77 research outputs found
Grid superfluid turbulence and intermittency at very low temperature
Low-temperature grid generated turbulence is investigated by using numerical
simulations of the Gross-Pitaevskii equation. The statistics of regularized
velocity increments are studied. Increments of the incompressible velocity are
found to be skewed for turbulent states. Results are later confronted with the
(quasi) homogeneous and isotropic Taylor-Green flow, revealing the universality
of the statistics. For this flow, the statistics are found to be intermittent
and a Kolmogorov constant close to the one of classical fluid is found for the
second order structure function
Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
We study the statistical properties of the Kelvin waves propagating along
quantized superfluid vortices driven by the Gross-Pitaevskii equation. No
artificial forcing or dissipation is added. Vortex positions are accurately
tracked. This procedure directly allows us to obtain the Kevin-waves
occupation-number spectrum. Numerical data obtained from long time integration
and ensemble-average over initial conditions supports the spectrum proposed in
[L'vov and Nazarenko, JETP Lett 91, 428 (2010)]. Kelvin wave modes in the
inertial range are found to be Gaussian as expected by weak-turbulence
predictions. Finally the dissipative range of the Kelvin-wave spectrum is
studied. Strong non-Gaussian fluctuations are observed in this range
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
An exact result in strong wave turbulence of thin elastic plates
An exact result concerning the energy transfers between non-linear waves of
thin elastic plate is derived. Following Kolmogorov's original ideas in
hydrodynamical turbulence, but applied to the F\"oppl-von K\'arm\'an equation
for thin plates, the corresponding K\'arm\'an-Howarth-Monin relation and an
equivalent of the -Kolmogorov's law is derived. A third-order
structure function involving increments of the amplitude, velocity and the Airy
stress function of a plate, is proven to be equal to ,
where is a length scale in the inertial range at which the increments
are evaluated and the energy dissipation rate. Numerical data
confirm this law. In addition, a useful definition of the energy fluxes in
Fourier space is introduced and proven numerically to be flat in the inertial
range. The exact results derived in this Letter are valid for both, weak and
strong wave-turbulence. They could be used as a theoretical benchmark of new
wave-turbulence theories and to develop further analogies with hydrodynamical
turbulence
Statistical steady state in turbulent droplet condensation
Motivated by systems in which droplets grow and shrink in a turbulence-driven
supersaturation field, we investigate the problem of turbulent condensation in
a general manner. Using direct numerical simulations we show that the turbulent
fluctuations of the supersaturation field offer different conditions for the
growth of droplets which evolve in time due to turbulent transport and mixing.
Based on that, we propose a Lagrangian stochastic model for condensation and
evaporation of small droplets in turbulent flows. It consists of a set of
stochastic integro-differential equations for the joint evolution of the
squared radius and the supersaturation along the droplet trajectories. The
model has two parameters fixed by the total amount of water and the
thermodynamic properties, as well as the Lagrangian integral timescale of the
turbulent supersaturation. The model reproduces very well the droplet size
distributions obtained from direct numerical simulations and their time
evolution. A noticeable result is that, after a stage where the squared radius
simply diffuses, the system converges exponentially fast to a statistical
steady state independent of the initial conditions. The main mechanism involved
in this convergence is a loss of memory induced by a significant number of
droplets undergoing a complete evaporation before growing again. The
statistical steady state is characterised by an exponential tail in the droplet
mass distribution. These results reconcile those of earlier numerical studies,
once these various regimes are considered.Comment: 24 pages, 12 figure
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