Growth rate and vertical propagation of the initial error in baroclinic models

The present study investigates the growth of error in baroclinic waves. It is found that stable or neutral waves are particularly sensitive to errors in the initial condition. Short stable waves are mainly sensitive to phase errors and the ultra long waves to amplitude errors. Analysis simulation experiments have indicated that the amplitudes of the very long waves become usually too small in the free atmosphere, due to the sparse and very irregular distribution of upper air observations. This also applies to the four-dimensional data assimilation experiments, since the amplitudes of the very long waves are usually underpredicted. The numerical experiments reported here show that if the very long waves have these kinds of amplitude errors in the upper troposphere or lower stratosphere the error is rapidly propagated (within a day or two) to the surface and to the lower troposphere.

Whistler mode wave growth and propagation in the prenoon magnetosphere

Pitch-angle scattering of electrons can limit the stably trapped particle flux in the magnetosphere and precipitate energetic electrons into the ionosphere. Whistler-mode waves generated by a temperature anisotropy can mediate this pitch-angle scattering over a wide range of radial distances and latitudes, but in order to correctly predict the phase-space diffusion, it is important to characterise the whistler-mode wave distributions that result from the instability. We use previously-published observations of number density, pitch-angle anisotropy and phase space density to model the plasma in the quiet pre-noon magnetosphere (defined as periods when AE<100nT). We investigate the global propagation and growth of whistler-mode waves by studying millions of growing ray paths and demonstrate that the wave distribution at any one location is a superposition of many waves at different points along their trajectories and with different histories. We show that for observed electron plasma properties, very few raypaths undergo magnetospheric reflection, most rays grow and decay within 30 degrees of the magnetic equator. The frequency range of the wave distribution at large L can be adequately described by the solutions of the local dispersion relation, but the range of wavenormal angle is different. The wave distribution is asymmetric with respect to the wavenormal angle. The numerical results suggest that it is important to determine the variation of magnetospheric parameters as a function of latitude, as well as local time and L-shell.

A simple model of the effects of the mid-latitude total ion trough in the bottomsideFlayer on HF radiowave propagation

Observations of the amplitudes and Doppler shifts of received HF radio waves are compared with model predictions made using a two-dimensional ray-tracing program. The signals are propagated over a sub-auroral path, which is shown to lie along the latitudes of the mid-latitude trough at times of low geomagnetic activity. Generalizing the predictions to include a simple model of the trough in the density and height of the F2 peak enables the explanation of the anomalous observed diurnal variations. The behavior of received amplitude, Doppler shift, and signal-to-noise ratio as a function of the Kp index value, the time of day, and the season (in 17 months of continuous recording) is found to agree closely with that predicted using the statistical position of the trough as deduced from 8 years of Alouette satellite soundings. The variation in the times of the observation of large signal amplitudes with the Kp value and the complete absence of such amplitudes when it exceeds 2.75 are two features that implicate the trough in these effects.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

ENSO related variation of equatorial MRG and Rossby waves and forcing from higher latitudes

The contrasting behaviour of westward-moving mixed Rossby-gravity (WMRG) and the first Rossby (R1) waves in El Niño (EN) and La Niña (LN) seasons is documented with a focus on the Northern Hemisphere winter. The eastward-moving variance in the upper troposphere is dominated by WMRG and R1 structures that appear to be Doppler-shifted by the flow and are referred to as WMRG-E and R1-E. In the East Pacific and Atlantic the years with stronger equatorial westerly winds have the stronger WMRG and WMRG- E. In the East Pacific, R1 is also a maximum in LN. However, R1-E exhibits an eastward-shift between LN and EN. The changes with ENSO phase provide a test-bed for the understanding of these waves. In the East Pacific and Atlantic, the stronger WMRG-E and WMRG with stronger westerlies are in accord with the dispersion relation with simple Doppler-shifting by the zonal flow. The possible existence of free waves can also explain stronger R1 in EN in the Eastern Hemisphere. 1-D free wave propagation theory based on wave activity conservation is also important for R1. However, this theory is unable to explain the amplitude maxima for other waves observed in the strong equatorial westerly regions in the Western Hemisphere, and certainly not their ENSO-related variation. The forcing of equatorial waves by higher latitude wave activity and its variation with ENSO phase is therefore examined. Propagation of extratropical eastward-moving Rossby wave activity through the westerly ducts into the equatorial region where it triggers WMRG-E is favoured in the stronger westerlies, in LN in the East Pacific and EN in the Atlantic. It is also found that WMRG is forced by Southern Hemisphere westward-moving wavetrains arching into the equatorial region where they are reflected. The most significant mechanism for both R1 and R1-E appear to be lateral forcing by subtropical wavetrains.

Rossby wave propagation tracks in southern hemisphere mean basic flows associated to generalized frosts over southern South America

Based on previous observational studies on cold extreme events over southern South America, some recent studies suggest a possible relationship between Rossby wave propagation remotely triggered and the occurrence of frost. Using the concept of linear theory of Rossby wave propagation, this paper analyzes the propagation of such waves in two different basic states that correspond to austral winters with maximum and minimum generalized frost frequency of occurrence in the Wet Pampa (central-northwest Argentina). In order to determine the wave trajectories, the ray tracing technique is used in this study. Some theoretical discussion about this technique is also presented. The analysis of the basic state, from a theoretical point of view and based on the calculation of ray tracings, corroborates that remotely excited Rossby waves is the mechanism that favors the maximum occurrence of generalized frosts. The basic state in which the waves propagate is what conditions the places where they are excited. The Rossby waves are excited in determined places of the atmosphere, propagating towards South America along the jet streams that act as wave guides, favoring the generation of generalized frosts. In summary, this paper presents an overview of the ray tracing technique and how it can be used to investigate an important synoptic event, such as frost in a specific region, and its relationship with the propagation of large scale planetary waves.

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.

Adiabatic propagation in potential structures

In this work the adiabatic approximation is applied to the propagation of matter waves in confined geometries like those experimentally realized in recent atom optical experiments. Adiabatic propagation along a channel is assumed not to mix the various transverse modes. Nonadiabatic corrections arise from the potential squeezing and bending. Here we investigate the effect of the former. Detailed calculations of two-dimensional propagation are carried out both exactly and in an adiabatic approximation. This offers the possibility to analyze the validity of adiabaticity criteria. A semiclassical (sc) approach, based on the sc Massey parameter is shown to be inadequate, and the diffraction due to wave effects must be included separately. This brings in the Fresnel parameter well known from optical systems. Using these two parameters, we have an adequate understanding of adiabaticity on the system analyzed. Thus quantum adiabaticity must also take cognizance of the intrinsic diffraction of matter waves.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

Single-mode acceleration of matter waves in circular waveguides

Ultracold gases in ring geometries hold promise for significant improvements of gyroscopic sensitivity. Recent experiments have realized atomic and molecular storage rings with radii in the centimeter range, sizes whose practical use in inertial sensors requires velocities significantly in excess of typical recoil velocities. We use a combination of analytical and numerical techniques to study the coherent acceleration of matter waves in circular waveguides, with particular emphasis on its impact on single-mode propagation. In the simplest case we find that single-mode propagation is best maintained by the application of time-dependent acceleration force with the temporal profile of a Blackmann pulse. We also assess the impact of classical noise on the acceleration process.

Traveling waves in the Lethargic Crab Disease

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

Theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of a sharp steplike initial discontinuity in a beam with one-dimensional striplike geometry. This approach is confirmed by numerical simulations, which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)