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

west wind drift
Same as antarctic circumpolar current.

Yanai wave
See Rossby-gravity wave.

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

T-S diagram
Abbreviation for temperature-salinity diagram.

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.

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.

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.

vbrave west winds
A nautical term for the strong and rather persistent westerly winds over the oceans in temperate latitudes. They occur between latitudes 40 and 65 in the northern hemisphere and 35 to 65 in the southern hemisphere, where they are more regular and are strongest between 40 and 50 (roaring forties). They are associated with the strong pressure gradient on the equatorial side of the frequent depressions passing eastward in sub-polar temperate latitudes; hence they fluctuate mainly between southwest …

vblind roller
Long high swells which have increased in height, almost to the breaking point, as they pass over shoals or run in shallow water

vamphidromic region
An oceanic region whose cotidal lines radiate from one amphidromic point.

Vaisala frequency
See buoyancy frequency.

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 permanen…

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.

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

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 ti…

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.

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.

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

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.

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

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.

surge
Water transported up a beach by breaking waves.

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.

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…

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 lati…

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

Somali current
An ocean current flowing southwestward along the coast of Somaliland (East Africa) as a continuation of the north equatorial current . In summer (Northern Hemisphere), when the north equatorial current and the equatorial countercurrent are replaced by an eastward flowing monsoon current , the Somali current reverses its direction and flows north from about 10=AE$=AFS.

shear instability
See Kelvin-Helmholtz instability.

shelf ice
Same as ice shelf.

solitary wave
A hump-shaped wave of permanent form. Solitary waves are well known for their tendency to travel long distances without dispersion and, despite being large amplitude (so that linear superposition principles do not apply) colliding waves effectively pass through each other.

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.

semidiurnal tide
A tide having two high waters and two low waters each lunar day , with little or no diurnal inequality . This applies equally to solar tides and to atmospheric tides .

seiche
An oscillation of a fluid body in response to a disturbing force having the same frequency as the natural frequency of the fluid system. Tides are now considered to be seiches induced primarily by the periodic forces caused by the sun and moon.

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.

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 .

salinity
A measure of the quantity of dissolved salts in sea water. It is formally defined as the total amount of dissolved solids in sea water in parts per thousand ([s]) by weight when all the carbonate has been converted to oxide, the bromide and iodide to chloride, and all organic matter is completely oxidized. These qualifications result from the chemical difficulty in drying in salts in sea water. In practice, salinity is not determined directly but is computed from chlorinity, electrical conductiv…

rotary_current
A tidal current that changes direction progressively through 360 degreesduring a tidal cycle.

Rossby-gravity wave
An equatorial wave whose dispersion relation is asymptotic to that for equatorial Kelvin waves for large positive (eastward) zonal wavenumbers and asymptotic to equatorial Rossby waves for large negative (westward) zonal wavenumbers. Rossby-gravity waves are also called Yanai waves and ``mixed'' Rossby-gravity waves. In the shallow water approximation, the dispersion relationship is given by frequency \omega= k c [1-(1+4\beta/(k^2 c))^(1/2)]/2, in which k is the zonal wavenumber, \beta is the me…

Rossby wave
A large scale, westward propagating wave that moves due to isentropic gradients of potential vorticity. Rossby waves are also called planetary waves. In particular, in the shallow water approximation, the waves move due to the variation of the Coriolis parameter with latitude, what is known as the ``beta''-effect. The dispersion relation in this approximation has frequency \omega = -\beta k/(k^2+l^2) in which \beta is the meridional gradient of the Coriolis parameter, and k and l are the zonal a…

Rossby radius
See Rossby deformation radius.

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.

Rossby deformation radius
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 …

rip tide
Also called rip current.

rollers
Swells coming from a great distance and forming large breakers on exposed coasts. They are best known on the islands of St. Helena and Ascension in the South Atlantic Ocean during the months from December to April, when they come from the northwest. = They arrive, often in calm weather, with practically no warning, and are dangerous to shipping. Rollers also occur at Fernando do Noronha, Tristan da Cunha, and on the coasts of West Africa, Peru, and the East Indies.

rip current
A strong water-surface current of short duration flowing seaward from the shore; the return movement of water piled up on the shore by incoming waves and wind. It usually appears as a visible band of agitated water; and, with the outward movement concentrated in a limited band, its velocity is somewhat accentuated. A rip current is often miscalled a ``rip tide.'' To swimmers, the phenomenon is known as ``undertow.''

reversing current
A tidal current which flows alternately in approximately opposite directions, with periods of slack water at each reversal. Such currents occur chiefly in restricted channels; open sea areas generally have rotary currents .

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.

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…

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.

red tide
A growth of dinoflagellates (single-celled plant-like animals) in surface waters in such quantities as to color the sea red and kill fish.

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 belo…

raoring forties
A popular nautical term for the stormy ocean regions between 40 degreesand 50 degreeslatitude. It nearly always refers to the southern hemisphere, where there is an almost completely uninterrupted belt of ocean with strong prevailing westerly winds.

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

pycnocline
A vertical density gradient (as determined by the vertical temperature and salinity gradients and equation of state) 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 pycnoclines in the ocean are either seasonal, due to heating of the surface water in summer or fresh water inputs, or permanent.

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.

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.

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.

point vorte
xIdealized 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.

potential temperature
In oceanography, the temperature that a water sample would attain if raised adiabatically to the sea surface. For the deepest points of the ocean, which are just over 10,000 meters, the adiabatic cooling would be less than 1.5=AE$=AFC.

planetary wave
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 w…

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 port…

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

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.

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.

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 .

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.

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 principa…

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 .

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 .

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 de…

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 n…

mixing efficiency
See Richardson number.

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.

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.

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

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.

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.

meddy
See Mediterranian lenses.

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.

Labrador current
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 .

line vorte
xIdealized 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.

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

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 w…

Kuroshio current
An ocean current flowing northeastward from Formosa to Riukiu and then close to the coast of Japan as far as latitude 35 degrees; part of the Kuroshio system . It is a density-distribution type current, and one of the swiftest of all ocean currents. Also called the Japan current. The Kuroshio is the northward flowing part of the north equatorial current (which divides east of Philippines). Beyond latitude 35=AE$=AFN, where it leaves the coast of Japan, it branches to form two sections of the Kur…

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 .

Kirchhoff vorte
xAn 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.

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.

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 she…

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.

Kelvin wave
Near a boundary in a rotating system, a Kelvin wave propagates with wave crests perpendicular to the side wall and wave height greatest at the side wall to the right of an observer looking in the direction of wave propagation. The wave height decreases exponentially from the side wall with e-folding length scale equal to the Rossby deformation radius c/f, in which f is the Coriolis parameter and c is the phase speed of the wave in the along boundary direction. In the shallow water approximation …