Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves

Abstract

An analytical spectral model of the barotropic divergent equations on a sphere is developed using the potential-stream function formulation and the normal modes as basic functions. Explicit expressions of the coefficients of nonlinear interaction are obtained in the asymptotic case of a slowly rotating sphere, i.e. when the normal modes can be expressed as single spherical harmonics.     

Shallow Water Dissipation Processes for Wind Waves off the Mackenzie Delta

This study focuses on two physical processes for waves in shallow waters off the Mackenzie Delta: bottom friction and depth-induced breaking terms. We use field observations of winds and waves, the state-of-the-art Simulating Waves Nearshore (SWAN) model, and reanalysis wind and wave data. The two field observation periods are an August 2008 field experiment, during which in situ field data were collected, and an Arctic storm when data were recorded by buoy measurements from 4 to 6 August 1991. Wind and wave development processes are analyzed during these two periods with comparisons to observed winds and waves. Our analyses show that bottom friction is the main shallow water physical process during the August 2008 field experiment, whereas depth-induced breaking is the dominant shallow water physical process during the 4–6 August 1991 storm, in conjunction with the effects of bottom friction. The SWAN wave model is used to investigate the shallow water physical processes during these two observation periods. Simulation results indicate that the model can give reasonable results, with an appropriate Collins coefficient of 0.006 and a wave breaking parameter of 0.55 to represent bottom friction and depth-induced breaking physics, respectively.

RÉSUMÉ?[Traduit par la rédaction] Cette étude porte sur deux processus physiques concernant les vagues dans les eaux peu profondes au large du delta du Mackenzie : les termes du frottement contre le fond et du déferlement lié à la profondeur. Nous utilisons des observations du vent et des vagues, le modèle d'avant-garde SWAN (Simulating Waves Nearshore) et des données de vent et de vagues réanalysées. Les deux périodes d'observations sont une expérience sur le terrain réalisée en août 2008, au cours de laquelle des données de terrain ont été recueillies, et une tempête arctique lors de laquelle des mesures faites par bouée du 4 au 6 août 1991 ont été enregistrées. Nous analysons les processus dévolution du vent et des vagues durant ces deux périodes, et comparons avec le vent et les vagues observées. Nos analyses montrent que le frottement contre le fond est le processus physique en eaux peu profondes le plus important durant l'expérience sur le terrain d'août 2008, alors que le déferlement lié à la profondeur est le processus physique en eaux peu profondes dominant pendant la tempête arctique du 4 au 6 août 1991, en combinaison avec les effets du frottement contre le fond. Nous nous servons du modèle de vagues SWAN pour étudier les processus physiques en eaux peu profondes durant ces deux périodes d'observations. Les résultats des simulations indiquent que le modèle peut donner des résultats raisonnables, avec un coefficient de Collins approprié de 0,006 et un paramètre de déferlement de 0,55 pour représenter la physique du frottement contre le fond et du déferlement lié à la profondeur, respectivement.     

The formation and evolution of an isolated submarine valley in the North Channel,Irish Sea: an investigation of Beaufort's Dyke

Beaufort's Dyke is a submarine depression located in the North Channel of the Irish Sea. With a maximum depth of 312 m, the dyke is one of the deepest areas within the European continental shelf. Integration and interpretation of 450 km of sparker seismic data and full‐coverage bathymetric data derived from multi‐beam echo sounder surveys allow for the investigation of the formation processes of Beaufort's Dyke and the evolution of geomorphological features within it. The dyke, formed by composite subglacial processes dominated by subglacial meltwater discharge, is interpreted as a tunnel valley. The regional isolation of Beaufort's Dyke may be explained by the bounding of the North Channel by the bedrock masses of Ireland and Scotland, coupled with the exploitation of structural weakness along a fault plane and presence of halite in the eroded substrate enhancing the erosive potential of the overlying glacier. Beaufort's Dyke has probably been maintained as an open feature by strong rectilinear tidal currents. The morphology of lunate sediment waves and a large parabolic bedform towards the south of the dyke contradict the observed dominant S–N mean hydrodynamic flow recorded within the North Channel, suggesting an alternative hydrodynamic regime either within the dyke or during bedform creation. Copyright © 2011 John Wiley & Sons, Ltd.     

Winds from clusters with non-uniform stellar distributions

We present the analytic and numerical models of the 'cluster wind' resulting from the multiple interactions of the winds ejected by the stars of a dense cluster of massive stars. We consider the case in which the distribution of stars (i.e. the number of stars per unit volume) within the cluster is spherically symmetric, has a power-law radial dependence, and drops discontinuously to zero at the outer radius of the cluster. We carry out comparisons between an analytic model (in which the stars are considered in terms of a spatially continuous injection of mass and energy) and 3D gasdynamic simulations (in which we include 100 stars with identical winds, located in 3D space by statistically sampling the stellar distribution function). From the analytic model, we find that for stellar distributions with steep enough radial dependencies, the cluster wind flow develops a very high central density and a non-zero central velocity, and for steeper dependencies, it becomes fully supersonic throughout the volume of the cluster (these properties are partially reproduced by the 3D numerical simulations). Therefore, the wind solutions obtained for stratified clusters can differ dramatically from the case of a homogeneous stellar distribution (which produces a cluster wind with zero central velocity, and a fully subsonic flow within the cluster radius). Finally, from our numerical simulations, we compute predictions of X-ray emission maps and luminosities, which can be directly compared with observations of cluster wind flows.     

Can the early X-ray afterglow of gamma-ray bursts be explained by a contribution from the reverse shock?

We propose to explain the recent observations of gamma-ray burst early X-ray afterglows with SWIFT by the dissipation of energy in the reverse shock that crosses the ejecta as it is decelerated by the burst environment. We compute the evolution of the dissipated power and discuss the possibility that a fraction of it can be radiated in the X-ray range. We show that this reverse shock contribution behaves in a way very similar to the observed X-ray afterglows if the following two conditions are satisfied. (i) The Lorentz factor of the material which is ejected during the late stages of source activity decreases to small values  Γ < 10  and (ii) a large part of the shock-dissipated energy is transferred to a small fraction  (ζ≲ 10⁻²)  of the electron population. We also discuss how our results may help to solve some puzzling problems raised by multiwavelength early afterglow observations such as the presence of chromatic breaks.     

An Introduction to Observations Relevant to Astrophysical Jets and Nebulae

This article reviews the basic physics and jargon associated with astronomical observations of nebulae, with an emphasis on processes relevant to shock waves in astrophysical jets.     

Shock drift electron acceleration and generation of waves

An analytically derived distribution function of reflected and accelerated electrons at a nearly perpendicular shock is presented. Then this distribution in a simplified form is introduced into a 1.5-D relativistic electromagnetic particle-in-cell (PIC) model and a generation of waves is studied. Numerical modeling shows not only a generation of Langmuir and high-frequency electromagnetic waves as expected, but also an efficient generation of whistler waves. Their role in emission processes of type II solar radio bursts is discussed.     

Instabilities in rotating relativistic stars driven by viscosity

We investigate the instability driven by viscosity in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study these factors on the critical value T/W for the instability. For a rigidly rotating star, the criterion T/W, where T is the rotational kinetic energy and W the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13–0.16, which slightly differ from that of Newtonian incompressible stars (∼0.14). For differentially rotating stars, the critical value of T/W is found to span the range 0.17–0.25. The value is significantly larger than in the rigidly rotating case with the same compactness of the star. Finally we discuss the possibility of detecting gravitational waves from viscosity-driven instabilities using ground-based interferometers.      

Solar p modes of high degree l: coupling by differential rotation

Accurate measurements of solar p-mode frequencies and frequency splittings at high degree l require an adequate theoretical knowledge of the effects of mode coupling, induced by the variation with latitude of the angular velocity of the solar internal rotation. Earlier results for expansion coefficients of composite solutions (coupling coefficients) are due to Woodard. In this paper, the analysis is extended to allow for the dependence of the differential rotation on depth, and the result is expressed in terms of measurable quantities (the rotational splitting coefficients), which makes it convenient for diagnostic purposes. The analysis is based on the approach of quasi-degenerate perturbation theory, and is extended further to address possible effects of mode coupling in the observational line profiles. It is shown, using approximations applicable at high degree l , that the expected line profiles of composite modes in the observational power spectra are not distorted by mode coupling.