Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids.  They were first identified by Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and oceans of planets owing to the rotation of planet. 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. Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean.
Atmospheric Rossby waves result from the conservation of potential vorticity and are influenced by the Coriolis force and pressure gradient. The rotation causes fluids to turn to the right as they move in the northern hemisphere and to the left in the southern hemisphere. For example, a fluid that moves from the equator toward the north pole will deviate toward the east; a fluid moving toward the equator from the north will deviate toward the west. These deviations are caused by the Coriolis force and conservation of potential vorticity which leads to changes of relative vorticity. This is analogous to conservation of angular momentum in mechanics. In planetary atmospheres, including Earth, Rossby waves are due to the variation in the Coriolis effect with latitude. Carl-Gustaf Arvid Rossby first identified such waves in the Earth's atmosphere in 1939 and went on to explain their motion.
One can identify a terrestrial Rossby wave as its phase velocity, marked by its wave crest, always has a westward component. However, the collected set of Rossby waves may appear to move in either direction with what is known as its group velocity. In general, shorter waves have an eastward group velocity and long waves a westward group velocity.
The terms "barotropic" and "baroclinic" are used to distinguish the vertical structure of Rossby waves. Barotropic Rossby waves do not vary in the vertical, and have the fastest propagation speeds. The baroclinic wave modes, on the other hand, do vary in the vertical. They are also slower, with speeds of only a few centimeters per second or less.
Most investigations of Rossby waves have been done on those in Earth's atmosphere. Rossby waves in the Earth's atmosphere are easy to observe as (usually 4-6) large-scale meanders of the jet stream. When these deviations become very pronounced, masses of cold or warm air detach, and become low-strength cyclones and anticyclones, respectively, and are responsible for day-to-day weather patterns at mid-latitudes. The action of Rossby waves partially explains why eastern continental edges in the Northern Hemisphere, such as the Northeast United States and Eastern Canada, are colder than Western Europe at the same latitudes.
Deep convection (heat transfer) to the troposphere is enhanced over very warm sea surfaces in the tropics, such as during El Niño events. This tropical forcing generates atmospheric Rossby waves that have a poleward and eastward migration.
Poleward-propagating Rossby waves explain many of the observed statistical connections between low- and high-latitude climates. One such phenomenon is sudden stratospheric warming. Poleward-propagating Rossby waves are an important and unambiguous part of the variability in the Northern Hemisphere, as expressed in the Pacific North America pattern. Similar mechanisms apply in the Southern Hemisphere and partly explain the strong variability in the Amundsen Sea region of Antarctica. In 2011, a Nature Geoscience study using general circulation models linked Pacific Rossby waves generated by increasing central tropical Pacific temperatures to warming of the Amundsen Sea region, leading to winter and spring continental warming of Ellsworth Land and Marie Byrd Land in West Antarctica via an increase in advection.
Oceanic Rossby waves are large-scale waves within an ocean basin. They have a low amplitude, on the order of centimetres (at the surface) to metres (at the thermocline), compared to a very long wavelength, on the order of hundreds of kilometres of atmospheric Rossby waves. They may take months to cross an ocean basin. They gain momentum from wind stress at the ocean surface layer and are thought to communicate climatic changes due to variability in forcing, due to both the wind and buoyancy. Both barotropic and baroclinic waves cause variations of the sea surface height, although the length of the waves made them difficult to detect until the advent of satellite altimetry. Satellite observations have confirmed the existence of oceanic Rossby waves.
Baroclinic waves also generate significant displacements of the oceanic thermocline, often of tens of meters. Satellite observations have revealed the stately progression of Rossby waves across all the ocean basins, particularly at low- and mid-latitudes. These waves can take months or even years to cross a basin like the Pacific.
It has been proposed that a number of regional weather extremes in the Northern Hemisphere associated with blocked atmospheric circulation patterns may have been caused by quasiresonant amplification of Rossby waves. Examples include the 2013 European floods, the 2012 China floods, the 2010 Russian heat wave, the 2010 Pakistan floods and the 2003 European heat wave. Even taking global warming into account, the 2003 heat wave would have been highly unlikely without such a mechanism.
Normally freely travelling synoptic-scale Rossby waves and quasistationary planetary-scale Rossby waves exist in the mid-latitudes with only weak interactions. The hypothesis, proposed by Vladimir Petoukhov, Stefan Rahmstorf, Stefan Petri, and Hans Joachim Schellnhuber, is that under some circumstances these waves interact to produce the static pattern. For this to happen, they suggest, the zonal (east-west) wave number of both types of wave should be in the range 6–8, the synoptic waves should be arrested within the troposphere (so that energy does not escape to the stratosphere) and mid-latitude waveguides should trap the quasistationary components of the synoptic waves. In this case the planetary-scale waves may respond unusually strongly to orography and thermal sources and sinks because of "quasiresonance".
To start with, a zonal mean flow, U, can be considered to be perturbed where U is constant in time and space. Let be the total horizontal wind field, where u and v are the components of the wind in the x- and y- directions, respectively. The total wind field can be written as a mean flow, U, with a small superimposed perturbation, u′ and v′.
The perturbation is assumed to be much smaller than the mean zonal flow.
Relative vorticity η, u and v can be written in terms of the stream function (assuming non-divergent flow, for which the stream function completely describes the flow):
Considering a parcel of air that has no relative vorticity before perturbation (uniform U has no vorticity) but with planetary vorticity f as a function of the latitude, perturbation will lead to a slight change of latitude, so the perturbed relative vorticity must change in order to conserve potential vorticity. Also the above approximation U >> u' ensures that the perturbation flow does not advect relative vorticity.
with . Plug in the definition of stream function to obtain:
This yields the dispersion relation:
where c is the phase speed, cg is the group speed, U is the mean westerly flow, is the Rossby parameter, k is the zonal wavenumber, and ℓ is the meridional wavenumber. It is noted that the zonal phase speed of Rossby waves is always westward (traveling east to west) relative to mean flow U, but the zonal group speed of Rossby waves can be eastward or westward depending on wavenumber.
The Rossby parameter is defined:
If , there will be no Rossby Waves; Rossby Waves owe their origin to the gradient of the tangential speed of the planetary rotation (planetary vorticity). A "cylinder" planet has no Rossby Waves. It also means that at the equator of any rotating, sphere-like planet, including Earth, one will still have Rossby Waves, despite the fact that , because . (Equatorial Rossby wave).
Carl-Gustaf Arvid Rossby (Swedish pronunciation: [kɑːɭ ²ɡɵsːtav ¹arːvɪd ¹rɔsːbʏ] 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.Equatorial Rossby wave
Equatorial Rossby waves, often called planetary waves, are very long, low frequency waves found near the equator and are derived using the equatorial beta plane approximation.Equatorial wave
Equatorial waves are oceanic and atmospheric waves trapped close to the equator, meaning that they decay rapidly away from the equator, but can propagate in the longitudinal and vertical directions. Wave trapping is the result of the Earth's rotation and its spherical shape which combine to cause the magnitude of the Coriolis force to increase rapidly away from the equator. Equatorial waves are present in both the tropical atmosphere and ocean and play an important role in the evolution of many climate phenomena such as El Niño. Many physical processes may excite equatorial waves including, in the case of the atmosphere, diabatic heat release associated with cloud formation, and in the case of the ocean, anomalous changes in the strength or direction of the trade winds.Equatorial waves may be separated into a series of subclasses depending on their fundamental dynamics (which also influences their typical periods and speeds and directions of propagation). At shortest periods are the equatorial gravity waves while the longest periods are associated with the equatorial Rossby waves. In addition to these two extreme subclasses, there are two special subclasses of equatorial waves known as the mixed Rossby-gravity wave (also known as the Yanai wave) and the equatorial Kelvin wave. The latter two share the characteristics that they can have any period and also that they may carry energy only in an eastward (never westward) direction.
The remainder of this article discusses the relationship between the period of these waves, their wavelength in the zonal (east-west) direction and their speeds for a simplified ocean.Eyewall replacement cycle
Eyewall replacement cycles, also called concentric eyewall cycles, naturally occur in intense tropical cyclones, generally with winds greater than 185 km/h (115 mph), or major hurricanes (Category 3 or above). When tropical cyclones reach this intensity, and the eyewall contracts or is already sufficiently small, some of the outer rainbands may strengthen and organize into a ring of thunderstorms—an outer eyewall—that slowly moves inward and robs the inner eyewall of its needed moisture and angular momentum. Since the strongest winds are in a cyclone's eyewall, the tropical cyclone usually weakens during this phase, as the inner wall is "choked" by the outer wall. Eventually the outer eyewall replaces the inner one completely, and the storm may re-intensify.The discovery of this process was partially responsible for the end of the U.S. government's hurricane modification experiment Project Stormfury. This project set out to seed clouds outside the eyewall, apparently causing a new eyewall to form and weakening the storm. When it was discovered that this was a natural process due to hurricane dynamics, the project was quickly abandoned.Almost every intense hurricane undergoes at least one of these cycles during its existence. Recent studies have shown that nearly half of all tropical cyclones, and nearly all cyclones with sustained winds over 204 kilometres per hour (127 mph; 110 kn), undergo eyewall replacement cycles. Hurricane Allen in 1980 went through repeated eyewall replacement cycles, fluctuating between Category 5 and Category 4 status on the Saffir-Simpson Hurricane Scale several times. Typhoon June (1975) was the first reported case of triple eyewalls, and Hurricane Juliette (2001) was a documented case of such.Geophysical fluid dynamics
Geophysical fluid dynamics, in its broadest meaning, refers to the fluid dynamics of naturally occurring flows, such as lava flows, oceans, and planetary atmospheres, on Earth and other planets.Two physical features that are common to many of the phenomena studied in geophysical fluid dynamics are rotation of the fluid due to the planetary rotation and stratification (layering). The applications of geophysical fluid dynamics do not generally include the circulation of the mantle, which is the subject of geodynamics, or fluid phenomena in the magnetosphere.Index of wave articles
This is a list of Wave topics.Indian Monsoon Current
The Indian Monsoon Current refers to the seasonally varying ocean current regime found in the tropical regions of the northern Indian Ocean. During winter, the flow of the upper ocean is directed westward from near the Indonesian Archipelago to the Arabian Sea. During the summer, the direction reverses, with eastward flow extending from Somalia into the Bay of Bengal. These variations are due to changes in the wind stress associated with the Indian monsoon. The seasonally reversing open ocean currents that pass south of India are referred to as the Winter Monsoon Current and the Summer Monsoon Current (alternately, the Northeast Monsoon Current and the Southwest Monsoon Current). The Somali Current, which is strongly linked to the Indian monsoon, is also discussed in this article.Kelvin wave
A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the group speed of the wave energy for all frequencies. This means that it retains its shape as it moves in the alongshore direction over time.
A Kelvin wave (fluid dynamics) is also a long scale perturbation mode of a vortex in superfluid dynamics; in terms of the meteorological or oceanographical derivation, one may assume that the meridional velocity component vanishes (i.e. there is no flow in the north–south direction, thus making the momentum and continuity equations much simpler). This wave is named after the discoverer, Lord Kelvin (1879).List of waves named after people
This is a list of waves named after people (eponymous waves).Long period tide
Long-Period tides are gravitational tides, typically with amplitudes of a few centimeters or less and periods longer than one day, generated by changes in the Earth's orientation relative to the Sun, Moon, and Jupiter. The distance between a reference point on the surface of the Earth relative to these objects can be expressed as an infinite combination of periods and, as the distance changes, so does the tidal forcing. An analysis of the changing distance by Pierre-Simon de Laplace in the 18th century shows that these periods at which gravity varies cluster into three species, the semi-diurnal and diurnal tide constituents which have periods of a day or less, and the long period tidal constituents (see also tide). Long period tidal constituents with relatively strong forcing include the lunar fortnightly (Mf) and monthly (Ms) as well as the solar semiannual (Ssa) and annual (Sa) constituents. In addition to having periods longer than a day-long period tidal forcing is distinguished from that of the first and second species by being zonally symmetric. The long period tides are also distinguished by the way in which the oceans respond. In contrast to the first and second species, the long period tidal forcings occur sufficiently slowly that they do not excite surface gravity waves. This property of exciting surface gravity waves is responsible for the high amplitude semi-diurnal tides in the Bay of Fundy, for example. In contrast, the ocean responds to long period tidal forcing with a combination of an equilibrium tidal response along with a possible excitation of barotropic Rossby wave normal modesLorenz Magaard
Lorenz Magaard (born May 21, 1934 in Wallsbüll, Germany) is a German-American mathematician and oceanographer. He made essential contributions to the theory of ocean waves and earned particular credit for organizing education and research.Low-pressure area
A low-pressure area, low, depression or cyclone is a region on the topographic map where the atmospheric pressure is lower than that of surrounding locations. Low-pressure systems form under areas of wind divergence that occur in the upper levels of the troposphere. The formation process of a low-pressure area is known as cyclogenesis. Within the field of meteorology, atmospheric divergence aloft occurs in two areas. The first area is on the east side of upper troughs, which form half of a Rossby wave within the Westerlies (a trough with large wavelength that extends through the troposphere). A second area of wind divergence aloft occurs ahead of embedded shortwave troughs, which are of smaller wavelength. Diverging winds aloft ahead of these troughs cause atmospheric lift within the troposphere below, which lowers surface pressures as upward motion partially counteracts the force of gravity.
Thermal lows form due to localized heating caused by greater sunshine over deserts and other land masses. Since localized areas of warm air are less dense than their surroundings, this warmer air rises, which lowers atmospheric pressure near that portion of the Earth's surface. Large-scale thermal lows over continents help drive monsoon circulations. Low-pressure areas can also form due to organized thunderstorm activity over warm water. When this occurs over the tropics in concert with the Intertropical Convergence Zone, it is known as a monsoon trough. Monsoon troughs reach their northerly extent in August and their southerly extent in February. When a convective low acquires a well-hot circulation in the tropics it is termed a tropical cyclone. Tropical cyclones can form during any month of the year globally, but can occur in either the northern or southern hemisphere during December.
Atmospheric lift will also generally produce cloud cover through adiabatic cooling once the air becomes saturated as it rises, although the low-pressure area typically brings cloudy skies, which act to minimize diurnal temperature extremes. Since clouds reflect sunlight, incoming shortwave solar radiation decreases, which causes lower temperatures during the day. At night the absorptive effect of clouds on outgoing longwave radiation, such as heat energy from the surface, allows for warmer diurnal low temperatures in all seasons. The stronger the area of low pressure, the stronger the winds experienced in its vicinity. Globally, low-pressure systems are most frequently located over the Tibetan Plateau and in the lee of the Rocky mountains. In Europe (particularly in the British Isles and Netherlands), recurring low-pressure weather systems are typically known as "depressions".Rossby-gravity waves
Rossby-gravity waves are equatorially trapped waves (much like Kelvin waves), meaning that they rapidly decay as their distance increases away from the equator (so long as the Brunt–Vaisala frequency does not remain constant). These waves have the same trapping scale as Kelvin waves, more commonly known as the equatorial Rossby deformation radius. They always carry energy eastward, but their 'crests' and 'troughs' may propagate westward if their periods are long enough.Rossby (disambiguation)
Carl-Gustaf Rossby (1898–1957) was a Swedish-born American meteorologist.
Rossby may also refer to:
Rossby (crater), impact crater on Mars
Rossby wave, a natural phenomenon in the atmosphere and oceans of planets
Rossby number, a dimensionless number used in describing fluid flow. The Rossby number is the ratio of inertial
Rossby parameter, used in geophysics and meteorology
Rossby whistle, oscillation of sea-level and bottom pressure in the Caribbean SeaRossby wave instability in astrophysical discs
Rossby Wave Instability (RWI) is a concept related to astrophysical discs. In non-self-gravitating discs, for example around newly forming stars, the instability can be triggered by an axisymmetric bump, at some radius , in the disc surface mass-density. It gives rise to exponentially growing non-axisymmetric perturbation [, ] in the vicinity of 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.
The theory of the Rossby wave instability (RWI) in accretion discs was developed by Lovelace et al. and Li et al. for thin Keplerian discs with negligible self-gravity and earlier by Lovelace and Hohlfeld for thin disc galaxies where the self-gravity may or may not be important and where the rotation is in general non-Keplerian. In the first case the instability can occur if there is an axisymmetric bump (as a function of radius) in the inverse potential vorticity
at some radius , where is the surface mass density of the disc, is the flow velocity of the disc, is the angular velocity of the flow (with the mass of the central star), is the specific entropy of the gas, and is the specific heat ratio. The approximations involve the neglect of the relatively small radial pressure force. Note that is related to the inverse of the vortensity which is defined as . A sketch of a bump in is shown in Figure 1.
Rossby waves, named after Carl-Gustaf Arvid Rossby are important in planetary atmospheres and oceans and are also known as it 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 the long-lived ( yr) Great Red Spot on Jupiter which is an anticyclonic vortex. The Rossby waves have the notable property of having the phase velocity opposite to the direction of motion of the atmosphere or disc in the comoving frame of the fluid.Rossby whistle
The Rossby whistle is the oscillation of sea-level and bottom pressure in the Caribbean Sea with the period of 120 days and influenced by propagating westward oceanic Rossby wave.
It is observed that a baroclinic Rossby wave propagating westward across the Caribbean Sea, oscillating with a period of 120 days, is rapidly returned to the east along the southern boundary as coastal shelf waves. The porous boundary of the Caribbean Sea results in this oscillation influencing a mass exchange with the wider ocean, leading to an almost uniform bottom pressure variability over the Grenada, Venezuela, and Colombia basins. These observations are based on satellite observation of the sea-level, monthly means of basin-averaged ocean bottom pressure using GRACE data, tide gauge measurements, and data from a bottom pressure recorder. The oscillation was first found in a numerical modelling simulation, from which is shown one cycle of the least squares fit of (left) sea level and (right) bottom pressure on basin averaged bottom pressure in the Caribbean Sea.Synoptic scale meteorology
The synoptic scale in meteorology (also known as large scale or cyclonic scale) is a horizontal length scale of the order of 1000 kilometers (about 620 miles) or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e.g., extratropical cyclones). Most high and low-pressure areas seen on weather maps such as surface weather analyses are synoptic-scale systems, driven by the location of Rossby waves in their respective hemisphere. Low-pressure areas and their related frontal zones occur on the leading edge of a trough within the Rossby wave pattern, while high-pressure areas form on the back edge of the trough. Most precipitation areas occur near frontal zones. The word synoptic is derived from the Greek word συνοπτικός (synoptikos), meaning seen together.
The Navier–Stokes equations applied to atmospheric motion can be simplified by scale analysis in the synoptic scale. It can be shown that the main terms in horizontal equations are Coriolis force and pressure gradient terms; therefore, one can use geostrophic approximation. In vertical coordinates, the momentum equation simplifies to the hydrostatic equilibrium equation.Trough (meteorology)
A trough is an elongated (extended) region of relatively low atmospheric pressure, often associated with fronts. Troughs may be at the surface, or aloft, or both under various conditions. Most troughs bring clouds, showers, and a wind shift, particularly following the passage of the trough. This results from convergence or "squeezing" which forces lifting of moist air behind the trough line.
Unlike fronts, there is not a universal symbol for a trough on a weather chart. The weather charts in some countries or regions mark troughs by a line. In the United States, a trough may be marked as a dashed line or bold line. In the UK, Hong Kong and Fiji, it is represented by a bold line extended from a low pressure center or between two low pressure centers; in Macau and Australia, it is a dashed line. If they are not marked, troughs may still be identified as an extension of isobars away from a low pressure center.Wave base
The wave base, in physical oceanography, is the maximum depth at which a water wave's passage causes significant water motion. For water depths deeper than the wave base, bottom sediments and the seafloor are no longer stirred by the wave motion above.