CAN ONE HEAR WHISTLER WAVES ?

The aim of this article is to propose a mathematical framework giving access to a better understanding of whistler-mode chorus emissions in space plasmas. There is presently a general agreement that the emissions of whistler waves involve a mechanism of wave-particle interaction which can be described in the framework of the relativistic Vlasov-Maxwell equations. In dimensionless variables, these equationsinvolve a penalized skew-symmetric term where the inhomogeneity of the strong exterior magnetic field plays an essential part. The description of the related phenomena is achieved in two stages. The first is based on a new approach allowing to extend in longer times the classical insights on fast rotating fluids; it justifies the existence and the validity of long time gyro-kinetic equations; it furnishes criterions to impose on a magnetic field in order to obtain the long time dynamical confinement of plasmas. The second stage is based on a study of oscillatory integrals implying special phases; it deals with the problem of the creation of light inside plasmas

Anomalous transport

International audienceThis article is concerned with the relativistic Vlasov equation, for collisionless axisymmetric plasmas immersed in a strong magnetic field, like in tokamaks. It provides a consistent kinetic treatment of the microscopic particle phase-space dynamics. It shows that the turbulent transport can be completely described through WKB expansions

Cascade of phases in turbulent flows

International audienceThis article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy

Counter-Examples to the Concentration-Cancellation Property

International audienceWe study the existence and the asymptotic behavior of large amplitude high-frequency oscillating waves subjected to the 2D Burger equation. This program is achieved by developing tools related to supercritical WKB analysis. By selecting solutions which are divergence free, we show that incompressible or compressible 2D Euler equations are not locally closed for the weak $L^2$ topology

Large amplitude oscillating solutions for three dimensional incompressible Euler equations

In this article, we construct large amplitude oscillating waves which are local solutions on some open domain of the time-space of both the three dimensional Burger equations (without source term) and the incompressible Euler equations (without pressure). The solutions are mainly characterized by the fact that the corresponding Jacobian matrices are nilpotent of rank one or two. Our purpose here is to describe the interesting geometrical features of the expressions obtained by this way

Semiclassical and spectral analysis of oceanic waves

In this work we prove that the shallow water flow, subject to strong wind forcing and linearized around an adequate stationary profile, develops for large times closed trajectories due to the propagation of Rossby waves, while Poincar\'e waves are shown to disperse. The methods used in this paper involve semi-classical analysis and dynamical systems for the study of Rossby waves, while some refined spectral analysis is required for the study of Poincar\'e waves, due to the large time scale involved which is of diffractive type

Compatibility conditions to allow some large amplitude WKB analysis for Burger's type systems

19 pagesInternational audienceIn this article, we study some new interesting nonlinear system of partial differential equations, linked with the propagation of large amplitude oscillations in the context of a quasilinear diagonal system of hyperbolic equations

Dispersion relations in cold magnetized plasmas

International audienceStarting from kinetic models of cold magnetized collisionless plasmas, we provide a complete description of the characteristic variety sustaining electromagnetic wave propagation. Our analysis is based on some asymptotic calculus exploiting the presence at the level of dimensionless relativistic Vlasov-Maxwell equations of a large parameter: the electron gyrofrequency. Our method is inspired from geometric optics. It allows to unify preceding results, while incorporating new aspects. Specifically, the non trivial effects of the spatial variations of the background density, temperature and magnetic field are exhibited. In this way, a comprehensive overview of the dispersion relations becomes available, with important possible applications in plasma physics