Rossby Wave Instability
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Rossby Wave Instability
Rossby Wave Instability (RWI) is a concept related to astrophysical accretion discs. In non-self-gravitating discs, for example around newly forming stars, the instability can be triggered by an axisymmetric bump, at some radius r_0, in the disc surface mass-density. It gives rise to exponentially growing non-axisymmetric perturbation in the vicinity of r_0 consisting of anticyclonic vortices. These vortices are regions of high pressure and consequently act to trap dust particles which in turn can facilitate planetesimal growth in proto-planetary discs. The Rossby vortices in the discs around stars and black holes may cause the observed quasi-periodic modulations of the disc's thermal emission. Rossby waves, named after Carl-Gustaf Arvid Rossby, are important in planetary atmospheres and oceans and are also known as planetary waves. These waves have a significant role in the transport of heat from equatorial to polar regions of the Earth. They may have a role in the formation of ...
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Rossby Wave Instability In A Keplerian Disk
Carl-Gustaf Arvid Rossby ( 28 December 1898 – 19 August 1957) was a Sweden, Swedish-born American meteorologist who first explained the large-scale motions of the Earth's atmosphere, atmosphere in terms of fluid mechanics. He identified and characterized both the jet stream and the long waves in the westerlies that were later named Rossby waves. Biography Carl-Gustaf Rossby was born in Stockholm, Sweden. He was the first of five children born to Arvid and Alma Charlotta (Marelius) Rossby. He attended Stockholm University, where he developed his first interest in mathematical physics. Rossby came into meteorology and oceanography while studying geophysics under Vilhelm Bjerknes at the Geophysical Institute, University of Bergen in Bergen, Norway, during 1919, where Bjerknes' group was developing the groundbreaking concepts that became known as the Bergen School of Meteorology, including theory of the polar front. He also studied at the University of Leipzig and at the Linde ...
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Accretion Disc
An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is most frequently a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other forces induce instabilities causing orbiting material in the disk to spiral inward toward the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology. Manifestations Accretion disks are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary disks, and gamma ray bursts all involve accretion disks. These disks ...
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Anticyclonic
A high-pressure area, high, or anticyclone, is an area near the surface of a planet where the atmospheric pressure is greater than the pressure in the surrounding regions. Highs are middle-scale meteorological features that result from interplays between the relatively larger-scale dynamics of an entire planet's atmospheric circulation. The strongest high-pressure areas result from masses of cold air which spread out from polar regions into cool neighboring regions. These highs weaken once they extend out over warmer bodies of water. Weaker—but more frequently occurring—are high-pressure areas caused by atmospheric subsidence: Air becomes cool enough to precipitate out its water vapor, and large masses of cooler, drier air descend from above. Within high-pressure areas, winds flow from where the pressure is highest, at the center of the area, towards the periphery where the pressure is lower. However, the direction is not straight from the center outwards, but curved du ...
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Black Holes
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. A black hole has a great effect on the fate and circumstances of an object crossing it, but has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John ...
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Rossby Wave
Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby in the Earth's atmosphere in 1939. They are observed in the atmospheres and oceans of Earth and other planets, owing to the rotation of Earth or of the planet involved. Atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather. These waves are associated with pressure systems and the jet stream (especially around the polar vortices). Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean. Rossby wave types Atmospheric waves Atmospheric Rossby waves result from the conservation of potential vorticity and are influenced by the Coriolis force and pressure gradient. The image on the left sketches fundamental principles of the wave, e.g., its restorin ...
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Carl-Gustaf Arvid Rossby
Carl-Gustaf Arvid Rossby ( 28 December 1898 – 19 August 1957) was a Swedish-born American meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics. He identified and characterized both the jet stream and the long waves in the westerlies that were later named Rossby waves. Biography Carl-Gustaf Rossby was born in Stockholm, Sweden. He was the first of five children born to Arvid and Alma Charlotta (Marelius) Rossby. He attended Stockholm University, where he developed his first interest in mathematical physics. Rossby came into meteorology and oceanography while studying geophysics under Vilhelm Bjerknes at the Geophysical Institute, University of Bergen in Bergen, Norway, during 1919, where Bjerknes' group was developing the groundbreaking concepts that became known as the Bergen School of Meteorology, including theory of the polar front. He also studied at the University of Leipzig and at the Lindenberg Observatory (''Meteo ...
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Planetary Waves
Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby in the Earth's atmosphere in 1939. They are observed in the atmospheres and oceans of Earth and other planets, owing to the rotation of Earth or of the planet involved. Atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather. These waves are associated with pressure systems and the jet stream (especially around the polar vortices). Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean. Rossby wave types Atmospheric waves Atmospheric Rossby waves result from the conservation of potential vorticity and are influenced by the Coriolis force and pressure gradient. The image on the left sketches fundamental principles of the wave, e.g., its restoring f ...
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Great Red Spot
The Great Red Spot is a persistent high-pressure area, high-pressure region in the atmosphere of Jupiter, producing an anticyclonic storm that is the largest in the Solar System. It is the most recognizable feature on Jupiter, owing to its red-orange color whose origin is still unknown. Located 22 Degree (angle), degrees south of Jupiter's equator, it produces wind-speeds up to . It was first observed in September 1831, with 60 recorded observations between then and 1878, when continuous observations began. A similar spot was observed from 1665 to 1713; if this is the same storm, it has existed for at least years, but a study from 2024 suggests this is not the case. Observation history First observations The Great Red Spot may have existed before 1665, but it could be that the present spot was first seen only in 1830, and was well studied only after a prominent appearance in 1879. The storm that was seen in the 17th century may have been different from the storm that exists ...
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Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined and slightly less than one-thousandth the mass of the Sun. Its diameter is 11 times that of Earth and a tenth that of the Sun. Jupiter orbits the Sun at a distance of , with an orbital period of . It is the List of brightest natural objects in the sky, third-brightest natural object in the Earth's night sky, after the Moon and Venus, and has been observed since prehistoric times. Its name derives from that of Jupiter (god), Jupiter, the chief deity of ancient Roman religion. Jupiter was the first of the Sun's planets to form, and its inward migration during the primordial phase of the Solar System affected much of the formation history of the other planets. Jupiter's atmosphere consists of 76% hydrogen and 24% helium by mass, with a denser ...
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Phase Velocity
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength (lambda) and time period as :v_\mathrm = \frac. Equivalently, in terms of the wave's angular frequency , which specifies angular change per unit of time, and wavenumber (or angular wave number) , which represent the angular change per unit of space, :v_\mathrm = \frac. To gain some basic intuition for this equation, we consider a propagating (cosine) wave . We want to see how fast a particular phase of the wave travels. For example, we can choose , the phase of the first crest. This implies , and so . Formally, we let the phase and see immediately that and . So, it immediately follows that : \frac = -\frac \frac = \frac ...
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Keplerian Disc
Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books '' Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae'', influencing among others Isaac Newton, providing one of the foundations for his theory of universal gravitation. The variety and impact of his work made Kepler one of the founders and fathers of modern astronomy, the scientific method, natural and modern science. He has been described as the "father of science fiction" for his novel '' Somnium''. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successor ...
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