Internal waves are
gravity waveIn fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media which has the restoring force of gravity or buoyancy....
s that
oscillateOscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power...
within, rather than on the surface of, a fluid medium. They arise from perturbations to hydrostatic equilibrium, where balance is maintained between the force of gravity and the
buoyantIn physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body. This force enables the object to float or at least seem lighter....
restoring force. A simple example is a wave propagating on the interface between two fluids of different
densitiesThe density of a material is defined as its mass per unit volume. The symbol of density is ρ .- Formula :Mathematically:where: is the density, is the mass, is the volume....
, such as oil and water. Internal waves typically have much lower frequencies and higher amplitudes than
surface gravity wavesIn fluid dynamics, wind waves or, more precisely, wind-generated waves are surface waves that occur on the free surface of oceans, seas, lakes, rivers, and canals or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Some waves...
because the density differences (and therefore the restoring forces) within a fluid are usually much smaller than the density of the fluid itself.
Internal waves are
gravity waveIn fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media which has the restoring force of gravity or buoyancy....
s that
oscillateOscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power...
within, rather than on the surface of, a fluid medium. They arise from perturbations to hydrostatic equilibrium, where balance is maintained between the force of gravity and the
buoyantIn physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body. This force enables the object to float or at least seem lighter....
restoring force. A simple example is a wave propagating on the interface between two fluids of different
densitiesThe density of a material is defined as its mass per unit volume. The symbol of density is ρ .- Formula :Mathematically:where: is the density, is the mass, is the volume....
, such as oil and water. Internal waves typically have much lower frequencies and higher amplitudes than
surface gravity wavesIn fluid dynamics, wind waves or, more precisely, wind-generated waves are surface waves that occur on the free surface of oceans, seas, lakes, rivers, and canals or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Some waves...
because the density differences (and therefore the restoring forces) within a fluid are usually much smaller than the density of the fluid itself. Internal wave motions are ubiquitous in both the ocean and atmosphere. Nonlinear solitary internal waves are called
solitonIn mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. "Dispersive effects" refer to dispersion relations between the frequency...
s.
The atmosphere and ocean are continuously stratified:
potential densityThe potential density of a fluid parcel at pressure is the density that the parcel would acquire if adiabatically brought to a reference pressure , often 1 bar . Whereas density changes with changing pressure, potential density of a fluid parcel is conserved as the pressure experienced by the...
generally increases steadily downward. Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The
dispersion relationDispersion relations describe the ways that wave propagation varies with the wavelength or frequency of a wave. This variation has long explained how white light is dispersed into different colors, thus making rainbows possible...
for such waves is curious: For a freely-propagating internal wave
packetIn physics, a wave packet is a short "burst" or "envelope" of wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere...
, the direction of propagation of energy (
group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
) is perpendicular to the direction of propagation of wave crests and troughs (
phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
). An internal wave may also become confined to a finite region of
altitudeAltitude is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object...
or depth, as a result of varying stratification or
windWind is the flow of air or other gases that compose an atmosphere . On Earth, wind consists of the bulk movement of air...
. Here, the wave is said to be
ducted or
trapped, and a vertically
standing waveA standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite...
may form, where the vertical component of
group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
approaches zero. A ducted internal wave
mode may
propagateWave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
horizontally, with parallel
groupThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
and
phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
vectors, analogous to
propagationWave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
within a
waveguideA waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguide for each type of wave...
.
At large scales, internal waves are influenced both by the rotation of the Earth as well as by the stratification of the medium. The frequencies of these geophysical wave motions vary from a lower limit of the
Coriolis frequencyThe Coriolis frequency ƒ, also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate Ω of the Earth multiplied by the sine of the latitude φ....
(inertial motions) up to the
Brunt-VäisäläIn atmospheric dynamics, oceanography, and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is the frequency at which a vertically displaced parcel will oscillate within a statically stable environment...
, or buoyancy frequency (buoyancy oscillations). Above the
Brunt-Väisälä frequencyIn atmospheric dynamics, oceanography, and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is the frequency at which a vertically displaced parcel will oscillate within a statically stable environment...
may exist
evanescentEvanescent may refer to:* Evanescent, as in skin lesions that last less than 24 hours* Evanescent wave* Evanescence, the musical band...
internal wave motions, for example those resulting from partial
reflectionReflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
. Internal waves at tidal frequencies are produced by
tidal flowTides are the rises and falls of sea level caused by the combined effect of rotation of the Earth and the gravitation of the Moon and the Sun. The tides occur with a period of approximately 12 and a half hours and are influenced by the shape of the near-shore bottom.Most coastal areas experience...
over topography/bathymetry, and are known as internal tides. Similarly, Atmospheric tides arise from, for example, non-uniform solar heating associated with
diurnal motionDiurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis, so every star apparently moves on a circle, that is called the diurnal circle...
.
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