212 research outputs found
Comment on "Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascade". [arXiv:0905.0159v1]
In this comment we point out that the high wavenumber power-law
observed by the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala
and M. Soe, arXiv:0905.0159] is an artifact stemming from the definition of the
kinetic energy spectra and is thus not directly related to a Kelvin wave
cascade. We also clarify a confusion about the wavenumber intervals on which
Kolmogorov and Kelvin wave cascades are expected to take place.Comment: submitted to PR
Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
We undertake a systematic, direct numerical simulation (DNS) of the
two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the
turbulent evolutions of its solutions for a variety of initial conditions and a
wide range of parameters. We find that the time evolution of this system can be
classified into four regimes with qualitatively different statistical
properties. First, there are transients that depend on the initial conditions.
In the second regime, power-law scaling regions, in the energy and the
occupation-number spectra, appear and start to develop; the exponents of these
power-laws and the extents of the scaling regions change with time and depended
on the initial condition. In the third regime, the spectra drop rapidly for
modes with wave numbers and partial thermalization takes place for
modes with ; the self-truncation wave number depends on the
initial conditions and it grows either as a power of or as .
Finally, in the fourth regime, complete-thermalization is achieved and, if we
account for finite-size effects carefully, correlation functions and spectra
are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms.Comment: 30 pages, 12 figure
Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation
We carry out extensive direct numerical simulations (DNSs) to investigate the
interaction of active particles and fields in the two-dimensional (2D)
Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The
particles are active in the sense that they affect the superfluid even as they
are affected by it. We tune the mass of the particles, which is an important
control parameter. At the one-particle level, we show how light, neutral, and
heavy particles move in the superfluid, when a constant external force acts on
them; in particular, beyond a critical velocity, at which a vortex-antivortex
pair is emitted, particle motion can be periodic or chaotic. We demonstrate
that the interaction of a particle with vortices leads to dynamics that depends
sensitively on the particle characteristics. We also demonstrate that
assemblies of particles and vortices can have rich, and often turbulent
spatiotemporal evolution. In particular, we consider the dynamics of the
following illustrative initial configurations: (a) one particle placed in front
of a translating vortex-antivortex pair; (b) two particles placed in front of a
translating vortex-antivortex pair; (c) a single particle moving in the
presence of counter-rotating vortex clusters; and (d) four particles in the
presence of counter-rotating vortex clusters. We compare our work with earlier
studies and examine its implications for recent experimental studies in
superfluid Helium and Bose-Einstein condensates.Comment: 24 figure
Self-truncation and scaling in Euler-Voigt- and related fluid models
A generalization of the Euler-Voigt- model is obtained by
introducing derivatives of arbitrary order (instead of ) in the
Helmholtz operator. The limit is shown to correspond to
Galerkin truncation of the Euler equation. Direct numerical simulations (DNS)
of the model are performed with resolutions up to and Taylor-Green
initial data. DNS performed at large demonstrate that this simple
classical hydrodynamical model presents a self-truncation behavior, similar to
that previously observed for the Gross-Pitaeveskii equation in Krstulovic and
Brachet [Phys. Rev. Lett. 106, 115303 (2011)]. The self-truncation regime of
the generalized model is shown to reproduce the behavior of the truncated Euler
equation demonstrated in Cichowlas et al. [Phys. Rev. Lett. 95, 264502 (2005)].
The long-time growth of the self-truncation wavenumber appears to
be self-similar.
Two related -Voigt versions of the EDQNM model and the Leith model
are introduced. These simplified theoretical models are shown to reasonably
reproduce intermediate time DNS results. The values of the self-similar
exponents of these models are found analytically.Comment: 14 figure
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