Gravity wave

In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the ocean, which gives rise to wind waves.

A gravity wave results when fluid is displaced from a position of equilibrium. The restoration of the fluid to equilibrium will produce a movement of the fluid back and forth, called a wave orbit.[1] Gravity waves on an air–sea interface of the ocean are called surface gravity waves or surface waves, while gravity waves that are within the body of the water (such as between parts of different densities) are called internal waves. Wind-generated waves on the water surface are examples of gravity waves, as are tsunamis and ocean tides.

Wind-generated gravity waves on the free surface of the Earth's ponds, lakes, seas and oceans have a period of between 0.3 and 30 seconds (3Hz to 30mHz). Shorter waves are also affected by surface tension and are called gravity–capillary waves and (if hardly influenced by gravity) capillary waves. Alternatively, so-called infragravity waves, which are due to subharmonic nonlinear wave interaction with the wind waves, have periods longer than the accompanying wind-generated waves.[2]

Waves
Surface gravity wave, breaking on an ocean beach.
Wave clouds
Wave clouds over Theresa, Wisconsin, United States.
Satellite view of the Shark Bay (cropped)
Atmospheric gravity waves seen from space

Atmosphere dynamics on Earth

In the Earth's atmosphere, gravity waves are a mechanism that produce the transfer of momentum from the troposphere to the stratosphere and mesosphere. Gravity waves are generated in the troposphere by frontal systems or by airflow over mountains. At first, waves propagate through the atmosphere without appreciable change in mean velocity. But as the waves reach more rarefied (thin) air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow. This transfer of momentum is responsible for the forcing of the many large-scale dynamical features of the atmosphere. For example, this momentum transfer is partly responsible for the driving of the Quasi-Biennial Oscillation, and in the mesosphere, it is thought to be the major driving force of the Semi-Annual Oscillation. Thus, this process plays a key role in the dynamics of the middle atmosphere.[3]

The effect of gravity waves in clouds can look like altostratus undulatus clouds, and are sometimes confused with them, but the formation mechanism is different.

Quantitative description

Deep water

The phase velocity of a linear gravity wave with wavenumber is given by the formula

where g is the acceleration due to gravity. When surface tension is important, this is modified to

where σ is the surface tension coefficient and ρ is the density.

Since is the phase speed in terms of the angular frequency and the wavenumber, the gravity wave angular frequency can be expressed as

The group velocity of a wave (that is, the speed at which a wave packet travels) is given by

and thus for a gravity wave,

The group velocity is one half the phase velocity. A wave in which the group and phase velocities differ is called dispersive.

Shallow water

Gravity waves traveling in shallow water (where the depth is much less than the wavelength), are nondispersive: the phase and group velocities are identical and independent of wavelength and frequency. When the water depth is h,

The generation of ocean waves by wind

Wind waves, as their name suggests, are generated by wind transferring energy from the atmosphere to the ocean's surface, and capillary-gravity waves play an essential role in this effect. There are two distinct mechanisms involved, called after their proponents, Phillips and Miles.

In the work of Phillips,[4] the ocean surface is imagined to be initially flat (glassy), and a turbulent wind blows over the surface. When a flow is turbulent, one observes a randomly fluctuating velocity field superimposed on a mean flow (contrast with a laminar flow, in which the fluid motion is ordered and smooth). The fluctuating velocity field gives rise to fluctuating stresses (both tangential and normal) that act on the air-water interface. The normal stress, or fluctuating pressure acts as a forcing term (much like pushing a swing introduces a forcing term). If the frequency and wavenumber of this forcing term match a mode of vibration of the capillary-gravity wave (as derived above), then there is a resonance, and the wave grows in amplitude. As with other resonance effects, the amplitude of this wave grows linearly with time.

The air-water interface is now endowed with a surface roughness due to the capillary-gravity waves, and a second phase of wave growth takes place. A wave established on the surface either spontaneously as described above, or in laboratory conditions, interacts with the turbulent mean flow in a manner described by Miles.[5] This is the so-called critical-layer mechanism. A critical layer forms at a height where the wave speed c equals the mean turbulent flow U. As the flow is turbulent, its mean profile is logarithmic, and its second derivative is thus negative. This is precisely the condition for the mean flow to impart its energy to the interface through the critical layer. This supply of energy to the interface is destabilizing and causes the amplitude of the wave on the interface to grow in time. As in other examples of linear instability, the growth rate of the disturbance in this phase is exponential in time.

This Miles–Phillips Mechanism process can continue until an equilibrium is reached, or until the wind stops transferring energy to the waves (i.e., blowing them along) or when they run out of ocean distance, also known as fetch length.

See also

Notes

  1. ^ Lighthill, James (2001), Waves in fluids, Cambridge University Press, p. 205, ISBN 9780521010450
  2. ^ Bromirski, Peter D.; Sergienko, Olga V.; MacAyeal, Douglas R. (2010), "Transoceanic infragravity waves impacting Antarctic ice shelves", Geophysical Research Letters, 37 (L02502): n/a, Bibcode:2010GeoRL..37.2502B, doi:10.1029/2009GL041488.
  3. ^ Fritts, D.C.; Alexander, M.J. (2003), "Gravity wave dynamics and effects in the middle atmosphere", Reviews of Geophysics, 41 (1), Bibcode:2003RvGeo..41.1003F, CiteSeerX 10.1.1.470.3839, doi:10.1029/2001RG000106.
  4. ^ Phillips, O. M. (1957), "On the generation of waves by turbulent wind", J. Fluid Mech., 2 (5): 417–445, Bibcode:1957JFM.....2..417P, doi:10.1017/S0022112057000233
  5. ^ Miles, J. W. (1957), "On the generation of surface waves by shear flows", J. Fluid Mech., 3 (2): 185–204, Bibcode:1957JFM.....3..185M, doi:10.1017/S0022112057000567

References

  • Gill, A. E., "Gravity wave". Glossary of Meteorology. American Meteorological Society (15 December 2014).
  • Crawford, Frank S., Jr. (1968). Waves (Berkeley Physics Course, Vol. 3), (McGraw-Hill, 1968) ISBN 978-0070048607 Free online version

Further reading

External links

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Edge wave

In fluid dynamics, an edge wave is a surface gravity wave fixed by refraction against a rigid boundary, often a shoaling beach. Progressive edge waves travel along this boundary, varying sinusoidally along it and diminishing exponentially in the offshore direction.

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G 117-B15A

G117-B15A is a small, well-observed variable white dwarf star of the DAV, or ZZ Ceti, type in the constellation of Leo Minor.

G117-B15A was found to be variable in 1974 by Richer and Ulrych, and this was confirmed in 1976 by McGraw and Robinson. In 1984 it was demonstrated that the star's variability is due to nonradial gravity wave pulsations. As a consequence, its timescale for period change is directly proportional to its cooling timescale, allowing its cooling rate to be measured using astroseismological techniques. Its age is estimated at 400 million years. Its light curve has a dominant period of 215.2 seconds, which is estimated to increase by approximately one second each 14 million years. G117-B15A has been claimed to be the most stable optical clock ever found, much more stable than the ticks of an atomic clock. It is also the first pulsating white dwarf to have its main pulsation mode index identified.

Gamma Doradus

Gamma Doradus (Gamma Dor, γ Doradus, γ Dor) is the third-brightest star in the constellation of Dorado. It has an apparent visual magnitude of approximately 4.25 and is a variable star, the type star of the class of Gamma Doradus variables. These stars, like γ Doradus, are pulsating variables which vary in brightness by less than a tenth of a magnitude owing to nonradial gravity wave oscillations. The magnitude of γ Doradus itself has been observed to have two sinusoidal variations with periods of approximately 17.6 and 18.2 hours. There is also some additional unexplained, apparently random fluctuation.

Gravitational wave

Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light. They were proposed by Henri Poincaré in 1905 and subsequently predicted in 1916 by Albert Einstein on the basis of his general theory of relativity. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed) – showing one of the ways the methods of classical physics are unable to explain phenomena associated with relativity.

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In 1993, Russell A. Hulse and Joseph H. Taylor, Jr. received the Nobel Prize in Physics for the discovery and observation of the Hulse-Taylor binary pulsar, which offered the first indirect evidence of the existence of gravitational waves.On 11 February 2016, the LIGO and Virgo Scientific Collaboration announced they had made the first direct observation of gravitational waves. The observation was made five months earlier, on 14 September 2015, using the Advanced LIGO detectors. The gravitational waves originated from a pair of merging black holes. After the initial announcement the LIGO instruments detected two more confirmed, and one potential, gravitational wave events. In August 2017, the two LIGO instruments and the Virgo instrument observed a fourth gravitational wave from merging black holes, and a fifth gravitational wave from a binary neutron star merger. Several other gravitational wave detectors are planned or under construction.In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in the direct detection of gravitational waves.

HL Tau 76

HL Tau 76 is a variable white dwarf star of the DAV (or ZZ Ceti) type. It was observed by G. Haro and W. J. Luyten in 1961, and was the first variable white dwarf discovered when, in 1968, Arlo U. Landolt found that it varied in brightness with a period of approximately 749.5 seconds, or 12.5 minutes. Like other DAV white dwarfs, its variability arises from non-radial gravity wave pulsations within itself., § 7. Later observation and analysis has found HL Tau 76 to pulsate in over 40 independent vibrational modes, with periods between 380 seconds and 1390 seconds.

Internal wave

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance (as in the case of the thermocline in lakes and oceans or an atmospheric inversion), the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid.

Internal waves, also called internal gravity waves, go by many other names depending upon the fluid stratification, generation mechanism, amplitude, and influence of external forces. If propagating horizontally along an interface where the density rapidly decreases with height, they are specifically called interfacial (internal) waves. If the interfacial waves are large amplitude they are called internal solitary waves or internal solitons. If moving vertically through the atmosphere where substantial changes in air density influences their dynamics, they are called anelastic (internal) waves. If generated by flow over topography, they are called Lee waves or mountain waves. If the mountain waves break aloft, they can result in strong warm winds at the ground known as Chinook winds (in North America) or Foehn winds (in Europe). If generated in the ocean by tidal flow over submarine ridges or the continental shelf, they are called internal tides. If they evolve slowly compared to the Earth's rotational frequency so that their dynamics are influenced by the Coriolis effect, they are called inertia gravity waves or, simply, inertial waves. Internal waves are usually distinguished from Rossby waves, which are influenced by the change of Coriolis frequency with latitude.

Magnetogravity wave

A magnetogravity wave is a type of plasma wave. A magnetogravity wave is an acoustic gravity wave which is associated with fluctuations in the background magnetic field. In this context, gravity wave refers to a classical fluid wave, and is completely unrelated to the relativistic gravitational wave.

Mesopause

The mesopause is the point of minimum temperature at the boundary between the mesosphere and the thermosphere atmospheric regions. Due to the lack of solar heating and very strong radiative cooling from carbon dioxide, the mesosphere is the coldest region on Earth with temperatures as low as -100 °C (-148 °F or 173 K). The altitude of the mesopause for many years was assumed to be at around 85 km (53 mi.), but observations to higher altitudes and modeling studies in the last 10 years have shown that in fact the mesopause consists of two minima - one at about 85 km and a stronger minimum at about 100 km (62 mi).Another feature is that the summer mesopause is cooler than the winter (sometimes referred to as the mesopause anomaly). It is due to a summer-to-winter circulation giving rise to upwelling at the summer pole and downwelling at the winter pole. Air rising will expand and cool resulting in a cold summer mesopause and conversely downwelling air results in compression and associated increase in temperature at the winter mesopause. In the mesosphere the summer-to-winter circulation is due to gravity wave dissipation, which deposits momentum against the mean east-west flow, resulting in a small north-south circulation.In recent years the mesopause has also been the focus of studies on global climate change associated with increases in CO2. Unlike the troposphere, where greenhouse gases result in the atmosphere heating up, increased CO2 in the mesosphere acts to cool the atmosphere due to increased radiative emission. This results in a measurable effect - the mesopause should become cooler with increased CO2. Observations do show a decrease of temperature of the mesopause, though the magnitude of this decrease varies and is subject to further study. Modeling studies of this phenomenon have also been carried out.

PG 1159-035

PG 1159-035 is the prototypical PG 1159 star after which the class of PG 1159 stars was named. It was discovered in the Palomar-Green survey of ultraviolet-excess stellar objects and, like the other PG 1159 stars, is in transition between being the central star of a planetary nebula and being a white dwarf.The luminosity of PG 1159-035 was observed to vary in 1979, and it was given the variable star designation GW Vir in 1985. Variable PG 1159 stars may be called GW Vir stars, or the class may be split into DOV and PNNV stars. The variability of PG 1139-035, like that of other GW Vir stars, arises from non-radial gravity wave pulsations within itself. Its light curve has been observed intensively by the Whole Earth Telescope over a 264-hour period in March 1989, and over 100 of its vibrational modes have been found in the resulting vibrational spectrum, with periods ranging from 300 to 1,000 seconds.

PG 1159 star

A PG 1159 star, often also called a pre-degenerate, is a star with a hydrogen-deficient atmosphere that is in transition between being the central star of a planetary nebula and being a hot white dwarf. These stars are hot, with surface temperatures between 75,000 K and 200,000 K, and are characterized by atmospheres with little hydrogen and absorption lines for helium, carbon and oxygen. Their surface gravity is typically between 104 and 106 meters per second squared. Some PG 1159 stars are still fusing helium., § 2.1.1, 2.1.2, Table 2. The PG 1159 stars are named after their prototype, PG 1159-035. This star, found in the Palomar-Green survey of ultraviolet-excess stellar objects, was the first PG 1159 star discovered.

It is thought that the atmospheric composition of PG 1159 stars is odd because, after they have left the asymptotic giant branch, they have reignited helium fusion. As a result, a PG 1159 star's atmosphere is a mixture of material which was between the hydrogen- and helium-burning shells of its AGB star progenitor., §1. They are believed to eventually lose mass, cool, and become DO white dwarfs.; , §4.Some PG 1159 stars have varying luminosities. These stars vary slightly (5–10%) in brightness due to non-radial gravity wave pulsations within themselves. They vibrate in a number of modes simultaneously, with typical periods between 300 and 3,000 seconds., Table 1. The first known star of this type is also PG 1159-035, which was found to be variable in 1979, and was given the variable star designation GW Vir in 1985. These stars are called GW Vir stars, after their prototype, or the class may be split into DOV and PNNV stars., § 1.1;

Pulsating white dwarf

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Resonance method of ice destruction

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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.

Special marine warning

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Sverdrup wave

A Sverdrup wave (also known as Poincaré wave, or rotational gravity wave ) is a wave in the ocean, which is affected by gravity and Earth's rotation (see Coriolis effect).

For a non-rotating fluid, shallow water waves are affected only by gravity (see Gravity wave), where the phase velocity of shallow water gravity wave (c) can be noted as

and the group velocity (cg) of shallow water gravity wave can be noted as

i.e.

where g is gravity, λ is the wavelength and H is the total depth.

Undular bore

In meteorology, an undular bore is a wave disturbance in the Earth's atmosphere and can be seen through unique cloud formations. They normally occur within an area of the atmosphere which is stable in the low levels after an outflow boundary or a cold front moves through.

In hydraulics, an undular bore is a gentle bore with an undular hydraulic jump pattern at the downstream (subcritical) side.

Waves and shallow water

When waves travel into areas of shallow water, they begin to be affected by the ocean bottom. The free orbital motion of the water is disrupted, and water particles in orbital motion no longer return to their original position. As the water becomes shallower, the swell becomes higher and steeper, ultimately assuming the familiar sharp-crested wave shape. After the wave breaks, it becomes a wave of translation and erosion of the ocean bottom intensifies.

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