On waves in incompressible Hall magnetohydrodynamics

2007 ◽  
Vol 73 (5) ◽  
pp. 723-730 ◽  
Author(s):  
FOUAD SAHRAOUI ◽  
SÉBASTIEN GALTIER ◽  
GÉRARD BELMONT

AbstractHall magnetohydrodynamics (HMHD) is a mono-fluid approximation extending the validity domain of the ordinary MHD system to spatial scales down to a fraction of the ion skin depth or frequencies comparable to the ion gyrofrequency. In the paper by Galtier (2006 J. Plasma Physics), an incompressible limit of the HMHD system is used for developing a wave turbulence theory. Nevertheless, the possibility and the consequences of such an approximation are different in HMHD and in MHD. Here, we analyse these differences by investigating the properties of the HMHD equations in the incompressible limit: the existence of linear modes, their dispersion relations and polarizations. We discuss the possibility of replacing the fluid closure equation of a complete HMHD system by an incompressibility hypothesis and determine the validity range.

2019 ◽  
Vol 85 (5) ◽  
Author(s):  
Oreste Pezzi ◽  
Giulia Cozzani ◽  
Francesco Califano ◽  
Francesco Valentini ◽  
Massimiliano Guarrasi ◽  
...  

We present a Vlasov–DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the nonlinear regime to guarantee a clean description of the plasma dynamics at fine spatial scales. The algorithm provides a low-noise description of proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov equation in phase space. Maxwell equations for the electric and magnetic fields are reorganized according to the Darwin approximation to remove light waves. Several numerical tests show that ViDA successfully reproduces the propagation of linear and nonlinear waves and captures the physics of magnetic reconnection. We also discuss preliminary tests of the parallelization algorithm efficiency, performed at CINECA on the Marconi-KNL cluster. ViDA will allow the running of Eulerian simulations of a non-relativistic fully kinetic collisionless plasma and it is expected to provide relevant insights into important problems of plasma astrophysics such as, for instance, the development of the turbulent cascade at electron scales and the structure and dynamics of electron-scale magnetic reconnection, such as the electron diffusion region.


Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1067
Author(s):  
Denys Dutykh

This article is devoted to Feller’s diffusion equation, which arises naturally in probability and physics (e.g., wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties, we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation, and the corresponding Matlab code is provided with this article under an open source license.


2011 ◽  
Vol 375 (35) ◽  
pp. 3149-3155 ◽  
Author(s):  
Bertrand Kibler ◽  
Kamal Hammani ◽  
Claire Michel ◽  
Christophe Finot ◽  
Antonio Picozzi

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 823
Author(s):  
Sergey Nazarenko ◽  
Avy Soffer ◽  
Minh-Binh Tran

We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of self-similar solutions for the porous medium equation. These solutions spread with time, and this fact answers the “weak turbulence” question for the nonlinear Schrödinger equation with random potentials. We also derive Ohm’s law for the porous medium equation.


2021 ◽  
Author(s):  
Costanza Rodda ◽  
Clement Savaro ◽  
Antoine Campagne ◽  
Miguel Calpe Linares ◽  
Pierre Augier ◽  
...  

<p>Atmospheric and oceanic energy spectra are characterized by global scaling laws, suggesting a common mechanism driving the energy route to dissipation. Although several possible theories have been proposed, it is not clear yet what the phenomena contributing the most to the energy at the different spatial scales are. One possible scenario is that internal gravity waves, which can be ubiquitously found in the atmosphere and the ocean and play a fundamental role in the energy transfer, cause the observed spectral slopes at the mesoscales in the atmosphere and submesoscales in the oceans. In the context of this open field of investigation, we present an experimental study where internal gravity waves are forced at a given frequency by the oscillating walls of a large pentagonal-shaped domain filled with a stably stratified fluid. The setup is built inside the 13-meters-diameter tank at the Coriolis facility in Grenoble, where geophysical regimes (with high Reynolds number and low Froude) can be achieved and rotation can also be added. The purpose of our investigation is to determine whether it is possible to induce a wave turbulence cascade by forcing internal waves at the large scales. Following a previous study<sup>1</sup>, where instead of the pentagonal a square domain was utilized, we obtained the velocity field employing time-resolved particle image velocimetry and then calculated the energy spectra. The previous study inside a square domain showed some evidence of a cascade, but it was strongly affected by 2D modes that sharpened the spectrum. Therefore, we changed the domain shape to a pentagon to reduce this finite-size effect. When the waves are forced at frequency <em>ω<sub>F</sub>=0.4 N</em>, our data shows that the spectra follow the scaling law <em>ω<sup>-2</sup></em> at frequencies larger than the forcing frequency and extending beyond <em>N</em>. The experimental spectra strikingly resemble the characteristic Garret-Munk spectrum measured in the ocean. As the interaction of weakly non-linear waves dominates the dynamics at frequencies smaller than the buoyancy frequency <em>N</em>, we can conclude that the experimental spectra are generated by weak internal wave turbulence driving the turbulent cascade at the high-frequency end of the spectrum. </p><p> </p><p>1 "<em>Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility", C. Savaro, A. Campagne, M. Calpe Linares, P. Augier, J. Sommeria, T. Valran, S. Viboud, and N. Mordant, PRF 2020</em></p>


2020 ◽  
Vol 69 (2) ◽  
pp. 165-186 ◽  
Author(s):  
Joana Seguin ◽  
Pavlos Avramidis ◽  
Annette Haug ◽  
Torben Kessler ◽  
Arndt Schimmelmann ◽  
...  

Abstract. A high quantity of well-dated, high-resolution, continuous geoarchives is needed to connect palaeoenvironmental reconstructions with socio-environmental and cultural transformations in a geographically heterogeneous region such as southern Greece. However, detailed and continuous palaeoclimatic and palaeoenvironmental archives from the NE Peloponnese are still sparse. Here, we present two new palaeolake archives of Pheneos and Kaisari covering the last 10 500 and 6500 years, respectively. For the last 5000 years, we compare them with sediment records from adjacent Lake Stymphalia and the Asea valley by applying the same set of sedimentological, geochemical, and statistical analyses to all four lacustrine archives. Continuous geochemical X-ray fluorescence (XRF) core scanning records provide evidence for hydrological variations and environmental changes since the Early Helladic period (5050 BP), the beginning of the Bronze Age in Greece. We hereby focus on different spatial scales to estimate the validity range of the proxy signals. Ten elements were selected (Al, Si, K, Ca, Ti, Mn, Fe, Rb, Sr, Zr) for a principal component analysis. The clr(Ca∕Ti) was chosen as the most meaningful proxy, reflecting varying input of carbonaceous vs. clastic input, which may be linked to changes in the hydrological conditions. Our results show phases when permanent lake water bodies existed (ca. 5000–3600 cal BP) as well as phases with periodic desiccation of the lakes during younger times. While Pheneos and Kaisari show a drying trend during the transition phase from the Late Helladic period to the Proto-Geometric period (ca. 3200–2800 cal BP), Stymphalia and Asea show a rather short dry peak around 3200 cal BP followed by a wetter phase. Although all our geoarchives show evidence for drier phases, their timing and duration display considerable site-to-site differences which may be explained by site-specific responses in individual ecosystems. Age uncertainties, however, may likewise explain some deviations, as the dating is based on bulk sediment samples including potential unknown reservoir effects. The high regional geographical diversity within the Peloponnese combined with the dating challenges in the limestone-rich area and the variation in our data testify that any hypothetical mono-causal connection between palaeoenvironmental changes in a single geoarchive and contemporaneous societal transformations across the Peloponnese would be an oversimplification.


2019 ◽  
Vol 47 (1) ◽  
pp. 15-17
Author(s):  
S. I. Badulin ◽  
V. G. Grigorieva ◽  
L. Aouf ◽  
A. Dalphinet

Results of high resolution sea wave modeling are treated within the theory of wave (weak) turbulence. Spatial resolution 1 km is shown likely to be excessive and lead to appearance of artificial structures in fields of wave periods and steepness. The research was supported by the state assignment of IO RAS, theme 0149-2019-0002.


2009 ◽  
Vol 642 ◽  
pp. 395-420 ◽  
Author(s):  
SERGEY NAZARENKO ◽  
SERGEI LUKASCHUK ◽  
STUART McLELLAND ◽  
PETR DENISSENKO

We present experimental results on simultaneous space–time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that the both wavenumber and frequency spectra are not universal and dependent on the wave strength, with some evidence in favour of the WTT at larger wave intensities when the finite-flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (p.d.f.) and the structure functions (SFs). Analysing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-Gaussian p.d.f. core and the low-order SFs and the latter in the p.d.f. tails and the high-order SFs. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than the t-space SFs do. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.


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