scholarly journals Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres

2009 ◽  
Vol 27 (11) ◽  
pp. 4221-4227 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Rossby Waves ◽  
Narrow Band ◽  
Boussinesq Approximation ◽  
The Other ◽  
The Earth ◽  
Propagating Waves ◽  
Inertial Wave ◽  
The One ◽  
Fifth Order ◽  
Critical Latitude

Abstract. This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona) are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Aristotle's Unmoved Movers

Traditio ◽  
1946 ◽  
Vol 4 ◽  
pp. 1-30 ◽  
Author(s):  
Philip Merlan
Keyword(s):  
Middle Ages ◽  
The Other ◽  
World Picture ◽  
The Earth ◽  
Concentric Spheres ◽  
The One ◽  
The Universe ◽  
The Middle Ages

According to Aristotle all heavenly movement is ultimately due to the activity of forty-seven (or fifty-five) ‘unmoved movers'. This doctrine is highly remarkable in itself and has exercised an enormous historical influence. It forms part of a world-picture the outlines of which are as follows. The universe consists of concentric spheres, revolving in circles. The outermost of these bears the fixed stars. The other either bear planets or, insofar as they do not, contribute indirectly to the movements of the latter. Each sphere is moved by the one immediately surrounding it, but also possesses a movement of its own, due to its mover, an unmoved, incorporeal being. (It was these beings which the schoolmen designated as theintelligentiae separatae.) The seemingly irregular movements of the planets are thus viewed as resulting from the combination of regular circular revolutions. The earth does not move and occupies the centre of the universe. Such was Aristotle's astronomic system, essential parts of which were almost universally adopted by the Arabic, Jewish, and Christian philosophers of the Middle Ages.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

2009 ◽  
Vol 66 (6) ◽  
pp. 1735-1748 ◽  
Author(s):  
W. T. M. Verkley
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Rossby Waves ◽  
Coriolis Parameter ◽  
Beta Plane ◽  
Propagating Waves ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity ◽  
The One

Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

scholarly journals Interactions between Rotation and Pulsation

2004 ◽  
Vol 215 ◽  
pp. 404-413
Author(s):  
Rich Townsend
Keyword(s):  
Angular Momentum ◽  
Coriolis Force ◽  
Rossby Waves ◽  
Narrow Band ◽  
Rotating Stars ◽  
Stellar Rotation ◽  
Coriolis Forces ◽  
Wave Dynamics ◽  
Propagating Waves ◽  
Physical Principles

In this contribution, I will examine the interaction between stellar rotation and pulsation. I begin with a brief review of the non-rotating case, emphasizing the character of pulsations as azimuthally-propagating waves. I then go on to discuss how these waves are modified under the influence of the centrifugal and Coriolis forces. Through simple arguments, I outline the conditions under which each force can become significant in determining the wave dynamics. Particular attention is paid to the Coriolis force, since it is responsible for the formation of a waveguide, which confines the pulsation to a narrow band centered on the stellar equator. Using the example of a prograde sectoral pulsation mode, I explain the basic physical principles underlying this trapping.The Coriolis force is also responsible for the existence of Rossby waves, which are not found in non-rotating stars. I demonstrate how these waves may be understood in terms of a conservation law for angular momentum, and review their most important characteristics. I then examine how rotation modifies the frequencies of pulsation, and explain how observations of such modifications can provide information regarding a star's rotation rate. To conclude, I focus on the converse of the pulsation-rotation interaction: how the transport of angular momentum by pulsation might be important in determining the evolution of a star's rotation profile.

Deep time and compressed time in the Anthropocene: The new timescape and the value of cosmic storytelling

2020 ◽  
Vol 7 (2) ◽  
pp. 125-137
Author(s):  
Boris Shoshitaishvili
Keyword(s):  
Technological Change ◽  
Scientific Discovery ◽  
The Other ◽  
Earth System ◽  
Human Beings ◽  
Geologic History ◽  
Deep Time ◽  
The Earth ◽  
The One

The scientific discovery of our universe’s immense cosmological history and Earth’s vast geologic history has radically altered common perceptions of time, prompting us to think in terms of millions and billions of years rather than hundreds and thousands. Meanwhile human societies impact the Earth System at accelerating rates and more comprehensively than ever before, leading scientists to propose the new geological epoch of the Anthropocene. These two contrasting temporal transformations have mostly been considered separately: the expanding awareness of cosmological and geologic duration, on the one hand, and the acute sense of swift technological change, on the other. However, their contrast and coexistence are important to recognize. The challenge of understanding the Anthropocene’s complex timescales is partly due to the inability of human institutions to reconcile this twofold disruption whereby time has both expanded (into deep time) and compressed (in techno-social acceleration). After theorizing this transformation, I evaluate the current cosmic stories helping human beings reconceptualize the new timescape.

scholarly journals Immigration, Humanity, and Morality

2019 ◽  
Vol 2 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Sunday Adeniyi Fasoro
Keyword(s):  
Political Theory ◽  
The Other ◽  
Moral Principles ◽  
A Value ◽  
The Earth ◽  
Other Hand ◽  
Common Ownership ◽  
Vulnerable People ◽  
The Common ◽  
The One

AbstractThe trend toward the concept of humanity in political theory has arisen largely as a reaction against the mistreatment of vulnerable people such as immigrants. The issue of immigrants’ vulnerability has led political thinkers to ponder on how to apply the principle of humanity to the question of the treatment of immigrants. I would like to address this matter by examining two questions: what is humanity, is it a value property, or a virtue? Does it really matter if the means by which an immigrant immigrates is demeaning to his own humanity as a person? The most common or intuitive reply to these questions would probably be: ‘humanity’ is simply a value-bestowing property, so regardless of immigrants’ actions they are owed respectful treatment. The aim of this paper is to emphasise instead that ‘humanity’ should be conceived as a virtue of actual commitment to act on moral principles. I explore three different meanings of humanity. First, I discuss ‘humanity’ as the common ownership of the earth. Second, I discuss ‘humanity’ as a value property. Third, I discuss humanity as a virtue of acting, on the one hand, with humanity, and on the other hand, on moral principles.

TECHNIQUES OF SEISMIC RECORDING

Geophysics ◽  
1964 ◽  
Vol 29 (6) ◽  
pp. 1031-1045
Author(s):  
Antonio C. Limón
Keyword(s):  
The Other ◽  
The Earth ◽  
Other Hand ◽  
Seismic Recording ◽  
The One

In order to obtain the best possible seismic field record, it is indispensible on the one hand to know the response of the earth to the explosion, and on the other hand to operate the seismograph equipment with suitable settings.

I.—The Physiographic Significance of Laterite in Western Australia

1918 ◽  
Vol 5 (9) ◽  
pp. 385-393 ◽  
Author(s):  
W. G. Woolnough
Keyword(s):  
Western Australia ◽  
The Other ◽  
Rock Weathering ◽  
The Earth ◽  
The One ◽  
Soluble Material

During the last six or seven years a series of valuable papers bearing on the origin of laterite has appeared in the Geological Magazine. The conclusions arrived at have been somewhat diverse and contradictory. Dr. Fermor, on the one hand, regarded the laterites of India as residual in character, and believed that they represented the insoluble residues left in the process of rock weathering after the soluble constituents had been removed in solution. Mr. Simpson, at the other extreme, suggested that they represented the soluble material, leached out of the subjacent rocks during weathering under peculiar conditions, and deposited as a chemically-formed rock by precipitation at the surface of the earth.

scholarly journals XII.—On Dust, Fogs, and Clouds

1881 ◽  
Vol 30 (1) ◽  
pp. 337-368 ◽  
Author(s):  
John Aitken
Keyword(s):  
The Other ◽  
Close Connection ◽  
Fair Weather ◽  
Human Interest ◽  
The North ◽  
The Earth ◽  
Regular Succession ◽  
The Subject ◽  
Successive Season ◽  
The One

Water is perhaps the most abundant and most universally distributed form of matter on the earth. It has to perform more varied functions and more important duties than any other kind of matter with which we are acquainted. From its close connection with all forms of life, it has been the subject of deepest interest in all ages. It is constantly changing from one of its states to another. At one time it is solid, now liquid, and then gaseous. These changes take place in regular succession, with every return of day and night, and every successive season; and these changes are constantly repeating themselves with every returning cycle. Of these changes, the one which perhaps has the greatest interest for us, and which has for long ages been the subject of special observation, is the change of water from its vaporous state, to its condensation into clouds, and descent as rain. Ever since man first “observed the winds “and “regarded the clouds,” and discovered that “fair weather cometh out of the north,” this has been the subject of intensest human interest, and at present forms one of the most important parts of the science of meteorology, a science in which perhaps more observations have been made and recorded than in all the other sciences together.

scholarly journals Eco-utopia or eco-catastrophe? Re-imagining California as an ecological utopia

Elem Sci Anth ◽  
2018 ◽  
Vol 6 ◽  
Author(s):  
Ronnie D. Lipschutz
Keyword(s):  
Climate Change ◽  
Cold War ◽  
Good Deal ◽  
The Other ◽  
Nuclear Threat ◽  
The Earth ◽  
Neal Stephenson ◽  
The One ◽  
The Cold War ◽  
Trump Administration

In this article, I explore four California-based eco-utopias: The Earth Abides (George Stewart, 1949), Ecotopia (Ernest Callenbach, 1975), Pacific Edge (Kim Stanley Robinson, 1990), and Snow Crash (Neal Stephenson, 1992). All four novels were written during, and deeply informed by, the Cold War (Although published in 1992, Snow Crash was clearly written toward the end of the Cold War and in the shadow of Soviet implosion), against a backdrop of imminent nuclear holocaust and a doubtful future. Since then, climate change has replaced the nuclear threat as a looming existential dilemma, on which a good deal of writing about the future is focused. Almost 70 years after the appearance of The Earth Abides, and 40 years after the publication of Ecotopia, eco-utopian imaginaries now seem both poignant yet more necessary than ever, given the tension between the anti-environmental proclivities of the Trump Administration, on the one hand, and the tendency of climate change to suck all of the air out of the room, on the other. And with drought, fire, flood, wind and climate change so much in the news, it is increasingly difficult to imagine eco-utopias of any sort; certainly they are not part of the contemporary zeitgeist—except in the minds of architects, bees and futurists, perhaps. But does this mean there is no point in thinking about them, or seeking insights that might make our future more sustainable? This article represents an attempt to revive eco-utopian visions and learn from them.

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