fluid system on a rotating table. Waves in our system propagate in the prograde direction and are exponentially localized near the boundary. Our experiments verify the theoretical dispersion relation of the wave and show that the wave amplitude decays exponentially along the propagation direction. We further demonstrate that the waves can robustly propagate along boundaries of complex geometries without being scattered and that adding obstacles to the wave propagation path does not cause additional attenuation.
The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of non-linear Schrodinger equations which are known to feature dynamical instability and collapse for attractive non-linear interactions. We show that the GPE with repulsive non-linear interactions typical for BECs features chaotic wave dynamics. We find positive Lyapunov exponents for BECs expanding in periodic and aperiodic smooth external potentials as well as disorder potentials. Our analysis demonstrates that wave chaos characterized by the exponential divergence of nearby initial wavefunctions is to be distinguished from the notion of non-integrability of non-linear wave equations. We discuss the implications of these observations for the limits of applicability of the GPE, the problem of Anderson localization, and the properties of the underlying many-body dynamics.
Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes and ribbons. As such, it has found myriads of applications in astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and in biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of vortex lines can be downright impossible to apply in complex and turbulent scenarios. We present a new definition of helicity which overcomes these problems. With it, we show that only certain reconnection events conserve helicity. In other cases helicity can change abruptly during reconnection. Furthermore, we show that these events can also excite Kelvin waves, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum turbulence.
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