506:
210:
501:{\displaystyle \overbrace {\rho {\Big (}\underbrace {\frac {\partial \mathbf {v} }{\partial t}} _{\begin{smallmatrix}{\text{Eulerian}}\\{\text{acceleration}}\end{smallmatrix}}+\underbrace {\mathbf {v} \cdot \nabla \mathbf {v} } _{\begin{smallmatrix}{\text{Advection}}\end{smallmatrix}}{\Big )}} ^{\text{Inertia (per volume)}}=\overbrace {\underbrace {-\nabla p} _{\begin{smallmatrix}{\text{Pressure}}\\{\text{gradient}}\end{smallmatrix}}+\underbrace {\mu \nabla ^{2}\mathbf {v} } _{\text{Viscosity}}} ^{\text{Divergence of stress}}+\underbrace {\mathbf {f} } _{\begin{smallmatrix}{\text{Other}}\\{\text{body}}\\{\text{forces}}\end{smallmatrix}}.}
1850:
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20:
631:, and the density of lake water by temperature. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a
189:
588:
Fluid that is less dense than its surroundings tends to rise until it has the same density as its surroundings. If there is not much energy input to the system, it will tend to become
105:
which cannot be solved analytically (yet). Therefore, further approximations are generally made in order to be able to solve these equations. First, the fluid is assumed to be
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1527:
511:
The left hand side represents the acceleration that a small parcel of fluid would experience in a reference frame that moved with the parcel (a
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46:, in its broadest meaning, refers to the fluid dynamics of naturally occurring flows, such as lava flows, oceans, and planetary
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1799:
1567:
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515:). In a stationary (Eulerian) frame of reference, this acceleration is divided into the local rate of change of velocity and
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69:(layering). The applications of geophysical fluid dynamics do not generally include the circulation of the
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1493:
737:
522:
The equation for energy conservation is essentially an equation for heat flow. If heat is transported by
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61:
Two physical features that are common to many of the phenomena studied in geophysical fluid dynamics are
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1986:
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2016:
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Soloviev, A.; Klinger, B. (2009). "Open ocean circulation". In Thorpe, Steve A. (ed.).
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717:
535:
523:
109:. Remarkably, this works well even for a highly compressible fluid like air as long as
1209:
Atmospheric and oceanic fluid dynamics : fundamentals and large-scale circulation
677:
If the pressure depends only on density and vice versa, the fluid dynamics are called
661:
In modeling buoyancy-driven flows, the Navier-Stokes equations are modified using the
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1951:
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Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
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The magnetic field of the earth: paleomagnetism, the core, and the deep mantle
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1981:
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665:. This ignores variations in density except where they are multiplied by the
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122:
1079:
Introduction to
Geophysical Fluid Dynamics: Physical and Numerical Aspects
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2011:
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Merrill, Ronald T.; McElhinny, Michael W.; McFadden, Phillip L. (1996).
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538:, also known as free convection, can occur. Convection in the Earth's
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681:. In the atmosphere, this corresponds to a lack of fronts, as in the
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89:
To describe the flow of geophysical fluids, equations are needed for
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690:
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997:
Encyclopedia of ocean sciences elements of physical oceanography
650:
The same buoyancy that gives rise to stratification also drives
31:. The arrows are wind vectors and the grey shading indicates an
2269:
1682:
654:. If the gravity waves occur within the fluid, they are called
55:
2631:
2450:
2229:
2184:
1253:
519:, a measure of the rate of flow in or out of a small region.
110:
51:
1076:
Cushman-Roisin, Benoit; Beckers, Jean-Marie (October 2011).
2063:
1432:
1211:(Reprint ed.). Cambridge: Cambridge University Press.
619:
The density of air is mainly determined by temperature and
558:(where the buoyancy is due to differences in salinity), or
19:
204:. Under these assumptions the Navier-Stokes equations are
965:
868:"Geophysical fluid dynamics: whence, whither and why?"
121:, meaning that there is a linear relation between the
1075:
213:
148:
117:
can be ignored. Second, the fluid is assumed to be a
35:
surface that highlights the surface inflow layer and
1109:
500:
183:
2479:North West Shelf Operational Oceanographic System
328:
223:
2776:
2469:Deep-ocean Assessment and Reporting of Tsunamis
994:
596:. Going upwards from the ground, these are the
567:
1521:
1269:
184:{\displaystyle \tau =\mu {\frac {du}{dx}},}
1528:
1514:
1276:
1262:
1133:Fundamentals of geophysical fluid dynamics
1130:
592:. On a large scale, Earth's atmosphere is
534:effects, for example hot air rising, then
1535:
1173:. Springer Science & Business Media.
929:
927:
925:
923:
921:
919:
899:
1168:
571:
18:
1116:( ed.). New York: Academic Press.
999:. London: Academic Press. p. 414.
933:
2777:
1800:one-dimensional Saint-Venant equations
1206:
1190:Lectures on Geophysical Fluid Dynamics
1187:
1152:Theoretical Geophysical Fluid Dynamics
959:
916:
866:Vallis, Geoffrey K. (24 August 2016).
865:
758:
1509:
1257:
1244:Geophysical Fluid Dynamics Laboratory
1149:
847:Geophysical Fluid Dynamics Laboratory
29:Geophysical Fluid Dynamics Laboratory
16:Dynamics of naturally occurring flows
2747:
1488:
1238:Woods Hole Oceanographic Institution
1135:. Cambridge: Cambridge Univ. Press.
1107:
1019:
647:(chemistry, including oxygenation).
1154:. Dordrecht: Springer Netherlands.
1047:"Barotropic and baroclinic defined"
1038:
685:. If there are fronts, the flow is
13:
2627:National Oceanographic Data Center
2054:World Ocean Circulation Experiment
1942:Global Ocean Data Analysis Project
1234:Geophysical Fluid Dynamics Program
1068:
550:. In the ocean, convection can be
407:
359:
296:
243:
233:
65:due to the planetary rotation and
14:
2811:
2474:Global Sea Level Observing System
1227:
526:, the heat flow is governed by a
462:
372:
311:
257:
2757:
2746:
2737:
2736:
1932:Geochemical Ocean Sections Study
1848:
1837:
1487:
1476:
1475:
1463:
1112:Atmosphere : Ocean dynamics
1051:Haby's weather forecasting hints
1044:
452:
417:
300:
289:
237:
33:equivalent potential temperature
2662:Ocean thermal energy conversion
2385:Vine–Matthews–Morley hypothesis
594:divided into a series of layers
84:
1283:
1013:
988:
859:
1:
1131:McWilliams, James C. (2006).
852:
828:
805:
513:Lagrangian frame of reference
1922:El Niño–Southern Oscillation
1892:Craik–Leibovich vortex force
1648:Luke's variational principle
1207:Vallis, Geoffrey K. (2006).
713:Kelvin's circulation theorem
689:, and instabilities such as
564:, a combination of the two.
530:equation. If there are also
77:, or fluid phenomena in the
7:
1423:Precession of the equinoxes
1192:. Oxford University Press.
840:
696:
568:Buoyancy and stratification
10:
2816:
1987:Ocean dynamical thermostat
1835:
1340:Geophysical fluid dynamics
1171:Geophysical Fluid Dynamics
1022:"Earth's Upper Atmosphere"
1020:Zell, Holly (2015-03-02).
667:gravitational acceleration
546:that is the source of the
101:. The former leads to the
73:, which is the subject of
44:Geophysical fluid dynamics
2732:
2571:
2545:
2522:Ocean acoustic tomography
2507:
2459:
2398:
2335:Mohorovičić discontinuity
2293:
2165:
2062:
1927:General circulation model
1857:
1563:Benjamin–Feir instability
1543:
1457:
1441:
1373:
1312:
1291:
1169:Pedlosky, Joseph (2012).
2652:Ocean surface topography
2027:Thermohaline circulation
2017:Subsurface ocean current
1957:Hydrothermal circulation
1790:Wave–current interaction
1568:Boussinesq approximation
1248:University of Washington
1108:Gill, Adrian E. (1982).
800:
780:Thermohaline circulation
663:Boussinesq approximation
623:content, the density of
91:conservation of momentum
2689:Sea surface temperature
2672:Outline of oceanography
1867:Atmospheric circulation
1805:shallow water equations
1795:Waves and shallow water
1688:Significant wave height
1350:Near-surface geophysics
943:Oxford University Press
939:Physical Fluid Dynamics
765:Atmospheric circulation
743:Hydrostatic equilibrium
738:Taylor–Proudman theorem
103:Navier–Stokes equations
2684:Sea surface microlayer
2049:Wind generated current
1398:Earth's magnetic field
892:10.1098/rspa.2016.0140
585:
576:Internal waves in the
548:Earth's magnetic field
502:
185:
99:conservation of energy
40:
2800:Physical oceanography
2517:Deep scattering layer
2499:World Geodetic System
2007:Princeton Ocean Model
1887:Coriolis–Stokes force
1537:Physical oceanography
1470:Geophysics portal
1393:Earth's energy budget
1188:Salmon, Rick (1998).
575:
503:
186:
63:rotation of the fluid
22:
2785:Atmospheric dynamics
2537:Underwater acoustics
2097:Perigean spring tide
1962:Langmuir circulation
1673:Rossby-gravity waves
1150:Monin, A.S. (1990).
441:Divergence of stress
341:Inertia (per volume)
211:
146:
2699:Science On a Sphere
2305:Convergent boundary
1977:Modular Ocean Model
1937:Geostrophic current
1653:Mild-slope equation
1442:Related disciplines
1408:Geothermal gradient
1082:(Second ed.).
941:(Second ed.).
884:2016RSPSA.47260140V
795:Subsurface currents
759:General circulation
728:Geostrophic current
627:by temperature and
95:Newton's second law
2355:Seafloor spreading
2345:Outer trench swell
2310:Divergent boundary
2210:Continental margin
2195:Carbonate platform
2092:Lunitidal interval
1325:Geophysical survey
878:(2192): 20160140.
718:Vorticity equation
586:
554:(driven by heat),
536:natural convection
498:
494:
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23:Model forecast of
2772:
2771:
2764:Oceans portal
2724:World Ocean Atlas
2714:Underwater glider
2657:Ocean temperature
2320:Hydrothermal vent
2285:Submarine volcano
2220:Continental shelf
2200:Coastal geography
2190:Bathymetric chart
2072:Amphidromic point
1760:Wave nonlinearity
1618:Infragravity wave
1503:
1502:
1418:Mantle convection
1161:978-94-009-1880-1
1093:978-0-12-088759-0
981:978-0-12-491246-5
580:(photographed by
578:Strait of Messina
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2679:Pelagic sediment
2617:Marine pollution
2411:Deep ocean water
2280:Submarine canyon
2215:Continental rise
2107:Rule of twelfths
2022:Sverdrup balance
1952:Humboldt Current
1877:Boundary current
1852:
1841:
1658:Radiation stress
1628:Iribarren number
1603:Equatorial waves
1558:Ballantine scale
1553:Airy wave theory
1530:
1523:
1516:
1507:
1506:
1491:
1490:
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1413:Gravity of Earth
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790:Sverdrup balance
785:Boundary current
733:Geostrophic wind
673:
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2484:Sea-level curve
2455:
2394:
2380:Transform fault
2330:Mid-ocean ridge
2296:
2289:
2255:Oceanic plateau
2161:
2147:Tidal resonance
2117:Theory of tides
2058:
1967:Longshore drift
1917:Ekman transport
1853:
1847:
1846:
1845:
1844:
1843:
1842:
1833:
1785:Wave turbulence
1718:Trochoidal wave
1643:Longshore drift
1539:
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1388:Coriolis effect
1383:Chandler wobble
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1345:Mineral physics
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1069:Further reading
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989:
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860:
855:
843:
831:
824:(Poincaré wave)
808:
803:
761:
703:Coriolis effect
699:
669:
643:(salinity), or
639:(temperature),
570:
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119:Newtonian fluid
87:
27:created by the
25:Hurricane Mitch
17:
12:
11:
5:
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2797:
2795:Fluid dynamics
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2787:
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2754:
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2704:Stratification
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2649:
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2594:Color of water
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2589:Benthic lander
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2496:
2494:Sea level rise
2491:
2489:Sea level drop
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2325:Marine geology
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2265:Passive margin
2262:
2260:Oceanic trench
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2019:
2014:
2009:
2004:
1999:
1994:
1992:Ocean dynamics
1989:
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1882:Coriolis force
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1335:Geomathematics
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1228:External links
1226:
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1218:978-0521849692
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972:Academic Press
958:
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935:Tritton, D. J.
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67:stratification
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2612:Marine energy
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2579:Acidification
2577:
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2532:SOFAR channel
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2340:Oceanic crust
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2315:Fracture zone
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2250:Oceanic basin
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2180:Abyssal plain
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2110:
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2100:
2098:
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2090:
2088:
2087:Internal tide
2085:
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2018:
2015:
2013:
2010:
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1982:Ocean current
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1623:Internal wave
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1573:Breaking wave
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1304:Geophysicists
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1201:
1199:9780195355321
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1180:9781468400717
1176:
1172:
1167:
1163:
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1142:9780521856379
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1016:
1008:
1006:9780123757210
1002:
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952:0-19-854489-8
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869:
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833:
832:
823:
822:Sverdrup wave
820:
818:
815:
813:
810:
809:
796:
793:
791:
788:
786:
783:
781:
778:
776:
773:
771:
770:Ocean current
768:
766:
763:
762:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
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721:
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709:
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704:
701:
700:
694:
692:
688:
684:
680:
675:
672:
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664:
659:
657:
653:
652:gravity waves
648:
646:
642:
638:
634:
630:
626:
622:
617:
615:
611:
607:
603:
599:
595:
591:
583:
579:
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557:
553:
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541:
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529:
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518:
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456:
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434:
422:
411:
403:
396:
366:
362:
356:
345:
334:
305:
293:
281:
251:
246:
218:
207:
206:
205:
203:
178:
172:
169:
164:
161:
155:
152:
149:
142:
141:
140:
137:
133:
124:
120:
116:
112:
108:
104:
100:
96:
92:
82:
80:
79:magnetosphere
76:
72:
68:
64:
59:
57:
53:
49:
45:
38:
34:
30:
26:
21:
2719:Water column
2667:Oceanography
2642:Observations
2637:Explorations
2607:Marginal sea
2600:
2558:OSTM/Jason-2
2390:Volcanic arc
2365:Slab suction
2082:Head of tide
1972:Loop Current
1912:Ekman spiral
1698:Stokes drift
1608:Gravity wave
1583:Cnoidal wave
1492:
1480:
1461:
1428:Seismic wave
1339:
1330:Geomagnetism
1208:
1189:
1170:
1151:
1132:
1111:
1097:. Retrieved
1078:
1054:. Retrieved
1050:
1045:Haby, Jeff.
1040:
1029:. Retrieved
1025:
1015:
996:
990:
967:
961:
938:
875:
871:
861:
835:Gravity wave
748:Ekman spiral
723:Thermal wind
676:
670:
660:
649:
618:
610:thermosphere
602:stratosphere
587:
561:thermohaline
559:
555:
551:
521:
510:
272:acceleration
193:
135:
123:shear stress
88:
85:Fundamentals
60:
43:
42:
2709:Thermocline
2426:Mesopelagic
2399:Ocean zones
2370:Slab window
2235:Hydrography
2175:Abyssal fan
2142:Tidal range
2132:Tidal power
2127:Tidal force
2012:Rip current
1947:Gulf Stream
1907:Ekman layer
1897:Downwelling
1872:Baroclinity
1859:Circulation
1755:Wave height
1745:Wave action
1728:megatsunami
1708:Stokes wave
1668:Rossby wave
1633:Kelvin wave
1613:Green's law
1320:Geodynamics
1099:October 14,
817:Rossby wave
812:Kelvin wave
753:Ekman layer
708:Circulation
693:can occur.
637:thermocline
635:(density),
621:water vapor
598:troposphere
542:drives the
115:shock waves
75:geodynamics
48:atmospheres
2790:Geophysics
2779:Categories
2647:Reanalysis
2546:Satellites
2527:Sofar bomb
2375:Subduction
2350:Ridge push
2245:Ocean bank
2225:Contourite
2152:Tide gauge
2137:Tidal race
2122:Tidal bore
2112:Slack tide
2077:Earth tide
1997:Ocean gyre
1817:Wind setup
1812:Wind fetch
1775:Wave setup
1770:Wave radar
1765:Wave power
1663:Rogue wave
1593:Dispersion
1360:Seismology
1285:Geophysics
1031:2017-02-20
853:References
829:Baroclinic
806:Barotropic
687:baroclinic
679:barotropic
645:chemocline
633:pycnocline
606:mesosphere
590:stratified
540:outer core
524:conduction
54:and other
2509:Acoustics
2461:Sea level
2360:Slab pull
2297:tectonics
2205:Cold seep
2167:Landforms
2044:Whirlpool
2039:Upwelling
1822:Wind wave
1750:Wave base
1678:Sea state
1598:Edge wave
1588:Cross sea
1403:Geodynamo
1376:phenomena
1374:Physical
1313:Subfields
1056:17 August
641:halocline
625:sea water
614:exosphere
544:geodynamo
528:diffusion
517:advection
457:⏟
435:⏞
429:Viscosity
423:⏟
408:∇
404:μ
367:⏟
360:∇
357:−
335:⏞
317:Advection
306:⏟
297:∇
294:⋅
252:⏟
244:∂
234:∂
219:ρ
202:viscosity
156:μ
150:τ
2742:Category
2694:Seawater
2421:Littoral
2416:Deep sea
2275:Seamount
2157:Tideline
2102:Rip tide
2032:shutdown
2002:Overflow
1735:Undertow
1578:Clapotis
1482:Category
1292:Overview
937:(1990).
910:27616918
841:See also
697:Rotation
691:cyclones
629:salinity
532:buoyancy
387:gradient
378:Pressure
263:Eulerian
130:and the
2752:Commons
2622:Mooring
2572:Related
2563:Jason-3
2553:Jason-1
2436:Pelagic
2431:Oceanic
2406:Benthic
1723:Tsunami
1693:Soliton
1494:Commons
1449:Geodesy
1299:Outline
901:5014103
880:Bibcode
683:tropics
552:thermal
200:is the
56:planets
39:region.
37:eyewall
2441:Photic
2270:Seabed
1683:Seiche
1215:
1196:
1177:
1158:
1139:
1120:
1090:
1003:
978:
949:
908:
898:
612:, and
556:haline
486:forces
197:μ
194:where
132:strain
127:τ
97:) and
71:mantle
2632:Ocean
2601:Alvin
2451:Swash
2295:Plate
2240:Knoll
2230:Guyot
2185:Atoll
2064:Tides
1827:model
1713:Swell
1545:Waves
801:Waves
582:ASTER
468:Other
111:sound
52:Earth
50:, on
2599:DSV
2584:Argo
2446:Surf
1902:Eddy
1433:Tide
1213:ISBN
1194:ISBN
1175:ISBN
1156:ISBN
1137:ISBN
1118:ISBN
1101:2010
1088:ISBN
1058:2017
1026:NASA
1001:ISBN
976:ISBN
947:ISBN
906:PMID
477:body
113:and
93:(or
896:PMC
888:doi
876:472
2781::
1086:.
1049:.
1024:.
974:.
970:.
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1126:.
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882::
671:g
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453:f
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418:v
412:2
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363:p
346:=
329:)
301:v
290:v
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247:t
238:v
224:(
179:,
173:x
170:d
165:u
162:d
153:=
136:u
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
