Geophysical fluid dynamics
Encyclopedia
Geophysical fluid dynamics is the study of naturally occurring, large-scale flows on Earth
and other planets. It is applied to the motion of fluids in the ocean
and outer core
, and to gases in the atmosphere
of Earth and other planets. Two 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
. Smaller scale flow features (those negligibly influenced by the rotation of the Earth) are the province of fields such as hydrology
, physical oceanography
and meteorology
.
. The former leads to the Navier-Stokes equations
. Further approximations are generally made. First, the fluid is assumed to be incompressible
. Remarkably, this works well even for a highly compressible fluid like air as long as sound
and shock wave
s can be ignored. Second, the fluid is assumed to be a Newtonian fluid
, meaning that there is a linear relation between the shear stress
and the strain
, for example
where is the viscosity
. Under these assumptions the Navier-Stokes equations are
The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (a Lagrangian frame of reference). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity and advection
, a measure of the rate of flow in or out of a small region.
The equation for energy conservation is essentially an equation for heat flow. If heat is transported by conduction, the heat flow is governed by a diffusion
equation. If there are also buoyancy
effects, for example hot air rising, then natural convection
can occur.
. On a large scale, the Earth's atmosphere is divided into a series of layers. Going upwards from the ground, these are the troposphere
, stratosphere
, mesosphere
, thermosphere
, and exosphere
.
The density of air is mainly determined by temperature and water vapor
content, the density of sea water by temperature and salinity
, and the density of lake water by temperature and oxygenation
. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a pycnocline
(density), thermocline
(temperature), halocline
(salinity), or chemocline
(chemistry, including oxygenation).
The same buoyancy that gives rise to stratification also drives gravity waves. If the gravity waves occur within the fluid, they are called internal waves.
In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using the Boussinesq approximation. This ignores variations in density except where they are multiplied by the gravitational acceleration
.
If the pressure depends only on density and vice versa, the fluid dynamics are called barotropic
. In the atmosphere, this corresponds to a lack of fronts, as in the tropics
. If there are fronts, the flow is baroclinic, and instabilities such as cyclones can occur.
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
and other planets. It is applied to the motion of fluids in the ocean
Ocean
An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...
and outer core
Outer core
The outer core of the Earth is a liquid layer about 2,266 kilometers thick composed of iron and nickel which lies above the Earth's solid inner core and below its mantle. Its outer boundary lies beneath the Earth's surface...
, and to gases in the atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
of Earth and other planets. Two features that are common to many of the phenomena studied in geophysical fluid dynamics are rotation of the fluid
Rotating reference frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. A rotating frame of reference is a special case of a non-inertial reference...
due to the planetary rotation and stratification
Stratification
Stratification is the building up of layers. Stratified is an adjective referring to the arranging of layers, and is also the past form of the verb stratify, to separate or become separated into layers...
(layering). The applications of geophysical fluid dynamics do not generally include the circulation of the mantle
Mantle
A mantle is an ecclesiastical garment in the form of a very full cape which extends to the floor, joined at the neck, that is worn over the outer garments....
, which is the subject of geodynamics
Geodynamics
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and...
, or fluid phenomena in the magnetosphere
Magnetosphere
A magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the intrinsic magnetic field of a planet or similar body. Earth is surrounded by a magnetosphere, as are the other planets with intrinsic magnetic fields: Mercury, Jupiter,...
. Smaller scale flow features (those negligibly influenced by the rotation of the Earth) are the province of fields such as hydrology
Hydrology
Hydrology is the study of the movement, distribution, and quality of water on Earth and other planets, including the hydrologic cycle, water resources and environmental watershed sustainability...
, physical oceanography
Physical oceanography
Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.Physical oceanography is one of several sub-domains into which oceanography is divided...
and meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
.
Fundamentals
To describe the flow of geophysical fluids, equations are needed for conservation of momentum (or Newton's second law) and conservation of energyConservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
. The former leads to the Navier-Stokes equations
Navier-Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous...
. Further approximations are generally made. First, the fluid is assumed to be incompressible
Incompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow refers to flow in which the material density is constant within an infinitesimal volume that moves with the velocity of the fluid...
. Remarkably, this works well even for a highly compressible fluid like air as long as sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
and shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
s can be ignored. Second, the fluid is assumed to be a Newtonian fluid
Newtonian fluid
A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:...
, meaning that there is a linear relation between the shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
and the strain
Strain
Strain can refer to:* Strain , variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes* Strain , a chemical stress of a molecule...
, for example
where is the viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
. Under these assumptions the Navier-Stokes equations are
The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (a Lagrangian frame of reference). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity and advection
Advection
Advection, in chemistry, engineering and earth sciences, is a transport mechanism of a substance, or a conserved property, by a fluid, due to the fluid's bulk motion in a particular direction. An example of advection is the transport of pollutants or silt in a river. The motion of the water carries...
, a measure of the rate of flow in or out of a small region.
The equation for energy conservation is essentially an equation for heat flow. If heat is transported by conduction, the heat flow is governed by a diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
equation. If there are also buoyancy
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
effects, for example hot air rising, then natural convection
Natural convection
Natural convection is a mechanism, or type of heat transport, in which the fluid motion is not generated by any external source but only by density differences in the fluid occurring due to temperature gradients. In natural convection, fluid surrounding a heat source receives heat, becomes less...
can occur.
Buoyancy and stratification
Fluid that is less dense than its surroundings tends to rise until it has the same density as its surroundings. If there is not much energy input to the system, it will tend to become stratifiedStratification
Stratification is the building up of layers. Stratified is an adjective referring to the arranging of layers, and is also the past form of the verb stratify, to separate or become separated into layers...
. On a large scale, the Earth's atmosphere is divided into a series of layers. Going upwards from the ground, these are the troposphere
Troposphere
The troposphere is the lowest portion of Earth's atmosphere. It contains approximately 80% of the atmosphere's mass and 99% of its water vapor and aerosols....
, stratosphere
Stratosphere
The stratosphere is the second major layer of Earth's atmosphere, just above the troposphere, and below the mesosphere. It is stratified in temperature, with warmer layers higher up and cooler layers farther down. This is in contrast to the troposphere near the Earth's surface, which is cooler...
, mesosphere
Mesosphere
The mesosphere is the layer of the Earth's atmosphere that is directly above the stratosphere and directly below the thermosphere. In the mesosphere temperature decreases with increasing height. The upper boundary of the mesosphere is the mesopause, which can be the coldest naturally occurring...
, thermosphere
Thermosphere
The thermosphere is the biggest of all the layers of the Earth's atmosphere directly above the mesosphere and directly below the exosphere. Within this layer, ultraviolet radiation causes ionization. The International Space Station has a stable orbit within the middle of the thermosphere, between...
, and exosphere
Exosphere
The exosphere is the uppermost layer of Earth's atmosphere. In the exosphere, an upward travelling molecule moving fast enough to attain escape velocity can escape to space with a low chance of collisions; if it is moving below escape velocity it will be prevented from escaping from the celestial...
.
The density of air is mainly determined by temperature and water vapor
Water vapor
Water vapor or water vapour , also aqueous vapor, is the gas phase of water. It is one state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from the sublimation of ice. Under typical atmospheric conditions, water vapor is continuously...
content, the density of sea water by temperature and salinity
Salinity
Salinity is the saltiness or dissolved salt content of a body of water. It is a general term used to describe the levels of different salts such as sodium chloride, magnesium and calcium sulfates, and bicarbonates...
, and the density of lake water by temperature and oxygenation
Oxygenation
Oxygenation may refer to:* Oxygenation , a measurement of dissolved oxygen concentration in soil or water* Oxygenation , the process by which concentrations of oxygen increase within a tissue...
. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a pycnocline
Pycnocline
A pycnocline is the cline or layer where the density gradient is greatest within a body of water. An ocean current is generated by the forces such as breaking waves, terms of temperature and salinity differences, wind, Coriolis effect, and tides caused by the gravitational pull of the Moon and the...
(density), thermocline
Thermocline
A thermocline is a thin but distinct layer in a large body of fluid , in which temperature changes more rapidly with depth than it does in the layers above or below...
(temperature), halocline
Halocline
In oceanography, a halocline is a subtype of chemocline caused by a strong, vertical salinity gradient within a body of water. Because salinity affects the density of seawater, it can play a role in its vertical stratification...
(salinity), or chemocline
Chemocline
A chemocline is a cline caused by a strong, vertical chemistry gradient within a body of water. A chemocline is analogous to a thermocline, the border at which warmer and cooler waters meet in an ocean, sea, lake, or other body of water...
(chemistry, including oxygenation).
The same buoyancy that gives rise to stratification also drives gravity waves. If the gravity waves occur within the fluid, they are called internal waves.
In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using the Boussinesq approximation. This ignores variations in density except where they are multiplied by the gravitational acceleration
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....
.
If the pressure depends only on density and vice versa, the fluid dynamics are called barotropic
Barotropic
In meteorology, a barotropic atmosphere is one in which the pressure depends only on the density and vice versa, so that isobaric surfaces are also isopycnic surfaces . The isobaric surfaces will also be isothermal surfaces, hence the geostrophic wind is independent of height...
. In the atmosphere, this corresponds to a lack of fronts, as in the tropics
Tropics
The tropics is a region of the Earth surrounding the Equator. It is limited in latitude by the Tropic of Cancer in the northern hemisphere at approximately N and the Tropic of Capricorn in the southern hemisphere at S; these latitudes correspond to the axial tilt of the Earth...
. If there are fronts, the flow is baroclinic, and instabilities such as cyclones can occur.
Rotation
- Coriolis force
- Circulation
- Kelvin's circulation theoremKelvin's circulation theoremIn fluid mechanics, Kelvin's circulation theorem states In an inviscid, barotropic flow with conservative body forces, the circulation around a closed curve moving with the fluid remains constant with time. The theorem was developed by William Thomson, 1st Baron Kelvin...
- Vorticity equationVorticity equationThe vorticity equation is an important prognostic equation in the atmospheric sciences. Vorticity is a vector, therefore, there are three components...
- Thermal windThermal windThe thermal wind is a vertical shear in the geostrophic wind caused by a horizontal temperature gradient. Its name is a misnomer, because the thermal wind is not actually a wind, but rather a wind shear.- Physical Intuition :...
- Geostrophic current
- Geostrophic windGeostrophic windThe geostrophic wind is the theoretical wind that would result from an exact balance between the Coriolis effect and the pressure gradient force. This condition is called geostrophic balance. The geostrophic wind is directed parallel to isobars . This balance seldom holds exactly in nature...
- Taylor–Proudman theoremTaylor–Proudman theoremIn fluid mechanics, the Taylor–Proudman theorem states that when a solid body is moved slowly within a fluid that is steadily rotated with a high \Omega, the fluid velocity will be uniform along any line parallel to the axis of rotation...
- Hydrostatic equilibriumHydrostatic equilibriumHydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force...
- Ekman spiralEkman spiralThe Ekman spiral refers to a structure of currents or winds near a horizontal boundary in which the flow direction rotates as one moves away from the boundary. It derives its name from the Swedish oceanographer Vagn Walfrid Ekman...
- Ekman layer
General circulation
- Atmospheric circulationAtmospheric circulationAtmospheric circulation is the large-scale movement of air, and the means by which thermal energy is distributed on the surface of the Earth....
- Ocean currentOcean currentAn ocean current is a continuous, directed movement of ocean water generated by the forces acting upon this mean flow, such as breaking waves, wind, Coriolis effect, cabbeling, temperature and salinity differences and tides caused by the gravitational pull of the Moon and the Sun...
- Ocean dynamicsOcean dynamicsOcean dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed layer, upper ocean , and deep ocean....
- Thermohaline circulationThermohaline circulationThe term thermohaline circulation refers to a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes....
- Boundary currentBoundary currentBoundary currents are ocean currents with dynamics determined by the presence of a coastline, and fall into two distinct categories: western boundary currents and eastern boundary currents.-Eastern boundary currents:...
- Sverdrup balanceSverdrup balanceThe Sverdrup balance, or Sverdrup relation, is a theoretical relationship between the wind stress exerted on the surface of the open ocean and the vertically integrated meridional transport of ocean water.- History :...
- Subsurface currentsSubsurface currentsA subsurface current is an oceanic current that beneath surface currents. Examples include the Equatorial Undercurrents of the Pacific, Atlantic, and Indian Oceans, the California Undercurrent, and the Agulhas Undercurrent, the deep thermohaline circulation in the Atlantic, and bottom gravity...
External links
- http://www.whoi.edu/page.do?pid=7937Geophysical Fluid Dynamics Program (Woods Hole Oceanographic InstitutionWoods Hole Oceanographic InstitutionThe Woods Hole Oceanographic Institution is a private, nonprofit research and higher education facility dedicated to the study of all aspects of marine science and engineering and to the education of marine researchers. Established in 1930, it is the largest independent oceanographic research...
)] - http://www.ocean.washington.edu/research/gfd/index.htmlGeophysical Fluid Dynamics Laboratory (University of WashingtonUniversity of WashingtonUniversity of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...
)]