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Taylor Math - Fluid dynamics Glossary Category: Mathematics and statistics > Fluid dynamics Date & country: 13/09/2007, CAN Words: 193

isobath
A contour of equal depth in a body of water, represented on a bathymetric chart.

isobathytherm
A line or surface showing the depths in oceans or lakes at which points have the same temperature. Isobathytherms are usually drawn to show cross sections of the water-mass.

isohaline
Of equal or constant salinity. A line on a chart connecting all points of equal salinity; an isopleth of salinity.

Japan current
Same as Kuroshio current.

internal wave
See internal gravity wave.

Irminger current
An ocean current that is one of the terminal branches of the Gulf Stream system (part of the northern branch of the North Atlantic current ); it flows toward the west off the south coast of Iceland. A small portion of the water of the Irminger Current bends around the west coast of Iceland but the greater amount turns south and becomes more or less mixed with the water of the east Greenland current .

inertio-gravity wave
An internal gravity wave propagating under the influence of both buoyancy and Coriolis forces. The dispersion relation is given by frequency \omega = +/- (N k_h + f m)/

internal gravity wave
Also called 'internal wave'. A wave that propagates in density stratified fluid under the influence of buoyancy forces. Internal gravity waves are also called internal waves and gravity waves. The dispersion relation is given by frequency \omega = +/- N k_h/

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.

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 direct…

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.

ice shelf
A thick ice formation with a fairly level surface, formed along a polar coast and in shallow bays and inlets, where it is fastened to the shore and often reaches bottom. It may grow hundreds of miles out to sea. It is usually an extension of land ice , and the seaward edge floats freely in deep water. The calving of an ice shelf forms tabular icebergs and ice islands. Also called shelf ice.

Humboldt current
Same as Peru current.

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

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 she…

halocline
A vertical salinity 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 haloclines in the ocean are either seasonal, due to fresh water inputs, or permanent.

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.

Gulf Stream
A warm, well-defined, swift, relatively narrow, ocean current which originates where the Florida current and the Antilles current begin to curve eastward from the continental slope off Cape Hatteras, North Carolina. East of the Grand Banks the Gulf Stream meets the cold Labrador current , and the two flow eastward separated by the cold wall . At about 40=AE$=AFN latitude, 50=AE$=AFW longitude, the Gulf Stream becomes the North Atlantic current which continues east-northeastward across the ocean.…

Guinea current
An ocean current flowing along the south coast of northwest Africa into the Gulf of Guinea. The Guinea current originates as an equatorial countercurrent flowing east across the Atlantic.

Guiana current
An ocean current flowing northwestward along the northern coast of South America (the Guianas). The Guiana current is an extension of the south equatorial current (flowing west across the ocean between the equator and 20 degrees), which crosses the equator and approaches the coast of South America. Eventually, it is joined by part of the north equatorial current and becomes, successively, the Caribbean current and the Florida current .

gravity wave
Waves that propagate under the influence of buoyancy forces. Gravity waves include surface gravity waves, such as waves on the surface of the ocean, interfacial gravity waves, such as waves at the interface between fresh surface water and underlying salty ocean water, and internal gravity waves which propagate vertically as well as horizontally in density stratified fluid.

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.

gradient current
In oceanography, a current associated with horizontal pressure gradients in the ocean and determined by the condition that the pressure force due to the distribution of mass balances the coriolis force due to the earth's rotation. The gradient current corresponds to the geostrophic wind in meteorology. In practice, the distribution of density is determined by measurements of salinity and temperature at a series of depths in a number of positions. From this the geopotential topography of any isob…

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.

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

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…

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.

feeling bottom
The action of a deep-water wave on running into shoal water and beginning to be influenced by the bottom.

fetch
The area in which ocean waves are generated by the wind. It is generally delineated by coast lines, fronts , or areas of wind curvature or divergence.

Florida current
All of the northward-moving water from the Straits of Florida to a point off Cape Hatteras where the current ceases to follow the continental slope. It is one of the swiftest of ocean currents (flowing at a rate of 2 to 5 knots). The Florida current can be traced directly back to the Yucatan Channel because the water flowing through the channel continues on the shortest route to the Straits of Florida and only a small amount sweeps into the Gulf of Mexico, later to join the Florida current. Afte…

fathom curve
Same as isobath.

falling tide
The portion of the tide cycle between high water and the following low water. Sometimes called ebb tide.

fathom
The common unit of depth in the ocean, equal to six feet. It is also sometimes used in expressing horizontal distances, in which case 100 fathoms make one cable or very nearly one-tenth nautical mile .

equilibrium solar tide
A theoretical concept in analogy to Laplace's oceanic equilibrium tide; roughly, the form of the atmosphere determined solely by gravitational forces in the absence of any rotation of the earth relative to the sun.

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.

Falkland current
In the Atlantic Ocean, an ocean current flowing northward along the Argentine coast. The Falkland current originates as a branch of the antarctic circumpolar current . At about 35 degrees it is joined by the Brazil current , both flowing east across the ocean as the South Atlantic current .

equatorial undercurrent
An ocean current flowing eastward (counter to and between the westward-flowing north equatorial current and south equatorial current ) through all the oceans. In the Atlantic Ocean, it flows east across the ocean between the north and south equatorial currents across the full width of the ocean in northern summer, and across the eastern half of the ocean in northern winter. It eventually becomes the Guinea current . In the Pacific Ocean, it is one of the swiftest ocean currents; it flows east ac…

equatorial tide
Tide occurring when the moon is near the equator; diurnal inequality is at a minimum.

equatorial Rossby wave
An equatorially trapped westward propagating wave that moves due to isentropic gradients of potential vorticity. The meridional velocity of the n'th mode of these waves has the form exp(-y^2/2R^2) H_n(y/R), in which y is the meridional distance from the equator, R is the equatorial Rossby deformation radius, and H_n is the n'th Hermite polynomial. In the shallow water approximation R^2=(gH)^(1/2)/\beta in which, \beta is the meridional gradient of the Coriolis parameter at the equator, g is the …

equatorial Poincare wave
By analogy with Poincare waves in a channel, these are inertio-gravity waves confined to a region about the equator. The meridional velocity of the n'th mode of these waves has meridional structure of the form exp(-y^2/2R^2) H_n(y/R), in which y is the meridional distance from the equator, R is the equatorial Rossby deformation radius, and H_n is the n'th Hermite polynomial. In the shallow water approximation R^2=(gH)^(1/2)/\beta in which, \beta is the meridional gradient of the Coriolis paramet…

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 mov…

El Nino
A warm ocean current setting south along the coast of Ecuador, so called because it generally develops just after Christmas. In exceptional years, concurrently with a southerly shift in the tropical rain belt, the current may extend along the coast of Peru to 12=AE$=AFS. When this occurs, plankton and fish are killed in the coastal waters and a phenomenon somewhat like the red tide of Florida results.

equatorial Kelvin wave
Eastward propagating wave centered about the equator with zonal but no meridional velocity. The zonal velocity has a Gaussian meridional structure centered about the equator with standard deviation equal to the equatorial Rossby deformation radius. In the shallow water approximation the waves are non-dispersive with frequency \omega = +/- c k, in which k is the zonal wavenumber and the phase speed c= (gH)^(1/2) with g the acceleration due to gravity and H the mean fluid depth. The equatorial Ros…

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 exa…

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.

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.

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.

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 …

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.

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.

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

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 …

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 .

deformation radius
See Rossby deformation radius.

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.

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

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.

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.

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

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

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.

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

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.

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.

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 .

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 .

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

Burgers vorte
xExact 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.

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.

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.

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.

Brunt-Vaisala frequency
See buoyancy frequency.

Brazil current
The warm ocean current flowing southward along the Brazilian coast. Its origin is in the westward flowing south equatorial current , part of which turns south and flows along the South American coast as the Brazil current, a tongue of water of high temperature and high salinity. At about 35=AE$=AFS it meets the Falkland (Malvinas) current , the two turning east and crossing the ocean as the South Atlantic current .

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…

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…

bittern region
The liquid remaining after sea water has been concentrated by evaporation until salt has crystallized.

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.

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

bathymetric chart
A map delineating the form of the bottom of a body of water, usually be means of depth contours ( isobaths ).

bathymetry
The study of water depths.

Benguela current
The northward flowing current along the west coast of Africa; it is one of the swiftest of ocean currents, the strongest current in the South Atlantic. It is a continuation of the South Atlantic current . Proceeding toward the equator, the Benguela current gradually leaves the coast and continues as the northern portion of the south equatorial current .

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.

baroclinic wave
Describes the synoptic scale disturbance that grows in mid-latitudes due to baroclinic instability.

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.

Antilles current
An ocean current, the northern branch of the north equatorial current flowing along the northern side of the Great Antilles carrying water that is identical with that of the Sargasso Sea. The Antilles current eventually joins the Florida current (after the latter emerges from the Straits of Florida) to form the Gulf Stream .

Antarctic circumpolar current
Also called west wind drift, the ocean current with the largest volume transport (approximately 110 x 10[s] m[s]/sec), and the swiftest current; it flows from west to east through all the oceans around the Antarctic Continent. It is locally deflected from its course, partly by the distribution of land and sea and partly by the submarine topography. Beside the bends that are associated with the bottom topography, the effects of the distribution of land and sea and of the currents in the adjacent …

amphidromic point
A point on a chart of cotidal lines from which the cotidal lines radiate.

Alaska current
An ocean current, the northward flowing division of the Aleutian current . It circulates cyclonically around the Gulf of Alaska; part of the water passes between the Aleutian Islands into the Bering Sea from which it emerges as the Oyashio , and part rejoins the Aleutian current. It enters the Gulf of Alaska along the American west coast and, since it comes from the south, it has the character of a warm current in spite of the fact that it carries subarctic water. It therefore exercises an influ…

Agulhas current
Also called Agulhas stream, a generally southwestward-flowing ocean current of the Indian Ocean; one of the swiftest of ocean currents. Throughout the year, part of the south equatorial current turns south along the east coast of Africa and feeds the strong Agulhas current. To the south of latitude 30=AE$=AFS, the Agulhas current is a well-defined and narrow current that extends less than 100 km from the coast. To the south of South Africa the greatest volume of its waters bends sharply to the s…