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as they would be if there were no externally generated field acting unequally at the given point and at the center of the reference body. The externally generated field is usually that produced by a perturbing third body, often the Sun or the Moon in the frequent example-cases of points on or above the Earth's surface in a geocentric reference frame.)
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1688:(and everything on its surface) is in free fall. When the force on the far particle is subtracted from the force on the near particle, this first term cancels, as do all other even-order terms. The remaining (residual) terms represent the difference mentioned above and are tidal force (acceleration) terms. When ∆
665:
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The relationship of an astronomical body's size, to its distance from another body, strongly influences the magnitude of tidal force. The tidal force acting on an astronomical body, such as the Earth, is directly proportional to the diameter of the Earth and inversely proportional to the cube of the
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is used to describe the forces due to tidal acceleration. Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant. (In other words, the comparison is with the conditions at the given point
205:
The tidal force corresponds to the difference in Y between two points on the graph, with one point on the near side of the body, and the other point on the far side. The tidal force becomes larger, when the two points are either farther apart, or when they are more to the left on the graph, meaning
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can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such
705:
Figure 8: Graphic of tidal forces. The top picture shows the gravity field of a body to the right (not shown); the lower shows their residual gravity once the field at the centre of the sphere is subtracted; this is the tidal force. For visualization purposes, the top arrows may be assumed as equal
142:
When a body (body 1) is acted on by the gravity of another body (body 2), the field can vary significantly on body 1 between the side of the body facing body 2 and the side facing away from body 2. Figure 2 shows the differential force of gravity on a spherical body (body 1) exerted by another body
561:
When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy as heat. In the case for the Earth, and Earth's Moon, the loss of rotational kinetic energy results in a gain of about 2 milliseconds per century. If the body is
209:
For example, even though the Sun has a stronger overall gravitational pull on Earth, the Moon creates a larger tidal bulge because the Moon is closer. This difference is due to the way gravity weakens with distance: the Moon's closer proximity creates a steeper decline in its gravitational pull as
154:
is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another. These strains would not occur if the gravitational field were uniform, because a
78:
of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearer side is attracted more strongly than the farther side. The difference is positive in the near side and negative in the far side, which causes a body to get stretched.
125:
Earth's rotation accounts further for the occurrence of two high tides per day on the same location. In this figure, the Earth is the central black circle while the Moon is far off to the right. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on
558:, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon.
585:
Tidal forces contribute to ocean currents, which moderate global temperatures by transporting heat energy toward the poles. It has been suggested that variations in tidal forces correlate with cool periods in the global temperature record at 6- to 10-year intervals, and that
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Gravitational attraction is inversely proportional to the square of the distance from the source. The attraction will be stronger on the side of a body facing the source, and weaker on the side away from the source. The tidal force is proportional to the difference.
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The Earth is 81 times more massive than the Moon, the Earth has roughly 4 times the Moon's radius. As a result, at the same distance, the tidal force of the Earth at the surface of the Moon is about 20 times stronger than that of the Moon at the Earth's surface.
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you move across Earth (compared to the Sun's very gradual decline from its vast distance). This steeper gradient in the Moon's pull results in a larger difference in force between the near and far sides of Earth, which is what creates the bigger tidal bulge.
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of the gravitational acceleration at the center of the body (due to the given externally generated field) from the gravitational acceleration (due to the same field) at the given point. Correspondingly, the term
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at the Earth's surface. Hence the tide-raising force (acceleration) due to the Sun is about 45% of that due to the Moon. The solar tidal acceleration at the Earth's surface was first given by Newton in the
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to 1 N, 2 N, and 3 N (from left to right); the resulting bottom arrows would equal, respectively, -1 N (negative, thus 180-degree rotated), 0 N (invisible), and 1 N. See Figure 2 for a more detailed version
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The tidal accelerations at the surfaces of planets in the Solar System are generally very small. For example, the lunar tidal acceleration at the Earth's surface along the Moon–Earth axis is about
168:
distance from another body producing a gravitational attraction, such as the Moon or the Sun. Tidal action on bath tubs, swimming pools, lakes, and other small bodies of water is negligible.
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In the case of an infinitesimally small elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an
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Figure 3 is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance (
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546:'s rings are inside the orbits of its principal moons. Tidal forces oppose gravitational coalescence of the material in the rings to form moons.
2646:), and wrote that the force to raise the sea along the Sun-Earth axis is "twice as great" (i.e., 2 to 38604600) which comes to about 0.52 × 10
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variations in tidal forcing may contribute to millennial climate changes. No strong link to millennial climate changes has been found to date.
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95:): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.
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1619:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}\pm {\hat {r}}~G~{\frac {2M}{R^{2}}}~{\frac {\Delta r}{R}}+\cdots }
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in a straight line under the influence of a gravitational field while still being influenced by (changing) tidal acceleration.
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Thus, the tidal force is also known as the differential force, residual force, or secondary effect of the gravitational field.
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calculation. In the plane perpendicular to that axis, the tidal acceleration is directed inwards (towards the center where ∆
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1696:, the terms after the first residual term are very small and can be neglected, giving the approximate tidal acceleration
3152:
1361:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}~{\frac {1}{\left(1\pm {\frac {\Delta r}{R}}\right)^{2}}}}
1079:. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass
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field at the surface of the Earth is known (along with another and weaker differential effect due to the Sun) as the
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Newton put the force to depress the sea at places 90 degrees distant from the Sun at "1 to 38604600" (in terms of
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cause strains on both bodies and may distort them or even, in extreme cases, break one or the other apart. The
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Figure 3: Graph showing how gravitational attraction drops off with increasing distance from a body
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1848:{\displaystyle {\vec {a}}_{t,{\text{axial}}}\approx \pm {\hat {r}}~2\Delta r~G~{\frac {M}{R^{3}}}}
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1115:. Leaving aside whatever gravitational acceleration may be experienced by the particle towards
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By generating conducting fluids within the interior of the Earth, tidal forces also affect the
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with two bulges, pointing towards and away from the other body. Larger objects distort into an
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only causes the entire body to accelerate together in the same direction and at the same rate.
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direction of the arrows on the right and left of the Earth indicates that where the Moon is at
122:. This is the primary mechanism driving tidal action, explaining two simultaneous tidal bulges.
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2130:
2009:, while the solar tidal acceleration at the Earth's surface along the Sun–Earth axis is about
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Tidal acceleration does not require rotation or orbiting bodies; for example, the body may be
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is zero. This term does not affect the observed acceleration of particles on the surface of
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s own mass, we have the acceleration on the particle due to gravitational force towards
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be the (relatively small) distance of the particle from the center of the body of mass
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Tidal effects become particularly pronounced near small bodies of high mass, such as
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Tidal accelerations can also be calculated away from the axis connecting the bodies
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A gravitational effect also known as the differential force and the perturbing force
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2326:
Gravity from the Ground Up: An
Introductory Guide to Gravity and General Relativity
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1091:, then the new particle considered may be located on its surface, at a distance (
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1223:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{(R\pm \Delta r)^{2}}}}
689:
638:
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63:
43:
24:
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The
Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics
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by
Mikolaj Sawicki of John A. Logan College and the University of Colorado.
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2706:"Stellar collisions: Tidal disruption of a star by a massive black hole"
2120:, I. N. Avsiuk, in "Soviet Astronomy Letters", vol. 3 (1977), pp. 96–99.
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2145:"Tidal forces carry the mathematical signature of gravitational waves"
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effect that stretches a body along the line towards and away from the
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1988:{\textstyle {\frac {1}{2}}\left|{\vec {a}}_{t,{\text{axial}}}\right|}
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Figure 7: Tidal force is responsible for the merge of galactic pair
562:
close enough to its primary, this can result in a rotation which is
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2489:
Munk, Walter; Dzieciuch, Matthew; Jayne, Steven (February 2002).
602:
126:
Earth's surface and center (label O) by the Moon (label S). The
98:
Tidal forces have also been shown to be fundamentally related to
27:
2329:(illustrated ed.). Cambridge University Press. p. 45.
867:{\displaystyle {\vec {F}}_{g}=-{\hat {r}}~G~{\frac {Mm}{R^{2}}}}
3500:
2913:
989:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}}
701:
578:
caused by tidal forces also cause a regular monthly pattern of
543:
131:
2491:"Millennial Climate Variability: Is There a Tidal Connection?"
2419:. Vol. 26. Encyclopedia Americana Corp. pp. 611–617.
1055:
experienced by a particle in the vicinity of the body of mass
3862:
3681:
3460:
3415:
2432:"Possible forcing of global temperature by the oceanic tides"
626:
555:
135:
2416:
The
Encyclopedia Americana: A Library of Universal Knowledge
1107:
may be taken as positive where the particle's distance from
710:
For a given (externally generated) gravitational field, the
3294:
2516:
10.1175/1520-0442(2002)015<0370:MCVITA>2.0.CO;2
673:
630:
622:
566:
to the orbital motion, as in the case of the Earth's moon.
55:
2268:
Sawicki, Mikolaj (1999). "Myths about gravity and tides".
19:
634:
202:) is inversely proportional to the cube of the distance.
50:
of another body due to spatial variations in strength in
1629:
The first term is the gravitational acceleration due to
1051:
Consider now the acceleration due to the sphere of mass
2381:
2358:
The NIST Reference on
Constants, Units, and Uncertainty
621:" of infalling matter. Tidal forces create the oceanic
2354:"2022 CODATA Value: Newtonian constant of gravitation"
1939:
66:, breaking apart of celestial bodies and formation of
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produces dramatic volcanic effects on
Jupiter's moon
320:
298:
275:
249:
1862:
is a distance along the axis joining the centers of
2682:
676:getting torn apart by the gravitational tides of a
2488:
2385:Hamiltonian Dynamical Systems: A Reprint Selection
2169:
2143:arXiv, Emerging Technology from the (2019-12-14).
1987:
1898:
1847:
1744:considered, along the axis joining the centers of
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1414:
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1222:
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778:
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304:
281:
255:
3710:North West Shelf Operational Oceanographic System
2623:The mathematical principles of natural philosophy
714:at a point with respect to a body is obtained by
601:in 1994 after breaking up under the influence of
4007:
1858:When calculated in this way for the case where ∆
3700:Deep-ocean Assessment and Reporting of Tsunamis
2436:Proceedings of the National Academy of Sciences
2412:
629:'s oceans, where the attracting bodies are the
605:'s tidal forces during a previous pass in 1992.
54:from the other body. It is responsible for the
2430:Keeling, C. D.; Whorf, T. P. (5 August 1997).
2136:
2752:
2584:
2263:
2261:
1733:{\displaystyle {\vec {a}}_{t,{\text{axial}}}}
91:cases called a tidal force (for example, the
2703:
2429:
2346:
1906:is directed outwards from to the center of
114:Figure 2: Shown in red, the Moon's gravity
2759:
2745:
2258:
2766:
2663:Analysis and Prediction of Tides: GeoTide
2514:
2465:
2455:
2406:
2291:
2167:
1466:{\displaystyle 1\mp 2x+3x^{2}\mp \cdots }
1995:in linear approximation as in Figure 2.
1099:) from the centre of the sphere of mass
700:
688:
658:
637:. Tidal forces are also responsible for
592:
537:
170:
109:
23:Figure 1: Tidal interaction between the
18:
2267:
2242:"The Tidal Force | Neil deGrasse Tyson"
2236:
2234:
217:
4008:
3031:one-dimensional Saint-Venant equations
2619:
2375:
2322:
2161:
617:, where they are responsible for the "
355:{\displaystyle Gm~{\frac {2r}{d^{3}}}}
229:Gravitational body causing tidal force
2740:
2142:
736:Newton's law of universal gravitation
3978:
2231:
2201:
1633:at the center of the reference body
746:from the center of a sphere of mass
162:
2683:Gray, Meghan; Merrifield, Michael.
2131:"Astronomy: a physical perspective"
2094:"Hubble Views a Cosmic Interaction"
1473:which gives a series expansion of:
1063:as the distance from the center of
738:and laws of motion, a body of mass
13:
3858:National Oceanographic Data Center
3285:World Ocean Circulation Experiment
3173:Global Ocean Data Analysis Project
2382:R. S. MacKay; J. D. Meiss (1987).
1813:
1660:
1598:
1333:
1201:
672:Figure 6: This simulation shows a
14:
4052:
3705:Global Sea Level Observing System
2656:
1237:term from the denominator gives:
58:and related phenomena, including
3988:
3977:
3968:
3967:
3163:Geochemical Ocean Sections Study
3079:
3068:
2677:Audio: Cain/Gay – Astronomy Cast
2640:Book 3, Proposition 36, Page 307
2211:; J -P Bibring; M Blanc (2003).
647:Tides may also induce seismicity
3893:Ocean thermal energy conversion
3616:Vine–Matthews–Morley hypothesis
2672:Case Western Reserve University
2613:
2578:
2553:
2523:
2482:
2423:
1933:is zero), and its magnitude is
206:closer to the attracting body.
2588:Admiralty manual of navigation
2565:ESA/Hubble Picture of the Week
2316:
2123:
2111:
2086:
1961:
1899:{\displaystyle {\vec {a}}_{t}}
1884:
1801:
1769:
1710:
1555:
1514:
1490:
1415:{\displaystyle 1/(1\pm x)^{2}}
1403:
1390:
1278:
1254:
1208:
1192:
1171:
1147:
1087:is itself a sphere of radius ∆
1012:
954:
930:
906:{\displaystyle {\vec {a}}_{g}}
891:
877:equivalent to an acceleration
827:
803:
779:{\displaystyle {\vec {F}}_{g}}
764:
684:
105:
1:
2719:Myths about Gravity and Tides
2080:
633:and, to a lesser extent, the
232:Body subjected to tidal force
3153:El Niño–Southern Oscillation
3123:Craik–Leibovich vortex force
2879:Luke's variational principle
2626:. Vol. 2. p. 307.
2561:"Inseparable galactic twins"
93:perturbing force on the Moon
7:
2731:Tides and centrifugal force
2670:by J. Christopher Mihos of
2531:"Hungry for Power in Space"
2038:
1653:, i.e., at the point where
10:
4057:
3218:Ocean dynamical thermostat
3066:
2026:gravitational acceleration
1021:{\displaystyle {\hat {r}}}
533:
3963:
3802:
3776:
3753:Ocean acoustic tomography
3738:
3690:
3629:
3566:Mohorovičić discontinuity
3524:
3396:
3293:
3158:General circulation model
3088:
2794:Benjamin–Feir instability
2774:
2679:Tidal Forces – July 2007.
2650:as expressed in the text.
2246:www.haydenplanetarium.org
2100:. NASA. February 11, 2022
1040:(here, acceleration from
509:
231:
228:
3883:Ocean surface topography
3258:Thermohaline circulation
3248:Subsurface ocean current
3188:Hydrothermal circulation
3021:Wave–current interaction
2799:Boussinesq approximation
2697:University of Nottingham
2413:Rollin A Harris (1920).
2323:Schutz, Bernard (2003).
2217:. Springer. p. 16.
1680:because with respect to
1669:{\displaystyle \Delta r}
74:, and in extreme cases,
3920:Sea surface temperature
3903:Outline of oceanography
3098:Atmospheric circulation
3036:shallow water equations
3026:Waves and shallow water
2919:Significant wave height
2541:: 52. 23 September 1989
2457:10.1073/pnas.94.16.8321
2178:Oxford University Press
1032:pointing from the body
678:supermassive black hole
30:and a smaller companion
3915:Sea surface microlayer
3280:Wind generated current
2620:Newton, Isaac (1729).
2585:The Admiralty (1987).
2133:, M. L. Kutner (2003).
1989:
1900:
1849:
1734:
1670:
1647:
1620:
1467:
1416:
1362:
1224:
1083:. If the body of mass
1022:
990:
907:
868:
780:
707:
698:
681:
654:Earth's magnetic field
606:
599:Comet Shoemaker-Levy 9
547:
515:gravitational constant
356:
306:
283:
257:
176:
139:
31:
4041:Concepts in astronomy
3748:Deep scattering layer
3730:World Geodetic System
3238:Princeton Ocean Model
3118:Coriolis–Stokes force
2768:Physical oceanography
2593:The Stationery Office
2149:MIT Technology Review
1990:
1901:
1850:
1735:
1692:is small compared to
1671:
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1621:
1468:
1417:
1363:
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1023:
991:
908:
869:
781:
704:
692:
671:
645:, and tidal heating.
596:
541:
357:
307:
284:
258:
174:
120:tide generating force
113:
40:tide-generating force
22:
3768:Underwater acoustics
3328:Perigean spring tide
3193:Langmuir circulation
2904:Rossby-gravity waves
2727:by Donald E. Simanek
2725:Tidal Misconceptions
2118:"On the tidal force"
1937:
1874:
1759:
1700:
1657:
1637:
1480:
1426:
1379:
1244:
1137:
1048:has negative sign).
1003:
920:
881:
793:
754:
318:
296:
273:
247:
218:Sun, Earth, and Moon
189:), while the slope (
3930:Science On a Sphere
3536:Convergent boundary
3208:Modular Ocean Model
3168:Geostrophic current
2884:Mild-slope equation
2668:Gravitational Tides
2507:2002JCli...15..370M
2448:1997PNAS...94.8321K
2284:1999PhTea..37..438S
2271:The Physics Teacher
2075:Spacetime curvature
1740:for the distances ∆
235:Tidal acceleration
100:gravitational waves
84:celestial mechanics
52:gravitational field
4036:Effects of gravity
3586:Seafloor spreading
3576:Outer trench swell
3541:Divergent boundary
3441:Continental margin
3426:Carbonate platform
3323:Lunitidal interval
2704:Pau Amaro Seoane.
2609:Chapter 11, p. 277
2495:Journal of Climate
2342:Extract of page 45
2168:R Penrose (1999).
1985:
1896:
1845:
1730:
1666:
1643:
1616:
1463:
1412:
1358:
1220:
1018:
986:
903:
864:
776:
716:vector subtraction
712:tidal acceleration
708:
699:
682:
643:tidal acceleration
607:
548:
352:
302:
279:
253:
177:
140:
32:
4003:
4002:
3995:Oceans portal
3955:World Ocean Atlas
3945:Underwater glider
3888:Ocean temperature
3551:Hydrothermal vent
3516:Submarine volcano
3451:Continental shelf
3431:Coastal geography
3421:Bathymetric chart
3303:Amphidromic point
2991:Wave nonlinearity
2849:Infragravity wave
2633:978-0-11-772880-6
2602:978-0-11-772880-6
2442:(16): 8321–8328.
2399:978-0-85274-205-1
2336:978-0-521-45506-0
2224:978-3-540-00241-3
2191:978-0-19-286198-6
2045:Amphidromic point
1977:
1964:
1948:
1887:
1843:
1827:
1821:
1809:
1804:
1785:
1772:
1726:
1713:
1646:{\displaystyle m}
1608:
1594:
1590:
1569:
1563:
1558:
1544:
1528:
1522:
1517:
1493:
1356:
1343:
1312:
1308:
1292:
1286:
1281:
1257:
1218:
1185:
1179:
1174:
1150:
1067:to the center of
1015:
984:
968:
962:
957:
933:
894:
862:
841:
835:
830:
806:
767:
669:
619:spaghettification
582:on Earth's Moon.
531:
530:
504:10 m⋅s
456:10 m⋅s
408:10 m⋅s
350:
329:
305:{\displaystyle d}
282:{\displaystyle r}
256:{\displaystyle m}
163:Size and distance
86:, the expression
76:spaghettification
60:solid-earth tides
4048:
3993:
3992:
3981:
3980:
3971:
3970:
3910:Pelagic sediment
3848:Marine pollution
3642:Deep ocean water
3511:Submarine canyon
3446:Continental rise
3338:Rule of twelfths
3253:Sverdrup balance
3183:Humboldt Current
3108:Boundary current
3083:
3072:
2889:Radiation stress
2859:Iribarren number
2834:Equatorial waves
2789:Ballantine scale
2784:Airy wave theory
2761:
2754:
2747:
2738:
2737:
2733:by Paolo Sirtoli
2715:
2713:
2712:
2700:
2651:
2637:
2617:
2611:
2606:
2582:
2576:
2575:
2573:
2571:
2557:
2551:
2550:
2548:
2546:
2527:
2521:
2520:
2518:
2486:
2480:
2479:
2469:
2459:
2427:
2421:
2420:
2410:
2404:
2403:
2379:
2373:
2372:
2370:
2369:
2350:
2344:
2340:
2320:
2314:
2313:
2302:10.1119/1.880345
2295:
2265:
2256:
2255:
2253:
2252:
2238:
2229:
2228:
2214:The Solar System
2209:Thérèse Encrenaz
2205:
2199:
2198:
2175:
2165:
2159:
2158:
2156:
2155:
2140:
2134:
2127:
2121:
2115:
2109:
2108:
2106:
2105:
2090:
2050:Disrupted planet
2019:
2014:
2008:
2003:
1994:
1992:
1991:
1986:
1984:
1980:
1979:
1978:
1975:
1966:
1965:
1957:
1949:
1941:
1905:
1903:
1902:
1897:
1895:
1894:
1889:
1888:
1880:
1854:
1852:
1851:
1846:
1844:
1842:
1841:
1829:
1825:
1819:
1807:
1806:
1805:
1797:
1788:
1787:
1786:
1783:
1774:
1773:
1765:
1739:
1737:
1736:
1731:
1729:
1728:
1727:
1724:
1715:
1714:
1706:
1675:
1673:
1672:
1667:
1652:
1650:
1649:
1644:
1625:
1623:
1622:
1617:
1609:
1604:
1596:
1592:
1591:
1589:
1588:
1579:
1571:
1567:
1561:
1560:
1559:
1551:
1545:
1543:
1542:
1530:
1526:
1520:
1519:
1518:
1510:
1501:
1500:
1495:
1494:
1486:
1472:
1470:
1469:
1464:
1456:
1455:
1421:
1419:
1418:
1413:
1411:
1410:
1389:
1373:Maclaurin series
1367:
1365:
1364:
1359:
1357:
1355:
1354:
1349:
1345:
1344:
1339:
1331:
1314:
1310:
1309:
1307:
1306:
1294:
1290:
1284:
1283:
1282:
1274:
1265:
1264:
1259:
1258:
1250:
1233:Pulling out the
1229:
1227:
1226:
1221:
1219:
1217:
1216:
1215:
1187:
1183:
1177:
1176:
1175:
1167:
1158:
1157:
1152:
1151:
1143:
1125:
1111:is greater than
1027:
1025:
1024:
1019:
1017:
1016:
1008:
995:
993:
992:
987:
985:
983:
982:
970:
966:
960:
959:
958:
950:
941:
940:
935:
934:
926:
912:
910:
909:
904:
902:
901:
896:
895:
887:
873:
871:
870:
865:
863:
861:
860:
851:
843:
839:
833:
832:
831:
823:
814:
813:
808:
807:
799:
785:
783:
782:
777:
775:
774:
769:
768:
760:
670:
527:
524:
522:
505:
503:
496:
494:
487:
485:
473:
471:
457:
455:
448:
446:
439:
437:
425:
423:
409:
407:
400:
398:
391:
389:
377:
375:
361:
359:
358:
353:
351:
349:
348:
339:
331:
327:
311:
309:
308:
303:
288:
286:
285:
280:
262:
260:
259:
254:
226:
225:
201:
196:
188:
4056:
4055:
4051:
4050:
4049:
4047:
4046:
4045:
4006:
4005:
4004:
3999:
3987:
3959:
3798:
3772:
3734:
3715:Sea-level curve
3686:
3625:
3611:Transform fault
3561:Mid-ocean ridge
3527:
3520:
3486:Oceanic plateau
3392:
3378:Tidal resonance
3348:Theory of tides
3289:
3198:Longshore drift
3148:Ekman transport
3084:
3078:
3077:
3076:
3075:
3074:
3073:
3064:
3016:Wave turbulence
2949:Trochoidal wave
2874:Longshore drift
2770:
2765:
2710:
2708:
2659:
2654:
2634:
2618:
2614:
2603:
2595:. p. 277.
2591:. Vol. 1.
2583:
2579:
2569:
2567:
2559:
2558:
2554:
2544:
2542:
2529:
2528:
2524:
2487:
2483:
2428:
2424:
2411:
2407:
2400:
2380:
2376:
2367:
2365:
2352:
2351:
2347:
2337:
2321:
2317:
2293:10.1.1.695.8981
2266:
2259:
2250:
2248:
2240:
2239:
2232:
2225:
2206:
2202:
2192:
2166:
2162:
2153:
2151:
2141:
2137:
2128:
2124:
2116:
2112:
2103:
2101:
2092:
2091:
2087:
2083:
2065:Tidal stripping
2060:Tidal resonance
2041:
2012:
2010:
2001:
1999:
1974:
1967:
1956:
1955:
1954:
1950:
1940:
1938:
1935:
1934:
1890:
1879:
1878:
1877:
1875:
1872:
1871:
1837:
1833:
1828:
1796:
1795:
1782:
1775:
1764:
1763:
1762:
1760:
1757:
1756:
1723:
1716:
1705:
1704:
1703:
1701:
1698:
1697:
1658:
1655:
1654:
1638:
1635:
1634:
1597:
1595:
1584:
1580:
1572:
1570:
1550:
1549:
1538:
1534:
1529:
1509:
1508:
1496:
1485:
1484:
1483:
1481:
1478:
1477:
1451:
1447:
1427:
1424:
1423:
1406:
1402:
1385:
1380:
1377:
1376:
1350:
1332:
1330:
1323:
1319:
1318:
1313:
1302:
1298:
1293:
1273:
1272:
1260:
1249:
1248:
1247:
1245:
1242:
1241:
1211:
1207:
1191:
1186:
1166:
1165:
1153:
1142:
1141:
1140:
1138:
1135:
1134:
1123:
1007:
1006:
1004:
1001:
1000:
978:
974:
969:
949:
948:
936:
925:
924:
923:
921:
918:
917:
897:
886:
885:
884:
882:
879:
878:
856:
852:
844:
842:
822:
821:
809:
798:
797:
796:
794:
791:
790:
770:
759:
758:
757:
755:
752:
751:
687:
659:
536:
525:
520:
518:
501:
499:
492:
490:
483:
481:
469:
467:
453:
451:
444:
442:
435:
433:
421:
419:
405:
403:
396:
394:
387:
385:
373:
371:
344:
340:
332:
330:
319:
316:
315:
297:
294:
293:
274:
271:
270:
248:
245:
244:
220:
194:
190:
180:
165:
124:
123:
108:
17:
12:
11:
5:
4054:
4044:
4043:
4038:
4033:
4028:
4023:
4018:
4001:
4000:
3998:
3997:
3985:
3975:
3964:
3961:
3960:
3958:
3957:
3952:
3947:
3942:
3937:
3935:Stratification
3932:
3927:
3922:
3917:
3912:
3907:
3906:
3905:
3895:
3890:
3885:
3880:
3875:
3870:
3865:
3860:
3855:
3850:
3845:
3840:
3835:
3827:
3825:Color of water
3822:
3820:Benthic lander
3817:
3812:
3806:
3804:
3800:
3799:
3797:
3796:
3791:
3786:
3780:
3778:
3774:
3773:
3771:
3770:
3765:
3760:
3755:
3750:
3744:
3742:
3736:
3735:
3733:
3732:
3727:
3725:Sea level rise
3722:
3720:Sea level drop
3717:
3712:
3707:
3702:
3696:
3694:
3688:
3687:
3685:
3684:
3679:
3674:
3669:
3664:
3659:
3654:
3649:
3644:
3639:
3633:
3631:
3627:
3626:
3624:
3623:
3618:
3613:
3608:
3603:
3598:
3593:
3588:
3583:
3578:
3573:
3568:
3563:
3558:
3556:Marine geology
3553:
3548:
3543:
3538:
3532:
3530:
3522:
3521:
3519:
3518:
3513:
3508:
3503:
3498:
3496:Passive margin
3493:
3491:Oceanic trench
3488:
3483:
3478:
3473:
3468:
3463:
3458:
3453:
3448:
3443:
3438:
3433:
3428:
3423:
3418:
3413:
3408:
3402:
3400:
3394:
3393:
3391:
3390:
3385:
3380:
3375:
3370:
3365:
3360:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3320:
3315:
3310:
3305:
3299:
3297:
3291:
3290:
3288:
3287:
3282:
3277:
3272:
3267:
3266:
3265:
3255:
3250:
3245:
3240:
3235:
3230:
3225:
3223:Ocean dynamics
3220:
3215:
3210:
3205:
3200:
3195:
3190:
3185:
3180:
3175:
3170:
3165:
3160:
3155:
3150:
3145:
3140:
3135:
3130:
3125:
3120:
3115:
3113:Coriolis force
3110:
3105:
3100:
3094:
3092:
3086:
3085:
3067:
3065:
3063:
3062:
3061:
3060:
3050:
3045:
3040:
3039:
3038:
3033:
3023:
3018:
3013:
3008:
3003:
2998:
2993:
2988:
2983:
2978:
2973:
2968:
2963:
2962:
2961:
2951:
2946:
2941:
2936:
2934:Stokes problem
2931:
2926:
2921:
2916:
2911:
2906:
2901:
2896:
2891:
2886:
2881:
2876:
2871:
2869:Kinematic wave
2866:
2861:
2856:
2851:
2846:
2841:
2836:
2831:
2826:
2821:
2816:
2811:
2806:
2801:
2796:
2791:
2786:
2780:
2778:
2772:
2771:
2764:
2763:
2756:
2749:
2741:
2735:
2734:
2728:
2722:
2716:
2701:
2685:"Tidal Forces"
2680:
2674:
2665:
2658:
2657:External links
2655:
2653:
2652:
2632:
2612:
2601:
2577:
2552:
2522:
2501:(4): 370–385.
2481:
2422:
2405:
2398:
2392:. p. 36.
2374:
2345:
2335:
2315:
2278:(7): 438–441.
2257:
2230:
2223:
2200:
2190:
2160:
2135:
2129:See p. 509 in
2122:
2110:
2084:
2082:
2079:
2078:
2077:
2072:
2067:
2062:
2057:
2052:
2047:
2040:
2037:
1983:
1973:
1970:
1963:
1960:
1953:
1947:
1944:
1925:, requiring a
1893:
1886:
1883:
1856:
1855:
1840:
1836:
1832:
1824:
1818:
1815:
1812:
1803:
1800:
1794:
1791:
1781:
1778:
1771:
1768:
1722:
1719:
1712:
1709:
1665:
1662:
1642:
1627:
1626:
1615:
1612:
1607:
1603:
1600:
1587:
1583:
1578:
1575:
1566:
1557:
1554:
1548:
1541:
1537:
1533:
1525:
1516:
1513:
1507:
1504:
1499:
1492:
1489:
1462:
1459:
1454:
1450:
1446:
1443:
1440:
1437:
1434:
1431:
1409:
1405:
1401:
1398:
1395:
1392:
1388:
1384:
1369:
1368:
1353:
1348:
1342:
1338:
1335:
1329:
1326:
1322:
1317:
1305:
1301:
1297:
1289:
1280:
1277:
1271:
1268:
1263:
1256:
1253:
1231:
1230:
1214:
1210:
1206:
1203:
1200:
1197:
1194:
1190:
1182:
1173:
1170:
1164:
1161:
1156:
1149:
1146:
1119:on account of
1014:
1011:
997:
996:
981:
977:
973:
965:
956:
953:
947:
944:
939:
932:
929:
900:
893:
890:
875:
874:
859:
855:
850:
847:
838:
829:
826:
820:
817:
812:
805:
802:
773:
766:
763:
750:feels a force
686:
683:
564:tidally locked
535:
532:
529:
528:
523:10 m⋅kg⋅s
507:
506:
497:
488:
479:
474:
465:
459:
458:
449:
440:
431:
426:
417:
411:
410:
401:
392:
383:
378:
369:
363:
362:
347:
343:
338:
335:
326:
323:
313:
301:
290:
278:
267:
264:
252:
241:
237:
236:
233:
230:
219:
216:
164:
161:
107:
104:
48:center of mass
15:
9:
6:
4:
3:
2:
4053:
4042:
4039:
4037:
4034:
4032:
4029:
4027:
4024:
4022:
4019:
4017:
4014:
4013:
4011:
3996:
3991:
3986:
3984:
3976:
3974:
3966:
3965:
3962:
3956:
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3916:
3913:
3911:
3908:
3904:
3901:
3900:
3899:
3896:
3894:
3891:
3889:
3886:
3884:
3881:
3879:
3876:
3874:
3871:
3869:
3866:
3864:
3861:
3859:
3856:
3854:
3851:
3849:
3846:
3844:
3843:Marine energy
3841:
3839:
3836:
3834:
3833:
3828:
3826:
3823:
3821:
3818:
3816:
3813:
3811:
3810:Acidification
3808:
3807:
3805:
3801:
3795:
3792:
3790:
3787:
3785:
3782:
3781:
3779:
3775:
3769:
3766:
3764:
3763:SOFAR channel
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3745:
3743:
3741:
3737:
3731:
3728:
3726:
3723:
3721:
3718:
3716:
3713:
3711:
3708:
3706:
3703:
3701:
3698:
3697:
3695:
3693:
3689:
3683:
3680:
3678:
3675:
3673:
3670:
3668:
3665:
3663:
3660:
3658:
3655:
3653:
3650:
3648:
3645:
3643:
3640:
3638:
3635:
3634:
3632:
3628:
3622:
3619:
3617:
3614:
3612:
3609:
3607:
3604:
3602:
3599:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3574:
3572:
3571:Oceanic crust
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3546:Fracture zone
3544:
3542:
3539:
3537:
3534:
3533:
3531:
3529:
3523:
3517:
3514:
3512:
3509:
3507:
3504:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3482:
3481:Oceanic basin
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3457:
3454:
3452:
3449:
3447:
3444:
3442:
3439:
3437:
3434:
3432:
3429:
3427:
3424:
3422:
3419:
3417:
3414:
3412:
3411:Abyssal plain
3409:
3407:
3404:
3403:
3401:
3399:
3395:
3389:
3386:
3384:
3381:
3379:
3376:
3374:
3371:
3369:
3366:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3318:Internal tide
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3300:
3298:
3296:
3292:
3286:
3283:
3281:
3278:
3276:
3273:
3271:
3268:
3264:
3261:
3260:
3259:
3256:
3254:
3251:
3249:
3246:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3213:Ocean current
3211:
3209:
3206:
3204:
3201:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3095:
3093:
3091:
3087:
3082:
3071:
3059:
3056:
3055:
3054:
3051:
3049:
3046:
3044:
3041:
3037:
3034:
3032:
3029:
3028:
3027:
3024:
3022:
3019:
3017:
3014:
3012:
3011:Wave shoaling
3009:
3007:
3004:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2971:Ursell number
2969:
2967:
2964:
2960:
2957:
2956:
2955:
2952:
2950:
2947:
2945:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2890:
2887:
2885:
2882:
2880:
2877:
2875:
2872:
2870:
2867:
2865:
2862:
2860:
2857:
2855:
2854:Internal wave
2852:
2850:
2847:
2845:
2842:
2840:
2837:
2835:
2832:
2830:
2827:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2805:
2804:Breaking wave
2802:
2800:
2797:
2795:
2792:
2790:
2787:
2785:
2782:
2781:
2779:
2777:
2773:
2769:
2762:
2757:
2755:
2750:
2748:
2743:
2742:
2739:
2732:
2729:
2726:
2723:
2720:
2717:
2707:
2702:
2698:
2694:
2690:
2689:Sixty Symbols
2686:
2681:
2678:
2675:
2673:
2669:
2666:
2664:
2661:
2660:
2649:
2645:
2641:
2635:
2629:
2625:
2624:
2616:
2610:
2604:
2598:
2594:
2590:
2589:
2581:
2566:
2562:
2556:
2540:
2536:
2535:New Scientist
2532:
2526:
2517:
2512:
2508:
2504:
2500:
2496:
2492:
2485:
2477:
2473:
2468:
2463:
2458:
2453:
2449:
2445:
2441:
2437:
2433:
2426:
2418:
2417:
2409:
2401:
2395:
2391:
2387:
2386:
2378:
2363:
2359:
2355:
2349:
2343:
2338:
2332:
2328:
2327:
2319:
2311:
2307:
2303:
2299:
2294:
2289:
2285:
2281:
2277:
2273:
2272:
2264:
2262:
2247:
2243:
2237:
2235:
2226:
2220:
2216:
2215:
2210:
2204:
2197:
2193:
2187:
2183:
2179:
2174:
2173:
2164:
2150:
2146:
2139:
2132:
2126:
2119:
2114:
2099:
2095:
2089:
2085:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2055:Galactic tide
2053:
2051:
2048:
2046:
2043:
2042:
2036:
2034:
2033:
2027:
2023:
2018:
2007:
1996:
1981:
1971:
1968:
1958:
1951:
1945:
1942:
1932:
1928:
1924:
1920:
1915:
1913:
1909:
1891:
1881:
1869:
1865:
1861:
1838:
1834:
1830:
1822:
1816:
1810:
1798:
1792:
1789:
1779:
1776:
1766:
1755:
1754:
1753:
1751:
1747:
1743:
1720:
1717:
1707:
1695:
1691:
1687:
1683:
1679:
1663:
1640:
1632:
1613:
1610:
1605:
1601:
1585:
1581:
1576:
1573:
1564:
1552:
1546:
1539:
1535:
1531:
1523:
1511:
1505:
1502:
1497:
1487:
1476:
1475:
1474:
1460:
1457:
1452:
1448:
1444:
1441:
1438:
1435:
1432:
1429:
1407:
1399:
1396:
1393:
1386:
1382:
1374:
1351:
1346:
1340:
1336:
1327:
1324:
1320:
1315:
1303:
1299:
1295:
1287:
1275:
1269:
1266:
1261:
1251:
1240:
1239:
1238:
1236:
1212:
1204:
1198:
1195:
1188:
1180:
1168:
1162:
1159:
1154:
1144:
1133:
1132:
1131:
1129:
1122:
1118:
1114:
1110:
1106:
1102:
1098:
1094:
1090:
1086:
1082:
1078:
1074:
1070:
1066:
1062:
1058:
1054:
1049:
1047:
1043:
1039:
1035:
1031:
1009:
979:
975:
971:
963:
951:
945:
942:
937:
927:
916:
915:
914:
898:
888:
857:
853:
848:
845:
836:
824:
818:
815:
810:
800:
789:
788:
787:
771:
761:
749:
745:
741:
737:
732:
730:
725:
722:
717:
713:
703:
696:
691:
679:
675:
657:
655:
650:
648:
644:
640:
639:tidal locking
636:
632:
628:
624:
620:
616:
612:
611:neutron stars
604:
600:
595:
591:
589:
588:harmonic beat
583:
581:
577:
573:
569:
568:Tidal heating
565:
559:
557:
553:
545:
540:
516:
512:
508:
498:
489:
480:
478:
475:
466:
464:
461:
460:
450:
441:
432:
430:
427:
418:
416:
413:
412:
402:
393:
384:
382:
379:
370:
368:
365:
364:
345:
341:
336:
333:
324:
321:
314:
299:
291:
276:
268:
265:
250:
242:
239:
238:
234:
227:
224:
215:
211:
207:
203:
200:
193:
187:
183:
173:
169:
160:
158:
153:
149:
144:
137:
133:
129:
121:
117:
112:
103:
101:
96:
94:
89:
85:
80:
77:
73:
69:
65:
64:tidal locking
61:
57:
53:
49:
45:
44:gravitational
41:
37:
29:
26:
25:spiral galaxy
21:
4016:Tidal forces
3950:Water column
3898:Oceanography
3873:Observations
3868:Explorations
3838:Marginal sea
3831:
3789:OSTM/Jason-2
3621:Volcanic arc
3596:Slab suction
3357:
3313:Head of tide
3203:Loop Current
3143:Ekman spiral
2929:Stokes drift
2839:Gravity wave
2814:Cnoidal wave
2709:. Retrieved
2688:
2647:
2643:
2622:
2615:
2587:
2580:
2568:. Retrieved
2564:
2555:
2543:. Retrieved
2538:
2534:
2525:
2498:
2494:
2484:
2439:
2435:
2425:
2415:
2408:
2384:
2377:
2366:. Retrieved
2357:
2348:
2325:
2318:
2275:
2269:
2249:. Retrieved
2245:
2213:
2203:
2196:tidal force.
2195:
2171:
2163:
2152:. Retrieved
2148:
2138:
2125:
2113:
2102:. Retrieved
2097:
2088:
2070:Tidal tensor
2030:
2021:
2016:
2005:
1997:
1930:
1922:
1918:
1916:
1911:
1907:
1867:
1863:
1859:
1857:
1749:
1745:
1741:
1693:
1689:
1685:
1681:
1677:
1630:
1628:
1370:
1234:
1232:
1127:
1120:
1116:
1112:
1108:
1104:
1100:
1096:
1092:
1088:
1084:
1080:
1076:
1072:
1068:
1064:
1060:
1056:
1052:
1050:
1045:
1041:
1037:
1036:to the body
1033:
998:
876:
747:
743:
742:at distance
739:
733:
726:
720:
711:
709:
651:
608:
584:
560:
549:
510:
476:
462:
428:
414:
380:
366:
221:
212:
208:
204:
198:
191:
185:
181:
178:
166:
148:tidal forces
147:
145:
141:
127:
119:
115:
97:
87:
81:
68:ring systems
39:
35:
33:
3940:Thermocline
3657:Mesopelagic
3630:Ocean zones
3601:Slab window
3466:Hydrography
3406:Abyssal fan
3373:Tidal range
3363:Tidal power
3358:Tidal force
3243:Rip current
3178:Gulf Stream
3138:Ekman layer
3128:Downwelling
3103:Baroclinity
3090:Circulation
2986:Wave height
2976:Wave action
2959:megatsunami
2939:Stokes wave
2899:Rossby wave
2864:Kelvin wave
2844:Green's law
2693:Brady Haran
1030:unit vector
729:freefalling
721:tidal force
685:Formulation
615:black holes
152:Roche limit
143:(body 2).
106:Explanation
88:tidal force
72:Roche limit
70:within the
36:tidal force
4010:Categories
3878:Reanalysis
3777:Satellites
3758:Sofar bomb
3606:Subduction
3581:Ridge push
3476:Ocean bank
3456:Contourite
3383:Tide gauge
3368:Tidal race
3353:Tidal bore
3343:Slack tide
3308:Earth tide
3228:Ocean gyre
3048:Wind setup
3043:Wind fetch
3006:Wave setup
3001:Wave radar
2996:Wave power
2894:Rogue wave
2824:Dispersion
2711:2018-12-28
2368:2024-05-18
2364:. May 2024
2251:2016-10-10
2180:. p.
2154:2023-11-12
2104:2022-07-09
2081:References
1914:is zero).
597:Figure 5:
580:moonquakes
542:Figure 4:
472:10 kg
424:10 kg
376:10 kg
292:Distance (
3740:Acoustics
3692:Sea level
3591:Slab pull
3528:tectonics
3436:Cold seep
3398:Landforms
3275:Whirlpool
3270:Upwelling
3053:Wind wave
2981:Wave base
2909:Sea state
2829:Edge wave
2819:Cross sea
2390:CRC Press
2310:0031-921X
2288:CiteSeerX
2032:Principia
1962:→
1885:→
1814:Δ
1802:^
1793:±
1790:≈
1770:→
1711:→
1661:Δ
1614:⋯
1599:Δ
1556:^
1547:±
1515:^
1506:−
1491:→
1461:⋯
1458:∓
1433:∓
1397:±
1334:Δ
1328:±
1279:^
1270:−
1255:→
1202:Δ
1199:±
1172:^
1163:−
1148:→
1013:^
955:^
946:−
931:→
892:→
828:^
819:−
804:→
765:→
552:ellipsoid
495:10 m
486:10 m
447:10 m
438:10 m
399:10 m
390:10 m
3973:Category
3925:Seawater
3652:Littoral
3647:Deep sea
3506:Seamount
3388:Tideline
3333:Rip tide
3263:shutdown
3233:Overflow
2966:Undertow
2809:Clapotis
2695:for the
2545:14 March
2476:11607740
2098:nasa.gov
2039:See also
2020:, where
2015:10
2004:10
1910:(where ∆
1044:towards
695:MRK 1034
576:Stresses
269:Radius (
155:uniform
116:residual
4026:Gravity
3983:Commons
3853:Mooring
3803:Related
3794:Jason-3
3784:Jason-1
3667:Pelagic
3662:Oceanic
3637:Benthic
2954:Tsunami
2924:Soliton
2570:12 July
2503:Bibcode
2444:Bibcode
2280:Bibcode
2024:is the
1071:, let ∆
1059:. With
603:Jupiter
534:Effects
526:
513:is the
128:outward
28:NGC 169
3672:Photic
3501:Seabed
2914:Seiche
2630:
2599:
2474:
2464:
2396:
2333:
2308:
2290:
2221:
2188:
1927:vector
1826:
1820:
1808:
1593:
1568:
1562:
1527:
1521:
1311:
1291:
1285:
1184:
1178:
1103:, and
999:where
967:
961:
840:
834:
544:Saturn
328:
243:Mass (
146:These
134:or at
132:zenith
4031:Force
4021:Tides
3863:Ocean
3832:Alvin
3682:Swash
3526:Plate
3471:Knoll
3461:Guyot
3416:Atoll
3295:Tides
3058:model
2944:Swell
2776:Waves
2467:33744
1976:axial
1784:axial
1725:axial
1124:'
1028:is a
627:Earth
556:ovoid
519:6.674
463:Earth
429:Earth
381:Earth
197:= −2/
157:field
136:nadir
56:tides
42:is a
3830:DSV
3815:Argo
3677:Surf
3133:Eddy
2628:ISBN
2597:ISBN
2572:2013
2547:2016
2472:PMID
2394:ISBN
2362:NIST
2331:ISBN
2306:ISSN
2219:ISBN
2186:ISBN
2011:0.52
1921:and
1866:and
1748:and
1371:The
1130:as:
674:star
631:Moon
623:tide
500:2.44
491:3.84
482:1.74
477:Moon
468:5.97
452:1.10
443:3.84
434:6.37
420:7.34
415:Moon
404:5.05
395:1.50
386:6.37
372:1.99
266:Body
240:Body
184:= 1/
34:The
2539:123
2511:doi
2462:PMC
2452:doi
2298:doi
2182:264
2000:1.1
1422:is
1375:of
734:By
635:Sun
625:of
613:or
367:Sun
82:In
38:or
4012::
2691:.
2687:.
2638:,
2607:,
2563:.
2537:.
2533:.
2509:.
2499:15
2497:.
2493:.
2470:.
2460:.
2450:.
2440:94
2438:.
2434:.
2388:.
2360:.
2356:.
2304:.
2296:.
2286:.
2276:37
2274:.
2260:^
2244:.
2233:^
2194:.
2184:.
2176:.
2147:.
2096:.
2035:.
1870:,
1752::
1684:,
1105:∆r
1097:∆r
1095:±
913:,
786:,
697:.
656:.
649:.
641:,
574:.
572:Io
517:=
102:.
62:,
2760:e
2753:t
2746:v
2714:.
2699:.
2648:g
2644:g
2636:.
2605:.
2574:.
2549:.
2519:.
2513::
2505::
2478:.
2454::
2446::
2402:.
2371:.
2339:.
2312:.
2300::
2282::
2254:.
2227:.
2157:.
2107:.
2022:g
2017:g
2013:×
2006:g
2002:×
1982:|
1972:,
1969:t
1959:a
1952:|
1946:2
1943:1
1931:r
1923:M
1919:m
1912:r
1908:m
1892:t
1882:a
1868:M
1864:m
1860:r
1839:3
1835:R
1831:M
1823:G
1817:r
1811:2
1799:r
1780:,
1777:t
1767:a
1750:M
1746:m
1742:r
1721:,
1718:t
1708:a
1694:R
1690:r
1686:m
1682:M
1678:m
1664:r
1641:m
1631:M
1611:+
1606:R
1602:r
1586:2
1582:R
1577:M
1574:2
1565:G
1553:r
1540:2
1536:R
1532:M
1524:G
1512:r
1503:=
1498:g
1488:a
1453:2
1449:x
1445:3
1442:+
1439:x
1436:2
1430:1
1408:2
1404:)
1400:x
1394:1
1391:(
1387:/
1383:1
1352:2
1347:)
1341:R
1337:r
1325:1
1321:(
1316:1
1304:2
1300:R
1296:M
1288:G
1276:r
1267:=
1262:g
1252:a
1235:R
1213:2
1209:)
1205:r
1196:R
1193:(
1189:M
1181:G
1169:r
1160:=
1155:g
1145:a
1128:M
1121:m
1117:m
1113:R
1109:M
1101:M
1093:R
1089:r
1085:m
1081:M
1077:m
1073:r
1069:m
1065:M
1061:R
1057:m
1053:M
1046:M
1042:m
1038:m
1034:M
1010:r
980:2
976:R
972:M
964:G
952:r
943:=
938:g
928:a
899:g
889:a
858:2
854:R
849:m
846:M
837:G
825:r
816:=
811:g
801:F
772:g
762:F
748:M
744:R
740:m
680:.
521:×
511:G
502:×
493:×
484:×
470:×
454:×
445:×
436:×
422:×
406:×
397:×
388:×
374:×
346:3
342:d
337:r
334:2
325:m
322:G
312:)
300:d
289:)
277:r
263:)
251:m
199:X
195:′
192:Y
186:X
182:Y
138:.
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