Gravity wave

Gravity wave

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Ocean wave

 

 

Wave clouds over Theresa, Wisconsin, USA

 

 

Atmospheric gravity waves as seen from space.

 

Gravity wave cloud pattern formed in the wake of the Île Amsterdam, a volcanic island in the southern Indian Ocean.

 

 

For the different concept in general relativity, see Gravitational wave.

 

In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two mediums (e.g. the atmosphere or ocean) which has the restoring force of gravity or buoyancy.

 

When a fluid parcel is displaced on an interface or internally to a region with a different density, gravity restores the parcel toward equilibrium resulting in an oscillation about the equilibrium state or wave orbit.

Gravity waves on an air-sea interface are called surface gravity waves or surface waves

while internal gravity waves are called internal waves.

 

Ocean waves generated by wind are examples of gravity waves.

Wind waves, as their name suggests, are generated by wind transferring energy from the atmosphere to the ocean's surface. At first capillary waves form on the ocean surface and grow in height at a linear rate proportional to the wind speed (as explained by Miles 1957; 1959). once these small waves have formed they start to interact with the atmosphere through pressure differences and due to the ocean surface roughness. The waves grow at rates exponentially proportional to the wind speed (as explained by Phillips 1957), producing larger and larger waves. 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.

Gravity waves have a period of between 1 and 30 seconds (0.033 to 1 Hz).

Alternatively, infragravity waves generally have a period between 30 seconds to 5 minutes (0.05 to 0.005 Hz). Infragravity waves can be felt rather than seen as they have a much greater wave energy.

 Atmosphere dynamics on Earth

Since the fluid is a continuous medium, a traveling disturbance will result. In the earth's atmosphere, gravity waves are important for transferring momentum from the troposphere to the mesosphere. Gravity waves are generated in the troposphere by frontal systems or by airflow over mountains. At first waves propagate through the atmosphere without affecting its mean velocity. But as the waves reach more rarefied air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow.

This process plays a key role in controlling the dynamics of the middle atmosphere.

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

 Quantitative Description

The phase speed c of a linear gravity wave with wavenumber k is given by the formula

where g is the acceleration due to gravity. Since c = ω / k is the phase speed in terms of the frequency ω and the wavenumber, the gravity wave 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.