Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

In this work, a new theoretical mechanism is presented in which equatorial Rossby and inertio-gravity wave modes may interact with each other through resonance with the diurnal cycle of tropical deep convection. We have adopted the two-layer incompressible equatorial primitive equations forced by a parametric heating that roughly represents deep convection activity in the tropical atmosphere. The heat source was parametrized in the simplest way according to the hypothesis that it is proportional to the lower-troposphere moisture convergence, with the background moisture state function mimicking the structure of the ITCZ. In this context, we have investigated the possibility of resonant interaction between equatorially trapped Rossby and inertio-gravity modes through the diurnal cycle of the background moisture state function. The reduced dynamics of a single resonant duo shows that when this diurnal variation is considered, a Rossby wave mode can undergo significant amplitude modulations when interacting with an inertio-gravity wave mode, which is not possible in the context of the resonant triad non-linear interaction. Therefore, the results suggest that the diurnal variation of the ITCZ can be a possible dynamical mechanism that leads the Rossby waves to be significantly affected by high frequency modes.

Origin of Convectively Coupled Kelvin Waves over South America

Convectively coupled Kelvin waves over the South American continent are examined through the use of temporal and spatial filtering of reanalysis, satellite, and gridded rainfall data. They are most prominent from November to April, the season analyzed herein. The following two types of events are isolated: those that result from preexisting Kelvin waves over the eastern Pacific Ocean propagating into the continent, and those that apparently originate over Amazonia, forced by disturbances propagating equatorward from central and southern South America. The events with precursors in the Pacific are mainly upper-level disturbances, with almost no signal at the surface. Those events with precursors over South America, on the other hand, originate as upper-level synoptic wave trains that pass over the continent and resemble the ""cold surges`` documented by Garreaud and Wallace. As the wave train propagates over the Andes, it induces a southerly low-level wind that advects cold air to the north. Precipitation associated with a cold front reaches the equator a few days later and subsequently propagates eastward with the characteristics of a Kelvin wave. The structures of those waves originating over the Pacific are quite similar to those originating over South America as they propagate to eastern South America and into the Atlantic. South America Kelvin waves that originate over neither the Pacific nor the midlatitudes of South America can also be identified. In a composite sense, these form over the eastern slope of the Andes Mountains, close to the equator. There are also cases of cold surges that reach the equator yet do not form Kelvin waves. The interannual variability of the Pacific-originating events is related to sea surface temperatures in the central-eastern Pacific Ocean. When equatorial oceanic conditions are warm, there tends to be an increase in the number of disturbances that reach South America from the Pacific.

Wolf-Rayet optically thick winds with Alfven waves

The Wolf-Rayet (WR) stars are hot luminous objects which are suffering an extreme mass loss via a continuous stellar wind. The high values of mass loss rates and high terminal velocities of the WR stellar winds constitute a challenge to the theories of radiation driven winds. Several authors incorporated magnetic forces to the line driven mechanism in order to explain these characteristics of the wind. Observations indicate that the WR stellar winds may reach, at the photosphere, velocities of the order of the terminal values, which means that an important part of the wind acceleration occurs at the optically thick region. The aim of this study is to analyze a model in which the wind in a WR star begins to be accelerated in the optically thick part of the wind. We used as initial conditions stellar parameters taken from the literature and solved the energy, mass and momentum equations. We demonstrate that the acceleration only by radiative forces is prevented by the general behavior of the opacities. Combining radiative forces plus a flux of Alfven waves, we found in the simulations a fast drop in the wind density profile which strongly reduces the extension of the optically thick region and the wind becomes optically thin too close its base. The understanding how the WR wind initiate is still an open issue. (C) 2010 COSPAR. Published by Elsevier Ltd. All rights reserved.

Alfven waves as a driving mechanism in stellar winds

Alfven waves have been invoked as an important mechanism of particle acceleration in stellar winds of cool stars. After their identification in the solar wind they started to be studied in winds of stars located in different regions of the FIR diagram. We discuss here some characteristics of these waves and we present a direct application in the acceleration of late-type stellar winds. (C) 2009 COSPAR. Published by Elsevier Ltd. All rights reserved.

Moho map of South America from receiver functions and surface waves

We estimate crustal structure and thickness of South America north of roughly 40 degrees S. To this end, we analyzed receiver functions from 20 relatively new temporary broadband seismic stations deployed across eastern Brazil. In the analysis we include teleseismic and some regional events, particularly for stations that recorded few suitable earthquakes. We first estimate crustal thickness and average Poisson`s ratio using two different stacking methods. We then combine the new crustal constraints with results from previous receiver function studies. To interpolate the crustal thickness between the station locations, we jointly invert these Moho point constraints, Rayleigh wave group velocities, and regional S and Rayleigh waveforms for a continuous map of Moho depth. The new tomographic Moho map suggests that Moho depth and Moho relief vary slightly with age within the Precambrian crust. Whether or not a positive correlation between crustal thickness and geologic age is derived from the pre-interpolation point constraints depends strongly on the selected subset of receiver functions. This implies that using only pre-interpolation point constraints (receiver functions) inadequately samples the spatial variation in geologic age. The new Moho map also reveals an anomalously deep Moho beneath the oldest core of the Amazonian Craton.

Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

BREAKING WAVES IN AN IDEAL QUARK GLUON PLASMA

We study the propagation of perturbations in the energy density in a quark gluon plasma. Expanding the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations we obtain a nonlinear differential equation called the breaking wave equation. We solve it numerically and follow the time-evolution of initially localized pulses. We find that, quite unexpectedly, these pulses live for a very long time (compared to the reaction time-scales) before breaking. In practice, they mimick the Korteweg-de Vries solitons. Their existence may have some observable consequences.

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ""radiation"". Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. (C) 2009 Elseiver. B.V. All rights reserved.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.