127 research outputs found
Depletion of nonlinearity in magnetohydrodynamic turbulence: insights from analysis and simulations
Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations
We build on recent developments in the study of fluid turbulence [Gibbon
\textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled,
order- moments, , of , where
and are, respectively, the vorticity and current density in
three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis,
for unit magnetic Prandtl number , how these moments can be used to
identify three possible regimes for solutions of the MHD equations; these
regimes are specified by inequalities for and . We then
compare our mathematical results with those from our direct numerical
simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its
fluid-turbulence counterpart insofar as all solutions, which we have
investigated, remain in \textit{only one of these regimes}; this regime has
depleted nonlinearity. We examine the implications of our results for the
exponents that characterize the power-law dependences of the energy
spectra on the wave number , in the inertial range of
scales. We also comment on (a) the generalization of our results to the case
and (b) the relation between and the order- moments
of gradients of hydrodynamic fields, which are used in characterizing
intermittency in turbulent flows.Comment: 14 pages, 3 figure
Cross-Component Energy Transfer in Superfluid Helium-4
\ua9 2024, Crown.The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly–Glaberson instability
Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
We investigate the ideal and incompressible magnetohydrodynamic (MHD)
equations in three space dimensions for the development of potentially singular
structures. The methodology consists in implementing the four-fold symmetries
of the Taylor-Green vortex generalized to MHD, leading to substantial computer
time and memory savings at a given resolution; we also use a re-gridding method
that allows for lower-resolution runs at early times, with no loss of spectral
accuracy. One magnetic configuration is examined at an equivalent resolution of
points, and three different configurations on grids of
points. At the highest resolution, two different current and vorticity sheet
systems are found to collide, producing two successive accelerations in the
development of small scales. At the latest time, a convergence of magnetic
field lines to the location of maximum current is probably leading locally to a
strong bending and directional variability of such lines. A novel analytical
method, based on sharp analysis inequalities, is used to assess the validity of
the finite-time singularity scenario. This method allows one to rule out
spurious singularities by evaluating the rate at which the logarithmic
decrement of the analyticity-strip method goes to zero. The result is that the
finite-time singularity scenario cannot be ruled out, and the singularity time
could be somewhere between and More robust conclusions will
require higher resolution runs and grid-point interpolation measurements of
maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review
Identification of Kelvin waves: numerical challenges
Kelvin waves are expected to play an essential role in the energy dissipation
for quantized vortices. However, the identification of these helical
distortions is not straightforward, especially in case of vortex tangle. Here
we review several numerical methods that have been used to identify Kelvin
waves within the vortex filament model. We test their validity using several
examples and estimate whether these methods are accurate enough to verify the
correct Kelvin spectrum. We also illustrate how the correlation dimension is
related to different Kelvin spectra and remind that the 3D energy spectrum E(k)
takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at
http://www.springerlink.co
Scattering of Line-Ring Vortices in a Superfluid
We study the scattering of vortex rings by a superfluid line vortex using the Gross-Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. By using a vortex extraction algorithm, we are able to track the location of the vortex ring as a function of time. Using this, we show that the scattering of the vortex ring in our Gross-Pitaevskii simulations is well captured by the local induction approximation of a vortex filament model for a wide range of impact parameters. The scattering of a vortex ring by a line vortex is characterised by the initial offset of the centre of the ring from the axis of the vortex. We find that a strong asymmetry exists in the scattering of a ring as a function of this initial scattering parameter
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Postprint (author's final draft
Large-Scale Spatio-Temporal Patterns of Mediterranean Cephalopod Diversity
Species diversity is widely recognized as an important trait of ecosystems’ functioning and resilience. Understanding the causes of diversity patterns and their interaction with the environmental conditions is essential in order to effectively assess and preserve existing diversity. While diversity patterns of most recurrent groups such as fish are commonly studied, other important taxa such as cephalopods have received less attention. In this work we present spatio-temporal trends of cephalopod diversity across the entire Mediterranean Sea during the last 19 years, analysing data from the annual bottom trawl survey MEDITS conducted by 5 different Mediterranean countries using standardized gears and sampling protocols. The influence of local and regional environmental variability in different Mediterranean regions is analysed applying generalized additive models, using species richness and the Shannon Wiener index as diversity descriptors. While the western basin showed a high diversity, our analyses do not support a steady eastward decrease of diversity as proposed in some previous studies. Instead, high Shannon diversity was also found in the Adriatic and Aegean Seas, and high species richness in the eastern Ionian Sea. Overall diversity did not show any consistent trend over the last two decades. Except in the Adriatic Sea, diversity showed a hump-shaped trend with depth in all regions, being highest between 200–400 m depth. Our results indicate that high Chlorophyll a concentrations and warmer temperatures seem to enhance species diversity, and the influence of these parameters is stronger for richness than for Shannon diversityVersión del editor4,411
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