Parametric instabilities of circularly polarized small-amplitude Alfvén waves in Hall plasmas

We study the stability of circularly polarized Alfvén waves (pump waves) in Hall plasmas. First we re-derive the dispersion equation governing the pump wave stability without making an ad hoc assumption about the dependences of perturbations on time and the spatial variable. Then we study the stability of pump waves with small non-dimensional amplitude a (a 1) analytically, restricting our analysis to b < 1, where b is the ratio of the sound and Alfvén speed. Our main results are the following. The stability properties of right-hand polarized waves are qualitatively the same as in ideal MHD. For any values of b and the dispersion parameter τ they are subject to decay instability that occurs for wave numbers from a band with width of order a. The instability increment is also of order a. The left-hand polarized waves can be subject, in general, to three different types of instabilities. The first type is the modulational instability. It only occurs when b is smaller than a limiting value that depends on τ. Only perturbations with wave numbers smaller than a limiting value of order a are unstable. The instability increment is proportional to a2. The second type is the decay instability. It has the same properties as in the case of right-hand polarized waves; however, it occurs only when b < 1 τ. The third type is the beat instability. It occurs for any values of b and τ, and only perturbations with the wave numbers from a narrow band with the width of order a2 are unstable. The increment of this instability is proportional to a2, except for τ close to τc when it is proportional to a, where τc is a function of b

Absolute and convective instabilities of an inviscid compressible mixing layer: Theory and applications

This study aims to examine the effect of compressibility on unbounded and parallel shear flow linear instabilities. This analysis is of interest for industrial, geophysical, and astrophysical flows. We focus on the stability of a wavepacket as opposed to previous single-mode stability studies. We consider the notions of absolute and convective instabilities first used to describe plasma instabilities. The compressible-flow modal theory predicts instability whatever the Mach number. Spatial and temporal growth rates and Reynolds stresses nevertheless become strongly reduced at high Mach numbers. The evolution of disturbances is driven by Kelvin -Helmholtz instability that weakens in supersonic flows. We wish to examine the occurrence of absolute instability, necessary for the appearance of turbulent motions in an inviscid and compressible two-dimensional mixing layer at an arbitrary Mach number subject to a three-dimensional disturbance. The mixing layer is defined by a parametric family of mean-velocity and temperature profiles. The eigenvalue problem is solved with the help of a spectral method. We ascertain the effects of the distribution of temperature and velocity in the mixing layer on the transition between convective and absolute instabilities. It appears that, in most cases, absolute instability is always possible at high Mach numbers provided that the ratio of slow-stream temperature over fast-stream temperature may be less than a critical maximal value but the temporal growth rate present in the absolutely unstable zone remains small and tends to zero at high Mach numbers. The transition toward a supersonic turbulent regime is therefore unlikely to be possible in the linear theory. Absolute instability can be also present among low-Mach-number coflowing mixing layers provided that this same temperature ratio may be small, but nevertheless, higher than a critical minimal value. Temperature distribution within the mixing layer also has an effect on the growth rate, this diminishes when the slow stream is heated. These results are applied to the dynamics of mixing layers in the interstellar medium and to the dynamics of the heliopause, frontier between the interstellar medium, and the solar wind. (C) 2009 American Institute of Physics

An accurate equation of state for the one component plasma in the low coupling regime

An accurate equation of state of the one component plasma is obtained in the low coupling regime $0 \leq \Gamma \leq 1$. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo simulations and asymptotic analytical expressions of the excess internal energy $u$. In particular, special attention has been brought to describe and take advantage of finite size effects on Monte Carlo results to get the thermodynamic limit of $u$. This combined approach reproduces very accurately the different plasma correlation regimes encountered in this range of values of $\Gamma$. This paper extends to low $\Gamma$'s an earlier Monte Carlo simulation study devoted to strongly coupled systems for $1 \leq \Gamma \leq 190$ ({J.-M. Caillol}, {J. Chem. Phys.} \textbf{111}, 6538 (1999)). Analytical fits of $u(\Gamma)$ in the range $0 \leq \Gamma \leq 1$ are provided with a precision that we claim to be not smaller than $p= 10^{-5}$. HNC equation and exact asymptotic expressions are shown to give reliable results for $u(\Gamma)$ only in narrow $\Gamma$ intervals, i.e. $0 \leq \Gamma \lesssim 0.5$ and $0 \leq \Gamma \lesssim 0.3$ respectively

Nonlinear internal waves in the upper atmosphere

This paper considers the large-scale dynamics generated in the upper atmosphere by the destabilization of a linear internal gravity wave and its eventual restabilization through nonlinear processes into a coherent pattern. The assumption of a strongly dissipative medium is relevant to wave propagation in the thermosphere range above 100 km. A parametric instability analysis is carried out involving the Froude, Reynolds and Prandtl numbers, and the following parameters: friction, wave incidence and disturbance periodicity. A solution of the motion is sought with the help of a multiscale technique based upon the hypothesis of large-scale flow. The leading-order amplitude equation governing this dynamics contains the Cahn-Hilliard equation, but possesses, as well, a dispersive term depending on the Prandtl number, a large-scale damping proportional to the overall Richardson number and a quadratic term modelling the incidence effects. A numerical and analytical study of this equation is given. An internal-wave stability criterion is obtained which shows the possibility of obtaining coherent structures for large Froude numbers

Exact Renormalization Group : A New Method for Blocking the Action

We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply related by a Legendre transformation up to a trivial quadratic form. An exact mapping between canonical and non-canonical theories is obtained as well as the relations between their flows. An application to the theory of liquids is sketched

Transport Coefficients of the Yukawa One Component Plasma

We present equilibrium molecular-dynamics computations of the thermal conductivity and the two viscosities of the Yukawa one-component plasma. The simulations were performed within periodic boundary conditions and Ewald sums were implemented for the potentials, the forces, and for all the currents which enter the Kubo formulas. For large values of the screening parameter, our estimates of the shear viscosity and the thermal conductivity are in good agreement with the predictions of the Chapman-Enskog theory.Comment: 11 pages, 2 figure

Steady multipolar planar vortices with nonlinear critical layers

This article considers a family of steady multipolar planar vortices which are the superposition of an axisymmetric mean flow, and an azimuthal disturbance in the context of inviscid, incompressible flow. This configuration leads to strongly nonlinear critical layers when the angular velocities of the mean flow and the disturbance are comparable. The poles located on the same critical radius possess the same uniform vorticity, whose weak amplitude is of the same order as the azimuthal disturbance. This problem is examined through a perturbation expansion in which relevant nonlinear terms are retained in the critical layer equations, while viscosity is neglected. In particular, the associated singularity at the meeting point of the separatrices is treated by employing appropriate re-scaled variables. Matched asymptotic expansions are then used to obtain a complete analytical description of these vortices

A singular vortex Rossby wave packet within a rapidly rotating vortex

This paper describes the quasi-steady régime attained by a rapidly rotating vortex after a wave packet has interacted with it. We consider singular, nonlinear, helical, and shear asymmetric modes within a linearly stable, columnar, axisymmetric, and dry vortex in the f-plane. The normal modes enter resonance with the vortex at a certain radius rc, where the phase angular speed is equal to the rotation frequency. The related singularity in the modal equation at rc strongly modifies the flow in the 3D helical critical layer, the region where the wave/vortex interaction occurs. This interaction induces a secondary mean flow of higher amplitude than the wave packet and that diffuses at either side of the critical layer inside two spiral diffusion boundary layers. We derive the leading-order equations of the system of nonlinear coupled partial differential equations that govern the slowly evolving amplitudes of the wave packet and induced mean flow a long time after this interaction started. We show that the critical layer imposes its proper scalings and evolution equations; in particular, two slow times are involved, the faster being secular. This system leads to a more complex dynamics with respect to the previous studies on wave packets where this coupling was omitted and where, for instance, a nonlinear Schrödinger equation was derived [D. J. Benney and S. A. Maslowe, “The evolution in space and time of nonlinear waves in parallel shear flows,” Stud. Appl. Math. 54, 181 (1975)]. Matched asymptotic expansion method lets appear that the neutral modes are distorted. The main outcome is that a stronger wave/vortex interaction takes place when a wave packet is considered with respect to the case of a single mode. Numerical simulations of the leading-order inviscid Burgers-like equations of the derived system show that the wave packet rapidly breaks and that the vortex, after intensifying in the transition stage, is substantially weakened before the breaking onset. This breaking could give a dynamical explanation of the formation of an inner spiral band through the prism of the critical layer theory

The Ideal Conductor Limit

This paper compares two methods of statistical mechanics used to study a classical Coulomb system S near an ideal conductor C. The first method consists in neglecting the thermal fluctuations in the conductor C and constrains the electric potential to be constant on it. In the second method the conductor C is considered as a conducting Coulomb system the charge correlation length of which goes to zero. It has been noticed in the past, in particular cases, that the two methods yield the same results for the particle densities and correlations in S. It is shown that this is true in general for the quantities which depend only on the degrees of freedom of S, but that some other quantities, especially the electric potential correlations and the stress tensor, are different in the two approaches. In spite of this the two methods give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge

Non-Perturbative Renormalization Group for Simple Fluids

We present a new non perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and in the framework of two equivalent scalar field theories as well. The exact mapping between the three renormalization flows is established rigorously. In the Grand Canonical ensemble the theory may be seen as an extension of the Hierarchical Reference Theory (L. Reatto and A. Parola, \textit{Adv. Phys.}, \textbf{44}, 211 (1995)) but however does not suffer from its shortcomings at subcritical temperatures. In the framework of a new canonical field theory of liquid state developed in that aim our construction identifies with the effective average action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich, \textit{Phys. Rep.}, \textbf{363} (2002))