46 research outputs found
Complex Networks Unveiling Spatial Patterns in Turbulence
Numerical and experimental turbulence simulations are nowadays reaching the
size of the so-called big data, thus requiring refined investigative tools for
appropriate statistical analyses and data mining. We present a new approach
based on the complex network theory, offering a powerful framework to explore
complex systems with a huge number of interacting elements. Although interest
on complex networks has been increasing in the last years, few recent studies
have been applied to turbulence. We propose an investigation starting from a
two-point correlation for the kinetic energy of a forced isotropic field
numerically solved. Among all the metrics analyzed, the degree centrality is
the most significant, suggesting the formation of spatial patterns which
coherently move with similar vorticity over the large eddy turnover time scale.
Pattern size can be quantified through a newly-introduced parameter (i.e.,
average physical distance) and varies from small to intermediate scales. The
network analysis allows a systematic identification of different spatial
regions, providing new insights into the spatial characterization of turbulent
flows. Based on present findings, the application to highly inhomogeneous flows
seems promising and deserves additional future investigation.Comment: 12 pages, 7 figures, 3 table
Complexity Phenomena and ROMA of the Magnetospheric Cusp, Hydrodynamic Turbulence, and the Cosmic Web
Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting
system within which multitudes of different sizes of large scale coherent
structures emerge, resulting in a globally nonlinear stochastic behavior vastly
different from that could be surmised from the underlying equations of
interaction. The hallmark of such nonlinear, complex phenomena is the
appearance of intermittent fluctuating events with the mixing and distributions
of correlated structures at all scales. We briefly review here a relatively
recent method, ROMA (rank-ordered multifractal analysis), explicitly
constructed to analyze the intricate details of the distribution and scaling of
such types of intermittent structures. This method is then applied to the
analyses of selected examples related to the dynamical plasmas of the cusp
region of the magnetosphere, velocity fluctuations of classical hydrodynamic
turbulence, and the distribution of the structures of the cosmic gas obtained
through large scale, moving mesh simulations. Differences and similarities of
the analyzed results among these complex systems will be contrasted and
highlighted. The first two examples have direct relevance to the geospace
environment and are summaries of previously reported findings. The third
example on the cosmic gas, though involving phenomena much larger in
spatiotemporal scales, with its highly compressible turbulent behavior and the
unique simulation technique employed in generating the data, provides direct
motivations of applying such analysis to studies of similar multifractal
processes in various extreme environments. These new results are both exciting
and intriguing.Comment: 36 page
Kolmogorov-Type Theory of Compressible Turbulence and Inviscid Limit of the Navier-Stokes Equations in
We are concerned with the inviscid limit of the Navier-Stokes equations to
the Euler equations for compressible fluids in . Motivated by the
Kolmogorov hypothesis (1941) for incompressible flow, we introduce a
Kolmogorov-type hypothesis for barotropic flows, in which the density and the
sonic speed normally vary significantly. We then observe that the compressible
Kolmogorov-type hypothesis implies the uniform boundedness of some fractional
derivatives of the weighted velocity and sonic speed in the space variables in
, which is independent of the viscosity coefficient . It is shown
that this key observation yields the equicontinuity in both space and time of
the density in and the momentum in , as well as the uniform
bound of the density in and the velocity in independent of
, for some fixed and , where is the
adiabatic exponent. These results lead to the strong convergence of solutions
of the Navier-Stokes equations to a solution of the Euler equations for
barotropic fluids in . Not only do we offer a framework for
mathematical existence theories, but also we offer a framework for the
interpretation of numerical solutions through the identification of a function
space in which convergence should take place, with the bounds that are
independent of , that is in the high Reynolds number limit.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1008.154