# Glossary of Scientific Terms

New terms are still being added

### breaker

A sea-surface wave which has become too steep to be stable. Waves in shoaling water become higher and shorter (hence steeper) as the water becomes shallower. When the steepness (ratio of wave height to wave length) exceeds 1/7, the laws which govern surface-wave motion can no longer be satisfied and the crest of the wave outraces the body of the wave to form a foaming white turbulent mass of water called a breaker. Roughly, three kinds of breakers can be distinguished, depending primarily on the gradient of the bottom: ( a) spilling breakers = (over nearly flat bottom) which form a foamy path at the crest and break gradually over a considerable distance; ( b) plunging breakers (over fairly steep bottom gradient) which peak up, curl over with a tremendous overhanging mass, and then break with a crash; ( c) surging breakers (over very steep bottom gradients) which do not spill or plunge but surge up the beach face. Waves also break in deep water if they build too high while being generated by the wind, but these are usually short-crested and are termed whitecaps .

### cable

A nautical unit of horizontal distance, equal to 600 feet (100 fathoms ) and approximately one-tenth of a nautical mile .

### California Current

The ocean current flowing southward along the west coast of the United States from approximately Washington to northern Baja California. It is the major branch of the Aleutian current . As a whole, the current represents a wide body of water that moves sluggishly toward the southeast. Off Central America, the California current turns toward the west and becomes the north equatorial current .

### Canaries current

The southern branch of the North Atlantic current (which divides on the eastern side of the ocean); it moves south past Spain and North Africa to join the north equatorial current .

### Caribbean current

An ocean current flowing westward through the Caribbean Sea. It is formed by the commingling of part of the waters of the north equatorial current with those of the Guiana current . It flows through the Caribbean Sea as a strong current and continues with increased speed through the Yucatan Channel; there it bends sharply to the right and flows eastward with great speed out through the Straits of Florida to form the Florida current .

### clapotis

A standing wave phenomenon associated with the reflection of an ocean-wave train from a vertical surface, such as a breakwater or pier.

### cold wall

The steep water-temperature gradient between the Gulf Stream and (a) the slope water inshore of the Gulf Stream or (b) the Labrador current.

### comber

A large ocean wave with high, breaking crest.

### continental borderland

A submarine plateau or irregular area adjacent to a continent , with depths greatly exceeding those on the continental shelf , but not as great as in the deep oceans.

### continental platform

The zone that includes both the continental shelf or continental borderland and the continental slope .

### continental shelf

The zone around the continents extending from the low-water mark seaward to where there is a marked increase in slope to greater depths.

### continental slope

The declivity from the outer edge of the continental shelf or continental borderland into greater depths.

### countercurrent

A current flowing adjacent to another current both in the opposite direction.

### Davidson current

A countercurrent of the Pacific Ocean running north along the west coast of the United States (from northern California to Washington to at least latitude 48 degrees) during the winter months.

### direct tide

A gravitational solar or lunar tide in the ocean or atmosphere which is in phase with the apparent motions of the attracting body, and consequently has its local maxima directly under the tide-producing body and on the opposite side of the earth. A gravitational tide which is in opposite phase to the apparent motions of the sun or moon is called a reversed tide .

### diurnal tide

A tide in which there is only one high water and one low water each lunar day .

### dynamic-height anomaly

In oceanography, the excess of the actual geopotential difference, between two given isobaric surfaces , over the geopotential difference in a homogeneous water column of salinity 35 per mille (%) and temperature 0 degrees. Also called anomaly of geopotential difference. The dynamic-height anomaly between two isobaric surfaces is the product of the mean specific-volume anomaly and the difference in pressure (in decibars); the latter is assumed to equal the difference in depth in meters.

### East Australia current

The ocean current flowing southward along the east coast of Australia. It is formed by the division of part of the south equatorial current as it approaches the coast of Australia. Part of the east Australia current joins the west wind drift flowing eastward toward South America. In the summer (Southern Hemisphere) part of this water flows westward along the south coast of Australia into the Indian Ocean.

### East Greenland current

An ocean current flowing south along the east coast of Greenland, carrying water of low salinity and low temperature. The east Greenland current is joined by most of the water of the Irminger current . The greater part of the current continues through Denmark Strait between Iceland and Greenland, but one branch turns to the east and forms a portion of the counterclockwise circulation in the southern part of the Norwegian Sea. Some of the east Greenland current curves to the right around the tip of Greenland, flowing northward into Davis Strait as the west Greenland current . The main discharge of the Arctic Ocean is via the east Greenland current.

### ebb current

The movement of a tidal current away from the coast or down an estuary or tidal waterway; the opposite of flood current. Nontechnically called ebb tide.

### edge wave

An ocean wave traveling parallel to a coast, with crests normal to the coast line. Such a wave has a height that diminishes rapidly seaward and is negligible at a distance of one wave length offshore.

### Ekman spiral

As originally applied by {Ekman} to ocean currents, a graphic representation of the way in which the theoretical wind-driven currents in the surface layers of the sea vary with depth. In an ocean which is assumed to be homogeneous, infinitely deep, unbounded and having a constant eddy viscosity , over which a uniform steady wind blows, Ekman has computed that the current induced in the surface layers by the wind will have the following characteristics: ( a) At the very surface the water will move at an angle of 45 degrees cum sole from the wind direction. ( b) In successively deeper layers the movement will be deflected farther and farther cum sole from the wind direction, and the speed will decrease. ( c) A hodograph of the velocity vectors would form a spiral descending into the water and decreasing in amplitude exponentially with depth. The depth at which the vector first points 180=AE$=AF from the wind vector is called the depth of frictional influence (or depth of frictional resistance ). At this depth the speed is [s] times that at the surface. The layer from the surface to the depth of frictional influence is called the layer of frictional influence =2E. If the velocity vectors from the surface to the depth of frictional influence are integrated, the resultant motion is 90=AE$=AF =

### Kuroshio countercurrent

Part of the Kuroshio system . Between longitudes 155 degrees and 160 degrees, considerable water turns south and southwest forming part of the Kuroshio countercurrent. It runs at a distance of approximately 700 km from the coast as the eastern branch of a large whirl on the right-hand side of the Kuroshio .

### Kuroshio extension

The warm, eastward-flowing ocean current that represents the direct continuation of the Kuroshio (in latitude 35 degrees where the Kuroshio leaves the coast of Japan), and flows eastward in two branches. The major branch of the Kuroshio extension turns due east; it retains its character as a well-defined flow approximately as far as longitude 160=AE$=AFE (eventually becoming the North Pacific current). The minor branch, to the north, continues toward the northeast as far as latitude 40=AE$=AFN where it bends east (eventually becoming the Aleutian current ). This northern branch becomes rapidly mixed with the cold waters of the Oyashio .

### Kuroshio system

A system of ocean currents including the Kuroshio , Kuroshio extension , North Pacific current , and the lesser Tsushima current and Kuroshio countercurrent .

An ocean current that flows southward from Baffin Bay, through the Davis Strait, thence southeastward past Labrador and Newfoundland. East of the Grand Banks, the Labrador current meets the Gulf Stream , and the two flow east separated by the cold wall .

### longshore current

The resultant current produced by waves being deflected at an angle by the shore. Also called littoral current. In this case the current runs roughly parallel to the shoreline. The longshore current is capable of carrying a certain amount of material as long as its velocity remains fairly constant; however, any obstruction, such as a submarine rock ridge or a land point cutting across the path of the current will cause loss of velocity and consequent loss of carrying power.

### meridional

Refers to motion or distance along lines of longitude. See also zonal.

### meteorological tide

Annual or semi-annual changes in sea level due to shifts in prevailing winds or seasonal changes in water temperature; distinguish from atmospheric tide.

### mixed layer

In oceanography, the surface layer of virtually isothermal water, which frequently exists above the thermocline .

### mixed tide

A tide in which the diurnal and semidiurnal components are both prominent. Diurnal inequality is present in high waters , low waters , or in both.

### monsoon current

A seasonal, eastward-flowing ocean current of the Indian Ocean. The monsoon current replaces the north equatorial current and the equatorial counter-current in summer (Northern Hemisphere), when the southwest monsoon forms a continuation of the southeast trade winds.

### Mozambique current

That portion of the Agulhas current north of 30 degrees along the east coast of Africa.

### neap tide

A tide of decreased amplitude, occurring semimonthly one or two days after quadrature .

### North Atlantic current

A continuation of the Gulf Stream , originating at about 40 degrees latitude and 50 degrees longitude, comprising all the easterly and northerly currents of the North Atlantic originating in the region east of the Grand Banks. The branches of the North Atlantic current are often masked by shallow and variable, wind-driven surface movements so that they are sometimes called the North Atlantic drift . Along the mid-Atlantic ridge the North Atlantic current is divided into two major branches; the northern branch flows between latitudes 50 degrees and 52 degrees separated from the Labrador current by the cold wall . The other branch flows approximately in latitude 45 degrees and carries undiluted Gulf Stream water. Of these branches the northern continues mainly toward the east-northeast and divides, part flowing into the Norwegian Sea and part turning toward the north and northwest eventually giving rise to the Irminger current .

### North Equatorial current

Any of several currents driven by the northeast trade winds blowing over the tropical oceans of the Northern Hemisphere. In the Atlantic ocean, it flows west between the equatorial countercurrent and 30 degrees. Part passes along the northeast side of the West Indies as the Antilles current while part joins the Guiana current and enters the Caribbean Sea and the Gulf of Mexico as the Caribbean current . In the Pacific Ocean, it crosses from east to west between the approximate latitudes of 10 degrees and 20 degrees. East of the Philippines it divides, part turning south to join the equatorial countercurrent, and part going north to form the Kuroshio . In the Indian Ocean, in northern winter when the northeast monsoon duplicates the trade winds of the other oceans, the north equatorial current flows west and turns to the southwest along the coast of Somaliland as the Somali current . In Northern Hemisphere summer, when the southwest monsoon forms a continuation of the southeast trade winds, the north equatorial current and the equatorial countercurrent are replaced by an eastward flowing monsoon current .

### Norwegian current

Part of the northern branch of the North Atlantic current , which flows northward along the coast of Norway. = The water of the Norwegian current eventually enters the Arctic Ocean, from which the main discharge is via the east Greenland current .

### occlusion

In meteorology, the process of formation of an occluded front . Some persons restrict the use of this time to the usual case where the process begins at the apex of a wave cyclone ; when the process begins at some distance from the apex, they call it seclusion .

### ocean current

A movement of ocean water characterized by regularity, either of a cylic nature, or more commonly as a continuous stream flowing along a definable path. Three general classes, by cause may be distinguished: ( a) currents related to sea water density gradients, comprising the various types of gradient current ; ( b) wind-driven currents , which are those directly produced by the stress exerted by the wind upon the ocean surface; ( c) currents produced by long-wave motions. The latter are principally tidal currents , but may include currents associated with internal waves , tsunamis , and seiches . The major ocean currents are of continuous, stream-flow character, and are of first-order importance in the maintenance of the earth's thermodynamic balance.

### oceanography

The study of the sea , embracing and integrating all knowledge pertaining to the sea's physical boundaries, the chemistry and physics of sea water, and marine biology.

### Oyashio current

A cold ocean current flowing from the Bering Sea southwest along the coast of Kamchatka, past the Kuril Islands, continuing close to the northeast coast of Japan and reaching nearly 35 degrees latitude. The Oyashio turns and continues east eventually jointing the Aleutian current . The cold waters of the Oyashio rapidly mix with those of the northern branch of the Kuroshio extension .

### perigean tide

Tide of increased range occurring when the moon is near perigee.

### Peru current

The cold ocean current flowing north along the coasts of Chile and Peru. It is one of the swiftest of ocean currents. The Peru current originates where part of the water that flows toward the east across the subantarctic Pacific Ocean is deflected toward the north as it approaches South America. The northern limit of the current can be placed a little south of the equator, where the flow turns toward the west, joining the south equatorial current . Also called Humboldt current. The southern portion of the Peru current is sometimes called the Chile current .

See Rossby wave.

### Poincare wave

Within a channel in a rotating system, a Poincare' wave has sinusoidally varying cross-channel velocity with an integral or half integral number of cross-channel waves spanning the channel. In the shallow water approximation the waves have dispersion relationship with squared frequency \omega^2 = f^2 + c^2 (k^2 + n^2 \pi^2/L^2), in which f is the Coriolis parameter, k is the along channel wavenumber, L is the width of the channel, n is any positive integer, and c is the phase speed for shallow water gravity waves: c=(gH)^(1/2), in which g is the acceleration due to gravity and H is the mean depth of the fluid. Related to Poincare' waves are Kelvin waves which take the role of the mode with n=0.

### South Atlantic current

An eastward flowing current of the South Atlantic Ocean that is continuous with the northern edge of the Antarctic circumpolar current .

### south equatorial current

Any of several ocean currents driven by the southeast trade winds flowing over the tropical oceans of the Southern Hemisphere.

In the Atlantic Ocean it flows westward between the equator and 20 degrees. Part crosses the equator and flows northwest along the coast of South America as the Guiana current . The rest turns to the left and flows south along the coast of Brazil as the Brazil current.

In the Pacific Ocean, the south equatorial current crosses the ocean from east to west between the latitudes of approximately 3 degrees and 10 degrees. Much of it turns south in mid-ocean forming a large anticyclonic whirl. The portion that continues across the ocean divides as it approaches Australia, part moving north toward New Guinea and part turning south along the east coast of Australia as the east Australia current .

In the Indian Ocean, the south equatorial current is displaced rather far to the south, and as it approaches the east coast of Africa it turns south, joining the Agulhas current .

### South Pacific current

An eastward flowing current of the South Pacific Ocean that is continuous with the northern edge of the antarctic circumpolar current .

### specific-volume anomaly

In oceanography, the excess of the actual specific volume of the sea water at any point in the ocean over the specific volume of sea water of salinity 35 per mile ([s]) and temperature 0 degrees at the same pressure. The integral of specific-volume anomaly with depth is the dynamic-height anomaly .

### stratified fluid

In a stratified fluid the effective density varies with depth. Such circumstances occur naturally, for example, due to variations in temperature in the atmosphere, and due to temperature and salinity variations in the ocean.

### subarctic current

Same as Aleutian current.

### sea surface temperature

In oceanography, the temperature of the layer of sea water nearest the atmosphere. It is generally determined either as bucket temperature or injection temperature .

### surface gravity wave

A wave that propagates, typically, on the surface of water under the influence of buoyancy forces. In water of uniform depth H, the dispersion relationship is given by squared frequency \omega^2 = gk tanh(kH), in which k is the wavenumber and g is the acceleration of gravity. In shallow water, when the wavelength is much larger than the fluid depth, the waves are nondispersive: the dispersion relationship is \omega = c k, in which phase speed c=(gH)^(1/2). In deep water the waves have dispersion relationship \omega = +/- (gk)^(1/2).

### surge

Water transported up a beach by breaking waves.

### swash

Intermittent landward flow of water across a beach where surf is breaking.

### synthetic schlieren

A new technique for visualising and measuring small density variations by digitally recording variations in an image observed through a stratified fluid.

### T-S diagram

Abbreviation for temperature-salinity diagram.

### temperature salinity diagram

A graph with temperature as ordinate and salinity as abscissa, on which the points observed at a single oceanographic serial station are joined by a curve (the T-S curve ).

### thermocline

A vertical temperature gradient in some layer of a body of water, which is appreciably greater than the gradients above and below it; also a layer in which such a gradient occurs. = The principal thermoclines in the ocean are either seasonal, due to heating of the surface water in summer, or permanent. thermohaline circulation - Circulation in water caused by changes in density brought about by the combined effect of variations in temperature and salinity.

### thermosteric anomally

The specific-volume anomaly ( steric anomaly ) that the sea water at any point would attain if the sea water were brought isothermally to a pressure of one standard atmosphere =2E. In other words, thermosteric anomaly is the specific-volume anomaly calculated for the given salinity and temperature but for a standard pressure.

### tidal current

The horizontal movement of water associated with the rise and fall of the tide. Also called a tidal stream. In relatively open positions, the direction of tidal currents rotates continuously through 360 degrees diurnally or semi-diurnally. = In coastal regions, the nature of tidal currents will be determined by local topography as well.

### tropic tide

Tide occurring when the moon is near maximum declination; the diurnal inequality is then at a maximum.

### tsunami

An ocean wave produced by a submarine earthquake, landslide, or volcanic eruption. These waves may reach enormous dimensions and have sufficient energy to travel across entire oceans. They proceed as ordinary gravity waves with a period between 15 and 60 minutes. Tsunamis steepen and increase in height on approaching shallow water, inundating low-lying areas; and where local submarine topography causes extreme steepening, they may break and cause great damage. Tsunamis have no connection with tides ; the popular name is entirely misleading.

### Tsushima current

A warm, northward-flowing ocean current following the western coast of Japan. The Tsushima current branches off on the left-hand side of the Kuroshio flowing north into the Japan Sea.

### undercurrent

In oceanography, a water current flowing beneath a surface current at a different speed or in a different direction.

### upwelling

The rising of water toward the surface from subsurface layers of a body of water. Upwelling is most prominent where persistent wind blows parallel to a coastline so that the resultant wind-driven current sets away from the coast ( see Ekman spiral ). It constitutes a distinct climatogenetic influence by bringing colder water to the surface. = Over the ocean, upwelling occurs wherever the wind circulation is cyclonic , but is appreciable only in areas where that circulation is relatively permanent. It is also observable when the southern trade winds cross the equator. The upwelled water, besides being cooler, is richer in plant nutrients, so that regions of upwelling are generally also areas of rich fisheries.

### West Australia current

The seasonal ocean current flowing along the west coast of Australia. In the Southern Hemisphere summer it flows northward, then curves toward the west to join the south equatorial current . During Southern Hemisphere winter the west Australia current flows southward.

### West Greenland current

The ocean current flowing northward along the west coast of Greenland into David Strait. It is a continuation of the east Greenland current . Part of the west Greenland current turns around when approaching the Davis Strait and joins the Labrador current ; the rest rapidly loses its character as a warm current as it continues into Baffin Bay.

### west wind drift

Same as antarctic circumpolar current.

### wind-driven current

A current produced in a body of water by blowing over the water surface. It flows to the right of the wind. Sometimes called wind drift; sometimes called drift current. Considerable evidence now exists to show that the Gulf Stream is such a current. Which of the ocean currents are wind driven and which thermally driven is a subject now under intensive investigation.

### Yanai wave

See Rossby-gravity wave.

### zonal

Refers to motion or distance along lines of latitude. See also meridional.

### hydrodynamic instability

The development of an infinitessimal disturbance in a mean flow field that grows by drawing energy from the mean flow.

### barotropic instability

An instability associated with shear and jet flows that grows by extracting kinetic energy from the mean flow.

### baroclinic instability

An instability associated with flows with vertical shear and meridional temperature gradients that grows by conversion of potential energy in the mean flow.

### Kelvin-Helmholtz instability

Also called "shear instability". An instability of an unbounded parallel shear flow to the growth and nonlinear development of waves with phase speed in the along flow direction approximately equal to the speed of the inflection point of the shear. This is also referred to as shear instability and is a specific example of barotropic instability. The instability, whether in homogeneous or stratified fluid, occurs due to a resonant coupling between wave-like disturbances on either flank of the shear flow where the gradient of the shear is non-zero. Increasing stratification acts to inhibit the growth of the instability.

### shear instability

See Kelvin-Helmholtz instability.

### Holmboe instability

An instability of an unbounded stratified parallel shear flow to the development of cusp-like waves that propagate with phase speed in the along flow direction significantly different from the speed of the inflection point of the shear. The propagating phase speed of Holmboe instability distinguishes it from Kelvin-Helmholtz instability. The instability occurs only in stratified fluid due to a resonant coupling between an internal gravity wave and a wave-like disturbance where the background shear varies vertically.

### convective instability

An instability due to the buoyancy force of heavy fluid over light fluid overcoming the stabilizing influence of viscous forces.

### inertial instability

An instability of geostrophic (cyclostrophic) motion due to imbalance between pressure gradient and inertial forces for an infinitessimal disturbance that meridionally (radially) displaces fluid. For geostrophic motion in the Northern (Southern) Hemisphere, inertially instability may occur only if the absolute vorticity (f- \partial u_g/\partial y) is negative (positive). Here f is the Coriolis parameter, u_g the zonal component of geostrophic velocity, and y is distance in the meridional direction.

### symmetric instability

Similar to inertial instability but due to imbalance between pressure gradient and inertial forces for infinitessimal disturbances that meridionally displaces fluid along isentropes (in atmosphere) or isopycnals (in ocean). For geostrophic motion in the Northern Hemisphere, symmetric instability may occur only if the potential vorticity is negative.

### line vortex

Idealized vortex in which vorticity is zero everywhere except along a line in space where it is infinite. The strength of a line vortex is \Gamma, the circulation along any circuit around the line.

### point vortex

Idealized vortex in two dimensions with zero vorticity everywhere except at a point where it is infinite. Specifically, a point vortex of strength \Gamma has vorticity \omega = \Gamma \delta( _r- _r_0}), in which \delta( _x) is the Kronecker delta and \Gamma is the circulation around the point vortex.

### Burgers vortex

Exact solution of the Navier-Stokes equation for a steady vortex in which the diffusion of vorticity is balanced by vortex stretching in an external strain field. The vortex has a Gaussian shape. For example, for a vertical axisymmetric vortex in an external velocity field given by (u,v,w)=\gamma (-x/2,-y/2,z), the vorticity is \omega = \omega_0 exp(-\gamma (x^2 + y^2)/4\nu) in which \nu is the kinematic viscosity.

### Kirchhoff vortex

An idealized vortex in unbounded fluid with uniform vorticity inside an elliptical patch and zero vorticity outside. For an ellipse with semi-axes a and b and vorticity \omega in its interior, it rotates steadily with angular velocity \omega ab/(a+b)^2.

### Rankine vortex

An idealized vortex in unbounded fluid with uniform vorticity inside a circular patch and zero vorticity outside.

### Kelvin-Helmholtz billows

Vortical structures that result from the growth and nonlinear development of unstable waves in a shear flow. The billows get their name from the instability responsible for the growth of the unstable waves: Kelvin-Helmholtz instability.

### Gulf Stream rings

Eddies formed by pinching off of meanders in the Gulf Stream. Eddies forming to the north (coastward side) of the Gulf Stream are called warm core rings and those forming to the south (oceanward side) are called cold core rings.

### Mediterranian lenses

A coherent mass of anticyclonically rotating, warm salty water in the Atlantic Ocean originating from the Mediterranian Sea. Also called Meddies'', these mesoscale lenses have been observed to persist for up to many months.

### meddy

See Mediterranian lenses.

### gravity current

A flow driven by horizontal pressure gradients, due typically to the flow of a fluid of one density intruding into an ambient fluid of different density. In non-rotating fluid, the head of the current travels with uniform horizontal speed C (g'H)^(1/2) in which g' is the reduced gravity, H is the current depth, and C is a constant of order unity. Sea breezes, landslides, and some instances of cold water formation are common manifestations of gravity currents in geophysical circumstances.

### convection

Fluid motion which results from the action of unbalanced buoyancy forces.

### double diffusive convection

Fluid motion that results from the release of potential energy from one of two or more factors that determine a fluid's density (for example, heat and salinity). Even if the density is statically stable, convection may result if one of the factors is statically unstable. There are three major types of double diffusive convection relevant to heat and mass transport in the ocean. Finger modes may occur when hot salty fluid overlays cold fresh fluid so that convection results in the form of narrow cells carrying salty water downwards and fresh water upwards. Diffusive modes occur when a stable salinity field is heated from below so that convection results in the form of a series of well mixed layers separated by sharp density gradients. Intrusive modes occur when there are horizontal density gradients in one of the components determining the fluid's density even if the fluid density as a whole is horizontally uniform. This instability develops in the form of interleaving intrusions.

Horizontal length scale of a rotating system measuring the distance over which the gravitational tendency to render a free surface flat is balanced by a tendency of the Coriolis acceleration to deform the surface. Also called the deformation radius or Rossby radius. In the shallow water approximation, the Rossby deformation radius is R = c/f in which c=(gH)^(1/2) with g the acceleration due to gravity and H the mean depth of the fluid. In stratified fluid, the appropriate length scale is called the internal Rossby deformation radius, and is given by R = ND/f in which N is the buoyancy frequency and D is a characteristic vertical length scale. At the equator, the effect of \beta (the meridional gradient of the Coriolis parameter) determines the equatorial Rossby deformation radius R=(c/\beta)^(1/2), and the equatorial internal Rossby deformation radius R=(ND/\beta)^(1/2).

### Coriolis effect

The tendency for linear motion to be deflected in a rotating (non-inertial) reference frame. In most geophysical circumstance, the horizontal deflection of horizontal motion is most significant. Zonal motion experiences an acceleration -f v and meridional motion experiences an accleration f u in which u and v are the zonal and meridional components of velocity, respectively, and f is the Coriolis parameter.

### Coriolis parameter

A measure of planetary rotation as a function of latitude. The parameter denoted by f varies with latitude \phi according to f= 2\Omega\sin\phi, in which \Omega is the frequency of planetary rotation.

### beta plane

An approximation, useful for the study of equatorial and midlatitude flow, whereby the Coriolis parameter is taken to vary linearly with latitude. Explicitly, the Coriolis parameter is given approximately by f \simeq f_0 + \beta y in which y is the meridional distance from some fixed latitude where the Coriolis parameter is f_0, and \beta (from which the beta plane'' gets its name) is the meridional gradient of f at that fixed latitude.

### beta effect

Denotes how fluid motion is affected by spatial changes of the Coriolis parameter, for example, due to the Earth's curvature. The term takes its name from the symbol \beta, representing the meridional gradient of the Coriolis parameter at a fixed latitude. A linearly sloping lower boundary to fluid in a rotating system also experiences the beta effect.

### hydrostatic balance

Describes a balance between vertical pressure gradient and buoyancy forces. Explicitly dp/dz = -\rho g. When this balance does not hold the fluid is non-hydrostatic.

### geostrophic balance

Describes a balance between Coriolis and horizontal pressure gradient forces. Explicitly, f v = (1/\rho) \partial p/\partial x and f u = -(1/\rho) \partial p/\partial y, in which f is the Coriolis parameter, u and v the zonal and meridional components of velocity, x and y the zonal and meridional co-ordinates, p the pressure, and \rho the density.

### buoyancy force

In a fluid with vertical density variation, the buoyancy force is the difference between the weight of an initial infinitessimal volume of fluid with the weight of a a fluid parcel of the same volume displaced to same location.

### reduced gravity

The effective change in the acceleration of gravity acting on one fluid in contact with a fluid of different density due to buoyancy forces. Explicitly, the reduced gravity is g'=g \Delta\rho/\rho_0, in which g is the acceleration of gravity, \rho_0 is the reference density, and \Delta\rho is the difference in density between the two fluids.

### buoyancy frequency

Also called the Brunt-Va'isa'la' frequency, or Va'isa'la' frequency. In a continuously stratified fluid, the buoyancy frequency is the natural frequency of vertical oscillation of fluid parcels. Explicitly the squared buoyancy frequency is N^2 = -(g/\rho) d\rho/dz, in which g is the acceleration due to gravity and \rho(z) is density as a function of height z.

### Brunt-Vaisala frequency

See buoyancy frequency.

### Vaisala frequency

See buoyancy frequency.

### Boussinesq approximation

An approximation to the dynamical equations of motion whereby density is assumed to be constant except in the buoyancy term, -g\rho', of the vertical velocity equation. The approximation is reasonable if the vertical extent of the dynamics being considered is much smaller than the density scale height - the height over which the density changes by a factor e. It is generally applicable to most oceanographic circumstances. If a system does not satisfy the Boussinesq approximation it is said to be non-Boussinesq.

### shallow water approximation

An approximation to the equations of motion whereby it is assumed the fluid is homogeneous and horizontal scales of interest are much larger than the depth of the fluid. Waves in this approximation are non-dispersive and have phase speed c=(gH)^(1/2) in which g is the acceleration due to gravity and H is the mean depth of the fluid.

### potential vorticity

A materially conserved quantity in adiabatic, frictionless flow that accounts for changes of vorticity due to vortex line stretching and Coriolis effects. In the shallow water approximation, the potential vorticity is q=(f+\zeta)/(H+\eta), in which f is the Coriolis parameter, \zeta is the relative vorticity, H is the mean fluid depth, and \eta is the surface elevation above the mean.

### wave packet

A collection of waves the amplitudes of which are largest for waves with frequency and wavelength in a range about some central frequency and wavelength.

### Gaussian wave packet

A collection of waves the amplitudes of which have a Gaussian dependence on wavenumber about some central wavenumber.

### evanescent level

A theoretical boundary between a region in the fluid where waves of some frequency are propagating and a region in the fluid where waves of the same frequency do not propagate (where they are evanescent). This is also called a critical level but is distinct from the critical level where the background flow has the same speed as the phase speed of the waves.

### power spectrum

The Fourier transform of the kinetic energy field. The power spectrum provides a useful diagnostic to measure a what length scales energy is concentrated and, in turbulent flow, over what length scales energy is transferred and dissipated.

### inertial range

The range of length scales over which energy is transferred and dissipation due to molecular viscosity is negligible. The power spectrum has power law behavior over the inertial range. In two dimensional turbulence the power spectrum is theoretically proportional to k^{-3} in which k is the wavenumber, and in three dimensional turbulence the power spectrum is theoretically proportional to k^{-5/3}. The latter is known as the Kolmogorov minus 5/3 law.

### Ozmidov scale

The horizontal extent of internal gravity waves, below which vertical overturning of waves may occur and above which overturning is inhibited by stratification. The length scale is proportional to \epsilon^(1/2)/N^(3/2) in which \epsilon is the flux of energy from large to small scales and N is the buoyancy frequency.

### Kolmogorov scale

Length scale of turbulent motion below which the effects of molecular viscosity are non-negligible. In three dimensional turbulence, the Kolmogorov scale is (\nu^2/\epsilon)^(1/4) in which \nu is the kinematic viscosity and \epsilon is the energy dissipation rate per unit mass.

### Garrett-Munk spectrum

An approximation to the internal gravity wave spectrum (for waves with large horizontal extent compared with the vertical extent) which is observed to have the same structure throughout the deep ocean. The energy density spectrum is proportional to Ef/\omega (\omega^2-f^2)^(-1/2) ~= Ef/\omega^2 (for \omega>>f) for waves of frequency \omega in which f is the Coriolis parameter and E is a nondimensional parameter empirically determined to be E ~= 6*10^(-5). For a wide range observations E has been found to vary by no more than a factor 2.

### eddy viscosity

An approximation to turbulent flow whereby the net effect of molecular diffusion enhanced by strain flows between eddies is parametrized by an eddy viscosity acting on large scale motion. Eddy viscosity may be taken as constant or dependent on the length scale of motion. The former case is equivalent to assuming that the Reynolds stresses are proportional to the gradients of the large scale flow velocity.

### turbulence

Describes fluid motion disturbed from its average behavior by random fluctuations over a range of temporal and spatial scales.

### Burger number

A dimensionless number comparing the buoyancy with Coriolis forces. Explicitly, the Burger number is Bu = N^2 D^2/(f^2 L^2) in which N is the buoyancy frequency, f is the Coriolis parameter, and D and L are characteristic vertical and horizontal length scales, respectively.

### Richardson number

A dimensionless number relating the ratio of buoyancy to inertial forces. In a stratified fluid with characteristic squared buoyancy frequency J,the bulk Richardson number is Ri = J/(U/L)^2 in which U and L are characteristic velocity and length scales. The gradient Richardson number is defined as a function of height for stratified parallel flows by Ri_g (z) = N^2(z)/(dU/dz)^2 in which U(z) is the mean horizontal velocity and N^2(z) is the squared buoyancy frequency as a function of height. The flux Richardson number is defined for stratified turbulent flows with perturbation horizontal and vertical velocity fields u' and w', respectively, by Ri_f = -(g/\rho_0)<\rho'w'>/[(dU/dz) ] which is the ratio of the rate of conversion to potential energy by the vertical flux of perturbation density \rho' to the rate of extraction of mean kinetic energy from the background horizontal velocity U(z). The flux Richardson number is also called the mixing efficiency.

### mixing efficiency

See Richardson number.

### Froude number

A dimensionless number relating the ratio of inertial to buoyancy forces applicable, in particular, to homogeneous shallow water flow, or two layer flow. Explicitly, in the shallow water approximation the Froude number is Fr=U^2/(gH) in which U is the characteristic velocity, H the characteristic fluid depth, and g the acceleration due to gravity.

### Reynolds number

Dimensionless number relating the ratio of inertial to viscous forces. Explicitly, the Reynolds number is Re=UL/\nu in which U and L are characteristic velocity and length scales, respectively, and \nu is the kinematic viscosity.

### Prandtl number

Dimensionless number relating the ratio of a fluid's capacity to diffuse momentum to its capacity to diffuse heat. Explicitly, the Prandtl number is Pr=\nu/\kappa in which \nu is the kinematic viscosity and \kappa is the thermal diffusivity.

### Pe'cle't number

Dimensionless number relating the ratio of inertial forces to thermal diffusion. Explicitly, the Pe'cle't number is Pe=UL/\kappa in which U and L are characteristic velocity and length scales, respectively, and \kappa is the thermal diffusivity.

### Schmidt number

A dimensionless number relating the ratio of inertial to molecular diffusive forces. Explicitly, Sc = UL/\kappa_D in which U and L are characteristic velocity and length scales, respectively, and \kappa_D is the diffusion constant of a solute in solution, such as salt in water.

### Rossby number

A dimensionless number relating the ratio of inertial to Coriolis forces. Explicitly, the Rossby number is Ro=U/(fL) in which U and L are characteristic velocity and horizontal length scales, respectively, and f is the Coriolis parameter at a fixed latitude. Flows with sufficiently small Rossby number are in geostrophic balance.

### Ekman number

A dimensionless number relating the ratio of eddy viscous forces to Coriolis forces. Explicitly the vertical Ekman number is E_v = 2 K_v/(fD^2), in which K_v is the vertical eddy viscosity, f the Coriolis parameter, and D the characteristic vertical length scale. The horizontal Ekman number is E_h = 2 K_h/(fL^2), in which K_h is the horizontal eddy viscosity, and L is the characteristic horizontal length scale. The Ekman number gives a measure of the rate at which stresses at a boundary (for example, wind induced stresses at the ocean surface) are communicated to the fluid interior.

### Rayleigh number

Expresses the ratio of the destabilizing effects of buoyancy to the stabilizing effects of diffusion of heat and momentum. Explicitly, Ra=g\beta \Delta T H^3/(\nu\kappa) in which g is the acceleration due to gravity, \beta is the thermal expansion coefficient, \Delta T is the temperature difference, h is the vertical length scale, \nu is the kinematic viscosity, and \kappa is the thermal diffusivity. The Rayleigh number is usually used to classify the stability of a fluid column heated from below, convection resulting when some relatively small value is exceeded.

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