A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data

We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to the dissipation field issue from 3D isotropic turbulence simulations. We comment on the need to revisiting previous box-counting analysis which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master non-conservative singular cascade measures.Comment: 5 pages, 3figures, submitted to Phys. Rev. Let

A large time-step and well-balanced Lagrange-Projection type scheme for the shallow-water equations

This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of compressibleflows, with or without stiff source terms. These methods enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, and maintain accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms in SWE and more specifically to the well-known well-balanced property. We prove that the proposed numerical strategy enjoys important non linear stability properties and we illustrate its behaviour past several relevant test cases

Automated Detection of Coronal Loops using a Wavelet Transform Modulus Maxima Method

We propose and test a wavelet transform modulus maxima method for the au- tomated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximise completeness while minimising detection of noise. For a test coronal image, we compare the global statistics (e.g., number of loops at each length) to previous automated coronal-loop detection algorithms

Thermo-compositional diabatic convection in the atmospheres of brown dwarfs and in Earth's atmosphere and oceans

This is the author accepted manuscript. The final version is available from the American Astronomical Society / IOP Publishing via the DOI in this record.The simulation outputs are available at http://opendata.erc-atmo.euBy generalizing the theory of convection to any type of thermal and compositional source terms (diabatic processes), we show that thermohaline convection in Earth oceans, fingering convection in stellar atmospheres, and moist convection in Earth atmosphere are deriving from the same general diabatic convective instability. We show also that "radiative convection" triggered by CO/CH4 transition with radiative transfer in the atmospheres of brown dwarfs is analog to moist and thermohaline convection. We derive a generalization of the mixing length theory to include the effect of source terms in 1D codes. We show that CO/CH4 radiative convection could significantly reduce the temperature gradient in the atmospheres of brown dwarfs similarly to moist convection in Earth atmosphere thus possibly explaining the reddening in brown-dwarf spectra. By using idealized two-dimensional hydrodynamic simulations in the Ledoux unstable regime, we show that compositional source terms can indeed provoke a reduction of the temperature gradient. The L/T transition could be explained by a bifurcation between the adiabatic and diabatic convective transports and could be seen as a giant cooling crisis: an analog of the boiling crisis in liquid/steam-water convective flows. This mechanism with other chemical transitions could be present in many giant and earth-like exoplanets. The study of the impact of different parameters (effective temperature, compositional changes) on CO/CH4 radiative convection and the analogy with Earth moist and thermohaline convection is opening the possibility to use brown dwarfs to better understand some aspects of the physics at play in the climate of our own planet.Science and Technology Facilities Council (STFC

The Breakdown of Alfven's Theorem in Ideal Plasma Flows

This paper presents both rigorous results and physical theory on the breakdown of magnetic flux conservation for ideal plasmas, by nonlinear effects. Our analysis is based upon an effective equation for magnetohydrodynamic (MHD) modes at length-scales $>\ell,$ with smaller scales eliminated, as in renormalization-group methodology. We prove that flux-conservation can be violated for an arbitrarily small length-scale $\ell,$ and in the absence of any non-ideality, but only if singular current sheets and vortex sheets both exist and intersect in sets of large enough dimension. This result gives analytical support to and rigorous constraints on theories of fast turbulent reconnection. Mathematically, our theorem is analogous to Onsager's result on energy dissipation anomaly in hydrodynamic turbulence. As a physical phenomenon, the breakdown of magnetic-flux conservation in ideal MHD is similar to the decay of magnetic flux through a narrow superconducting ring, by phase-slip of quantized flux lines. The effect should be observable both in numerical MHD simulations and in laboratory plasma experiments at moderately high magnetic Reynolds numbers.Comment: 38 pages, 1 figur

Decomposing multifractal crossovers

Physiological processes-such as, the brain's resting-state electrical activity or hemodynamic fluctuations-exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. Here, we present two methods to identify breakpoints or crossovers in multimodal multifractal scaling functions. These methods incorporate the robust iterative fitting approach of the focus-based multifractal formalism (FMF). The first approach (moment-wise scaling range adaptivity) allows for a breakpoint-based adaptive treatment that analyzes segregated scale-invariant ranges. The second method (scaling function decomposition method, SFD) is a crossover-based design aimed at decomposing signal constituents from multimodal scaling functions resulting from signal addition or co-sampling, such as, contamination by uncorrelated fractals. We demonstrated that these methods could handle multimodal, mono- or multifractal, and exact or empirical signals alike. Their precision was numerically characterized on ideal signals, and a robust performance was demonstrated on exemplary empirical signals capturing resting-state brain dynamics by near infrared spectroscopy (NIRS), electroencephalography (EEG), and blood oxygen level-dependent functional magnetic resonance imaging (fMRI-BOLD). The NIRS and fMRI-BOLD low-frequency fluctuations were dominated by a multifractal component over an underlying biologically relevant random noise, thus forming a bimodal signal. The crossover between the EEG signal components was found at the boundary between the δ and θ bands, suggesting an independent generator for the multifractal d rhythm. The robust implementation of the SFD method should be regarded as essential in the seamless processing of large volumes of bimodal fMRI-BOLD imaging data for the topology of multifractal metrics free of the masking effect of the underlying random noise. © 2017 Nagy, Mukli, Herman and Eke