Alejandro G. González

Magnetoacoustic surface gravity waves

The effect of gravity on the surface magnetoacoustic waves may be important when considering applications to solar and laboratory plasmas. The linear magnetoacoustic waves, which may appear in a configuration with an interface between two plasmas or a plasma and an ordinary gas, are studied. Compressibility and gravity are taken into account. The different types of couplings between internal and surface modes are analyzed. Magnetoacoustic surface waves are studied in detail in a configuration consisting of an interface between an isothermal plasma and an ordinary gas. The possible regions where these modes may exist are discussed. A general way of grouping and classifying the complicated spectra of modes is presented. New groups of modes appear as a consequence of gravity and stratification, in addition to those already present in the absence of gravity. The results may be of help in studying more complicated cases.

Compressible Kelvin-Helmholtz instability at the terrestrial magnetopause

The compressible magnetohydrodynamic Kelvin-Helmholtz instability occurs in two varieties, one that can be called incompressible as it exists in the limit of vanishing compressibility (primary instability), while the other exists only when compressibility is included in the model (secondary instability). In previous work we developed techniques to investigate the stability of a surface of discontinuity between two different uniform ows. Our treatment includes arbitrary jumps of the velocity and magnetic fields as well as of density and temperature, with no restriction on the wave vector of the modes. Then it allows stability analyses of complex configurations not previously studied in detail. Here we apply our methods to investigate the stability of various typical situations occurring at different regions of the front side, and the near anks of the magnetopause. The physical conditions of the vector and scalar fields that characterize the equilibrium interface at the positions considered are obtained both from experimental data and from results of simulation codes of the magnetosheath available in the literature. We give particular attention to the compressible modes in configurations in which the incompressible modes are stabilized by the magnetic shear. For configurations of the front of the magnetopause, which have small relative velocities, we find that the incompressible MHD model gives reliable estimates of their stability, and compressibility effects do not introduce significant changes. However, at the anks of the magnetopause the occurrence of the secondary instability and the shift of the boundary of the primary instability play an important role. Consequently, configurations that are stable if compressibility is neglected turn out to be unstable when it is considered and the stability properties are quite sensitive on the values of the parameters. Then compressibility should be taken into account when assessing the stability properties of these configurations, since the estimates based on incompressible MHD may be misleading. A careful analysis is required in each case, since no simple rule of thumb can be given.

Reaction forces on a ladder leaning on a rough wall

The determination of the reactions on a ladder is discussed including friction against the wall. In a recent article, this problem was studied considering elastic compression and it was argued that an additional condition holds that allows one to find all the reactions. We show that this condition is incorrect for typical ladders, when flexion is important. We clarify the issues of static determinacy by means of an analysis that takes into account both compression and flexion. We find that when the climber arrives at the top, the result depends on which deformation prevails. We conclude that the reactions can never be determined using only statics, because there is no way to ascertain which kind of deformation dominates, and so which limiting condition will be attained, if any.

A minimum dissipation principle for the Rayleigh-Taylor problem in viscous magnetohydrodynamics

Abstract A variational principle for magnetohydrodynamic gravitational modes, including isotropic viscosity and the shear of magnetic field lines, is given. It is shown to imply a minimum dissipation requirement for the modes. A sufficient condition for stability given in the literature for the case of ordinary fluids is corrected here.

Mhd Leaky Waves in a Layered Plasma: III Numerical Solutions

We study numerically the Fourier pseudomodes of complex frequency, that represent leaky waves, for two configurations consisting of three layers of uniform plasma in equilibrium, using the methods developed in the previous papers. The spectra consist of an infinite set of branches. We introduce a shorthand notation that allows us to identify the branches and we discuss their behavior. We show examples of leaky waves that in the neighborhood of certain limiting cases correspond to some of the four basic mechanisms discussed in a previous paper.

Mhd Leaky Waves in a Layered Plasma: II Mechanisms of Leakage

The application of Fourier analysis to study leaky waves has the advantage of simplicity, but it is not clear why the complex roots of the dispersion relations represent leaky waves, nor how the leakage occurs. We investigate the different kinds of leakage that can occur in a three layer plasma, and to which Fourier pseudomodes they are associated. We find four basic mechanisms, called “surface mode ...”, “single interface ...”, “trapped wave ...” and “lost insulation leakage”. These mechanisms appear in pure form only near certain limiting cases, in which the parameters of the problem take some special values. As soon as the parameters depart significantly from the limiting values, the behavior of the leaky wave complicates and mixtures of the mechanisms occur, in varying amounts. In consequence different points of the same complex branch of the spectrum may correspond to different mechanisms. All the complex branches of the spectrum correspond to leaky waves, but in general it is not possible to classify them according to type of leakage, except close to a limiting case. Since in a three layer configuration there are many of these, the spectrum of leaky waves is very complicated.

Wetting and dewetting processes in the axial retraction of liquid filaments

We study the hydrodynamic mechanisms involved in the motion of the contact line formed at the end region of a liquid filament laying on a planar and horizontal substrate. Since the flow develops under partially wetting conditions, the tip of the filament recedes and forms a bulged region (head) that subsequently develops a neck region behind it. Later the neck breaks up leading to a separated drop, while the rest of the filament restarts the sequence. One main feature of this flow is that the whole dynamics and final drop shapes are strongly influenced by the hysteresis of the contact angle typical in most of the liquid-substrate systems. The time evolution till breakup is studied experimentally and pictured in terms of a hybrid wettability theory which involves the Cox-Voinov hydrodynamic approach combined with the molecular kinetic theory developed by Blake. The parameters of this theory are determined for our liquid-substrate system (silicone oil-coated glass). The experimental results of the retracting filament are described in terms of a simple heuristic model and compared with numerical simulations of the full Navier-Stokes equations. This study is of special interest in the context of pulsed laser-induced dewetting.

Stability of accelerated plasma: Effects of compressibility and viscosity

The linear stability of accelerated plasmas is studied. It is considered an unperturbed state that allows stratification of density and magnetic field in the plasma, as well as a plasma‐vacuum interface. We consider the effect of compressibility and show that it enlarges the spectrum of unstable modes, as well as increases the growth rate. Stability criteria and growth rates are given both for internal and surface modes. On the other hand, viscous effects on solenoidal modes are considered. The limiting cases of highly collisional and strongly magnetized plasmas are analyzed, showing different behavior. General properties of the spectrum are derived by means of normal mode and variational analysis.

The Kelvin‐Helmholtz Instability in Compressible Plasmas with Magnetic Field Shear

We investigate the effect of compressibility and magnetic field shear on the Kelvin‐Helmholtz instability in compressible stratified plasmas. We obtain two main results. First, for sufficiently low velocities the compressibility stabilizes the unstable modes present in an incompressible model (called main modes). This represents an important difference with the case without magnetic field shear. Second, new unstable modes appear (called secondary) which owe their existence to compressive perturbations. The secondary modes (of compressive character) determine the stability for values of velocity of the unperturbed flow that correspond to stable primary modes. In these cases the compressive modes do not disappear and may have appreciable growth rates. Therefore, compressibility effects may be relevant when discussing the stability of problems with magnetic field shear. Diagrams of stability and growth rates are shown that allow an easy visualization of the stability properties of a configuration

Magnetohydrodynamical leaky waves in a layered plasma

We investigate the existence of MHD leaky waves in compressible and layered plasmas. We consider perturbations of complex frequency in a slab model with three layers. We develop a general method that includes the ‘cubic modes’ as well as other kinds of leaky waves, and allows us to derive many results in closed form. There are several physical mechanisms that can produce leakage. We give two numerical examples to exhibit the different behaviours that can arise. Finally we comment on the connection of the present results with those obtained by other authors, and correct some errors.