Graciela Gnavi

Spatial stability of similarity solutions for viscous flows in channels with porous walls

The spatial stability of similarity solutions for an incompressible fluid flowing along a channel with porous walls and driven by constant uniform suction along the walls is analyzed. This work extends the results of Durlofsky and Brady [Phys. Fluids 27, 1068 (1984)] to a wider class of similarity solutions, and examines the spatial stability of small amplitude perturbations of arbitrary shape, generated at the entrance of the channel. It is found that antisymmetric perturbations are the best candidates to destabilize the solutions. Temporally stable asymmetric solutions with flow reversal presented by Zaturska, Drazin, and Banks [Fluid Dyn. Res. 4, 151 (1988)] are found to be spatially unstable. The perturbed similarity solutions are also compared with fully bidimensional ones obtained with a finite difference code. The results confirm the importance of similarity solutions and the validity of the stability analysis in a region whose distance to the center of the channel is more than three times the chan...

On the possible excitation of electromagnetic ion cyclotron waves in solar ejecta

We study the possibility of exciting electromagnetic ion cyclotron waves (EICWs) in solar ejecta (CMEs) by a kinetic instability driven by ion temperature anisotropies. Our approach is to vary key parameters about assumed baseline values. Since Tp,‖ > Tp,⊥ in most solar ejecta, the polarization of the unstable waves is right-handed. If the average proton beta is low (βp ≤ 0.3), the activity is negligible for moderate temperature ratios, Tp,‖/Tp,⊥. Increasing βp increases both the frequency range and the instability growth rate. Increasing the temperature anisotropy brings about qualitatively similar effects as increasing βp, with comparable growth rates. Increasing the relative alpha-to-proton density ratio η has two effects: the active frequency range is shifted toward lower frequencies and the growth rate increases. Between η = 0 and η = 0.15, the maximum growth rate increases by a factor of ∼20, highlighting the importance of the alphas for generating this instability. A case that may represent some magnetic clouds with exceptional parameters, βp = 0.2, Tp,‖/Tp,⊥ = 10, and η = 0.08 − 0.15, is considered. The maximum growth rate is found to be twice the reference CME case, while the active frequency range is 3 times wider. We conclude that EICWs should be present in some ejecta and possibly also in those magnetic clouds with relatively weak magnetic field, high He++ content, and large Tp,‖/Tp,⊥ ratios, and whose βp is high, for example, through interaction with a succeeding fast stream. We also suggest that substantial changes with respect to normal conditions should occur in the power spectrum of EICWs in the terrestrial plasma depletion layer when a CME, or a magnetic cloud, with negative anisotropy passes Earth.

Effects of temperature-dependent viscosity in channels with porous walls

The influence of temperature-dependent viscosity on the flow along a channel with porous walls at different temperatures was analyzed. Numerical schemes were developed to solve the Navier–Stokes equation and the energy equation, coupled through the dependence of viscosity on temperature. Bifurcation diagrams are presented. Local analysis of the behavior of these bifurcations was also performed. The temporal and spatial stability of stationary solutions was studied by solving eigenvalue problems. The parameter space was explored and the regions where different stationary and periodic solutions appear are described. Periodic solutions obtained by solving the time-dependent problem are also presented.

Theoretical properties of electromagnetic ion cyclotron waves in the terrestrial, dayside, low‐latitude plasma depletion layer under uncompressed magnetosheath conditions

We present a numerical study of electromagnetic ion cyclotron wave (EICW) activity (growth and damping) in the terrestrial plasma depletion layer (PDL) under typical solar wind conditions. Aside from the α particles, all parameters in this study are as measured by AMPTE/IRM during 13 magnetosheath passes under low magnetic shear made in 1984-1985 and calculated with the superposed epoch analysis technique [Phan et al., 1994]. Three locations within the PDL are specified using minutes before the key time identifying the magnetopause crossing in the superposed epoch analysis (0, -5, -10 min). Our work thus characterizes average properties of EICWs along radial profiles in the PDL in the magnetic latitude and local time ranges of ±30° and 0800 to 1600 hours, respectively. In order to study the situation in the subsolar region more closely, we calculate also with PDL parameters acquired by AMPTE/IRM during the pass nearest to local noon (October 24, 1985). For a particle parameters we take reasonable estimates but also study the effect of varying the a particle temperature anisotropy. The influence of a small a particle-proton relative drift is also included. At the magnetopause we find one peak of activity in the frequency range from 0.2 to 0.3 Ω p (the proton cyclotron frequency), which is thus below the resonance frequency of the α particles (0.5 Ω p ) At locations 10 min and 5 min prior to the magnetopause crossing, the activity spectrum bifurcates, with both peaks below the α resonance and separated by an absorption band. Our explanation of this result is that as we move away from the magnetopause, the increasing plasma β enables the protons to overcome the a absorption. With a relative a particle-proton drift of 10% of the local Alfven speed, the absorption band is removed, but all excited frequencies are still less than 0.5 Ω p . The absorption band may also be removed by a high a particle thermal anisotropy coupled with a low a particle β along the magnetic field. On October 24, 1985, the PDL was characterized by a wider variation of β and a larger proton temperature anisotropy. Under these conditions a second EICW activity peak appears between 0.5 and 0.6 Ω p at the two locations away from the magnetopause, in addition to the α peak mentioned above, which we ascribe to the larger anisotropy of the protons. Again, a small α particle drift can remove the activity minimum. With the stagnation line flow pattern in the PDL found by AMPTE/IRM on these passes, we hypothesize that EICWs excited near noon subsequently travel along the magnetic field, bringing EICW activity to high latitudes. However, EICWs generated away from noon will be damped out while being carried to the magnetopause flanks.

Supersonic mixing layers: Stability of magnetospheric flanks models

Compressibility has a strong influence on the stability of velocity shear layers when the difference of velocity ?V across the flow becomes supersonic. The flanks of the Earths magnetopause are normally supersonic Ms > 1, and super-Alfv?nic MA > 1, depending on the distance from the dayside terminator (Ms and MA are the sonic and Alfv?n Mach numbers of the magnetosheath plasma, respectively). The stability of MHD supersonic flows depends, also on several other features, such as the finite thickness ? of the boundary layer, the relative orientation of velocity and magnetic fields, the density jump across the boundary and the magnetic shear angle. We analyze the MHD stability of some representative flank sites modeled after data from spacecraft crossings of the magnetopause under different interplanetary conditions, complementing these cases with extrapolations of likely conditions upstream, and downstream of the crossing site. Under northward interplanetary magnetic field conditions, there are solar wind regimes such that the near, but already supersonic, flank of the magnetopause may be locally stable. Stability is possible, e.g., when Ms becomes larger than ~1.2?1.4 while MA remains smaller than 1.2, and there is magnetic shear between the geomagnetic and the interplanetary magnetic field. Solar winds favouring local stability of the boundary layer are cold, not-too-dense plasmas, with strong magnetic fields, so that MA is smaller, while Ms is larger, than normal values of the magnetosheath flow. A gap between dayside and tail amplifying regions of Kelvin-Helmholtz disturbances over the magnetopause may exist when the above conditions are realized.

Two‐stream instability in convergent geometry

The problem of the instability of counterstreaming beams of charged particles is extended to cylindrical and spherical geometries. For well‐focused configurations it can be solved by complex contour integral representations. The effects of the convergence of the flow and the density gradient along the trajectories of the particles are considered. The linear spectrum for the cylindrical case is obtained, together with the proof that the solution has finite energy and satisfies two physical matching conditions through the origin. The properties of the special functions which solve this problem are presented. Although the density of the ideally focused model diverges as 1/r at the origin, the growth rate of the instability, for a system of radius R, is given by ω2pR/V02ξn, where V0 is the beam velocity, ξn are the zeros of the Bessel function of zeroth order, and the plasma frequency ωp is evaluated at one‐half the average density of particles.

Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes

A special class of Pierce diodes, that consists of a pair of grounded coaxial cylindrical electrodes, with electrons streaming radially between them, is studied. The full set of roots of the dispersion relation of the Pierce instability is obtained by solving the dispersion relation numerically. The nonlinear behaviour of the system is then investigated using particle simulation. It is shown that the behaviour of cylindrical systems depends on two nondimensional parameters. Linear and nonlinear properties are different for convergent and divergent configurations. Several remarkable differences between cylindrical and planar Pierce diodes are reported.

Models of ion beam interactions for the stability analysis of migma

Abstract The stability of the central region of the triple delta distribution function for a migma is shown to be reducible to the analysis of fourth and sixth order ordinary differential equations for radial electrostatic modes, including axial oscillations and electron shielding effects. A normal mode study shows that a cylindrically counterstriming ion instability appears for ω pi > ω ci . This effect should attenuated by the introduction of some spread in pθ . It is noted that a spherical system of counterstreaming beams is stable for radial modes. An instability of the Harristpe is discussed with a migma slab model, which includes finite axial extent and a bias electric field. It is suggested that a microinstability observed during the Migma IV experiment was stabilized by the combined influence of small axial wavelenghts and electron heating.

The Polarization Response Function and Electrostatic Modes of Focused Beams

It is shown that the method of percussion for obtaining the spatial-temporal representation of the polarization response function directly [1] can also be used to study stability problems in nonuniform plasmas, thus providing a physical and mathematical alternative to the traditional approach. As an example, the stability analysis of particle beams is given, focused with cylindrical symmetry through an axis. The integral equation for electrostatic modes is set up with the polarization response, and solved with a technique that provides both the characteristic values and an integral representation for the field. The instability of this model, which is the cylindrical counterpart of the plane symmetric counterstreaming configuration, is then discussed.

Factorization of J-expansive meromorphic operator-valued functions

The factorization theorems are a generalization for J-biexpansive meromorphic operator-valued functions on an infinite-dimensional Hilbert space of the theorems on decomposition of J-expansive matrix functions on a finite-dimensional Hilbert space due to A. V. Efimov and V. P. Potapov [Uspekhi Mat. Nauk28 (1973), 65-130; Trudy Moskov. Mat. Obsc.4 (1955), 125-236]. They also generalize theorems on factorization of J-expansive meromorphic operator functions due to Ju. P. Ginzburg [Izv. Vyss. Ucebn. Zaved. Matematika32 (1963), 45-53]. Within the framework of generalized network theory, the results can be applied to the J-biexpansive real operators that characterize a Hilbert port. Application of the extraction procedure to a given real operator leads to its splitting into a product of real factors, corresponding to Hilbert ports of a simpler structure. This can be interpreted as an extension of the classical method of synthesis of passive n-ports by factor decomposition.