3713:
2741:
928:
103:
3708:{\displaystyle {\begin{aligned}{\bar {u}}_{\text{S}}&={\overline {u_{x}({\boldsymbol {\xi }},t)}}-{\overline {u_{x}(\mathbf {x} ,t)}}\\&={\overline {\left}}-{\overline {u_{x}(\mathbf {x} ,t)}}\\&\approx {\overline {(\xi _{x}-x){\frac {\partial ^{2}\xi _{x}}{\partial x\,\partial t}}}}+{\overline {(\xi _{z}-z){\frac {\partial ^{2}\xi _{x}}{\partial z\,\partial t}}}}\\&={\overline {\left\left}}\\&+{\overline {\left\left}}\\&={\overline {\omega ka^{2}{\text{e}}^{2kz}\left}}\\&=\omega ka^{2}{\text{e}}^{2kz}.\end{aligned}}}
657:
4628:
923:{\displaystyle {\begin{aligned}{\bar {\mathbf {u} }}_{\text{E}}&={\overline {\mathbf {u} (\mathbf {x} ,t)}},\\{\bar {\mathbf {u} }}_{\text{L}}&={\overline {{\dot {\boldsymbol {\xi }}}({\boldsymbol {\alpha }},t)}}={\overline {\left({\frac {\partial {\boldsymbol {\xi }}({\boldsymbol {\alpha }},t)}{\partial t}}\right)}}={\overline {{\boldsymbol {u}}{\big (}{\boldsymbol {\xi }}({\boldsymbol {\alpha }},t),t{\big )}}}.\end{aligned}}}
5516:
5537:
2691:
1704:
4617:
1629:
5526:
2443:
434:
1387:
2130:
2686:{\displaystyle {\begin{aligned}\xi _{x}&=x+\int {\frac {\partial \varphi }{\partial x}}\,{\text{d}}t=x-a{\text{e}}^{kz}\sin(kx-\omega t),\\\xi _{z}&=z+\int {\frac {\partial \varphi }{\partial z}}\,{\text{d}}t=z+a{\text{e}}^{kz}\cos(kx-\omega t).\end{aligned}}}
47:
1067:
25:
332:
628:
246:
The Stokes drift velocity equals the Stokes drift divided by the considered time interval. Often, the Stokes drift velocity is loosely referred to as Stokes drift. Stokes drift may occur in all instances of oscillatory flow which are
1624:{\displaystyle \xi (\xi _{0},t)\approx \xi _{0}+{\frac {\hat {u}}{\omega }}\cos(k\xi _{0}-\omega t)-{\frac {1}{4}}{\frac {k{\hat {u}}^{2}}{\omega ^{2}}}\sin 2(k\xi _{0}-\omega t)+{\frac {1}{2}}{\frac {k{\hat {u}}^{2}}{\omega }}t.}
2334:
1381:
1993:
1694:
2746:
2448:
662:
274:
Lagrangian velocity and Stokes drift velocity, which can be attributed to a certain fixed position, is by no means a trivial task. However, such an unambiguous description is provided by the
1189:
983:
1834:
532:
520:
4250:
Viscosity has a pronounced effect on the mean
Eulerian velocity and mean Lagrangian (or mass transport) velocity, but much less on their difference: the Stokes drift outside the
1233:
1282:
4204:
4169:
429:{\displaystyle {\dot {\boldsymbol {\xi }}}={\frac {\partial {\boldsymbol {\xi }}}{\partial t}}=\mathbf {u} {\big (}{\boldsymbol {\xi }}({\boldsymbol {\alpha }},t),t{\big )},}
2396:
5256:
5246:
4305:
576:
4041:
Solutions of the particle trajectories in fully nonlinear periodic waves and the
Lagrangian wave period they experience can for instance be found in:
2258:
5162:
4577:
4345:
1110:. A mathematically sound basis for an unambiguous mapping between average Lagrangian and Eulerian quantities is provided by the theory of the
4089:
3948:
3929:
3867:
1291:
4809:
2125:{\displaystyle {\bar {u}}_{\text{S}}\approx \omega ka^{2}{\text{e}}^{2kz}={\frac {4\pi ^{2}a^{2}}{\lambda T}}{\text{e}}^{4\pi z/\lambda }.}
4699:
4298:
3734:
308:
267:
236:
232:
228:
190:
183:
5404:
4831:
4719:
5251:
4522:
4669:
4709:
1730:
flow velocities. Black solid line: average
Eulerian velocity; red dashed line: average Lagrangian velocity, as derived from the
5529:
5439:
4425:
5112:
5519:
4291:
1637:
4567:
4627:
1732:
1111:
276:
4139:, pages 71–72. There is a typo in the coefficient of the superharmonic term in Eq. (2.20) on page 71, i.e
1129:
102:
4764:
3877:
1062:{\displaystyle {\bar {\mathbf {u} }}_{\text{S}}={\bar {\mathbf {u} }}_{\text{L}}-{\bar {\mathbf {u} }}_{\text{E}}.}
4664:
3724:
5299:
4704:
235:
is obtained by following a specific fluid parcel during the time interval. The corresponding end position in the
3979:
5429:
4804:
4794:
4734:
4370:
4340:
2356:
1783:
243:
at a fixed position—equal to the initial position in the
Lagrangian description—during the same time interval.
291:
of various kinds of material and organisms by oscillatory flows. It plays a crucial role in the generation of
5562:
5466:
5449:
5286:
4779:
4644:
4582:
4572:
4465:
5461:
5399:
4826:
4512:
2149:. Further, the Stokes drift velocity decays exponentially with depth: at a depth of a quarter wavelength,
270:, fluid parcels may drift far from their initial positions. As a result, the unambiguous definition of an
1198:
5294:
5276:
4784:
4679:
4314:
4251:
1755:
1239:
977:
is defined as the difference between the average
Eulerian velocity and the average Lagrangian velocity:
205:
4174:
4142:
5567:
5481:
5314:
5017:
4874:
4739:
4450:
4053:
3967:
3917:
3889:
3830:
3766:
292:
2365:
5476:
5361:
5356:
5082:
4754:
4714:
4430:
3818:
3739:
1192:
123:
5419:
5132:
5122:
5087:
4987:
4972:
4869:
4069:
3958:
Kubota, M. (1994). "A mechanism for the accumulation of floating marine debris north of Hawaii".
3905:
3846:
2242:
2238:
2223:
2199:
454:
5501:
5491:
5434:
5414:
5097:
5062:
4997:
4977:
4967:
4849:
4537:
4395:
4085:
3944:
3925:
3863:
1901:
1073:
296:
260:
5456:
5424:
5394:
5203:
5188:
5057:
4992:
4884:
4799:
4729:
4654:
4435:
4405:
4335:
4330:
4061:
3975:
3897:
3838:
3774:
2704:
2249:
1766:
1741:
1708:
957:
623:{\displaystyle {\boldsymbol {\xi }}({\boldsymbol {\alpha }},t_{0})={\boldsymbol {\alpha }}.}
201:
173:
138:
115:
92:
at a fixed horizontal position (as indicated by the light-blue circles). This is due to the
75:
3778:
5261:
5157:
5107:
5072:
5032:
4924:
4894:
4744:
4694:
4604:
4562:
4495:
4420:
4380:
1093:
312:
70:. The white dots are fluid particles, also followed in time. In the cases shown here, the
63:
52:
Stokes drift in shallow water waves, with a wave length much longer than the water depth.
4616:
4057:
3971:
3893:
3834:
3770:
1126:
For the
Eulerian velocity as a monochromatic wave of any nature in a continuous medium:
637:
value of a quantity is denoted by an overbar, then the average
Eulerian velocity vector
5371:
5366:
5271:
5266:
5102:
5042:
5037:
4769:
4659:
4480:
4415:
4390:
3800:
2231:
2215:
938:
142:
5556:
5541:
5389:
5309:
5198:
5117:
5092:
5027:
4957:
4864:
4759:
4636:
4557:
4517:
4490:
4400:
4350:
4073:
3909:
2174:
1719:
963:
288:
248:
240:
193:
186:
127:
93:
59:
299:
water waves, accurate results on the Stokes drift have been computed and tabulated.
5536:
5496:
5444:
5384:
5335:
5213:
5208:
5183:
5167:
5142:
4859:
4749:
4689:
4385:
4360:
3850:
3729:
2406:
2227:
2219:
2196:
2181:
2158:
1851:
1774:
223:
is the difference in end positions, after a predefined amount of time (usually one
165:
85:
46:
58:
The red circles are the present positions of massless particles, moving with the
5486:
5218:
5147:
5012:
4952:
4919:
4909:
4904:
4789:
4724:
4684:
4674:
4649:
4532:
4505:
4485:
4445:
4410:
2352:
2348:
2340:
1965:
1955:
1875:
1751:
1745:
252:
224:
213:
169:
119:
89:
81:
67:
66:
of these particles, and the light-blue circles the particle position after each
35:
31:
2329:{\displaystyle \varphi ={\frac {\omega }{k}}a{\text{e}}^{kz}\sin(kx-\omega t).}
5304:
5152:
5127:
5022:
5002:
4929:
4914:
4899:
4889:
4854:
4774:
4594:
4589:
4552:
4547:
4542:
4440:
3842:
2344:
1941:
1931:
1770:
1703:
161:
24:
5376:
5238:
5223:
5137:
4982:
4821:
4816:
4599:
4527:
4455:
4375:
4365:
4322:
2193:
2177:
2143:
1865:
1847:
107:
4065:
3901:
5471:
5193:
5052:
4944:
4934:
4879:
4355:
4044:
J.M. Williams (1981). "Limiting gravity waves in water of finite depth".
2211:
1759:
510:
153:
4283:
3821:(1978). "An exact theory of nonlinear waves on a Lagrangian mean flow".
2192: = 0. The waves propagate under the action of gravity, with a
179:
More generally, the Stokes drift velocity is the difference between the
5340:
5330:
4500:
4470:
2410:
2203:
1727:
1376:{\displaystyle {\dot {\xi }}=u(\xi ,t)={\hat {u}}\sin(k\xi -\omega t),}
934:
634:
271:
180:
150:
1987:) of the Stokes drift velocity for deep-water waves is approximately:
5047:
4460:
2414:
1969:
1921:
1917:
1891:
1763:
3757:
A.D.D. Craik (2005). "George
Gabriel Stokes on water wave theory".
5409:
5228:
5007:
4962:
1702:
951:
197:
157:
111:
101:
1235:
as a small parameter – for the particle position
4841:
2185:
945:
542:
256:
135:
71:
4287:
2355:
may not be chosen arbitrarily, but must satisfy the deep-water
172:, experiences a net Stokes drift velocity in the direction of
3980:
10.1175/1520-0485(1994)024<1059:AMFTAO>2.0.CO;2
1714: = 5 s and a mean water depth of 25 m.
3786:
G.G. Stokes (1847). "On the theory of oscillatory waves".
1707:
Stokes drift under periodic waves in deep water, for a
1689:{\displaystyle {\tfrac {1}{2}}k{\hat {u}}^{2}/\omega .}
1634:
Here the last term describes the Stokes drift velocity
126:– is one of the relevant processes in the transport of
4182:
4150:
1642:
495:) is the Lagrangian position vector of a fluid parcel,
4177:
4145:
2744:
2703:
of the Stokes drift velocity is estimated by using a
2446:
2368:
2261:
1996:
1786:
1640:
1390:
1294:
1242:
1201:
1132:
986:
660:
579:
555:
are chosen to coincide with the
Eulerian coordinates
335:
937:
may be used, depending on the subject of study (see
16:
Average velocity of a fluid parcel in a gravity wave
5349:
5323:
5285:
5237:
5176:
5071:
4943:
4840:
4635:
4321:
3788:
Transactions of the
Cambridge Philosophical Society
1948:
direction pointing out of the fluid layer (meters),
4198:
4163:
3707:
2685:
2390:
2328:
2124:
1828:
1688:
1623:
1375:
1276:
1227:
1183:
1076:of average quantities from some Eulerian position
1061:
922:
622:
428:
5257:North West Shelf Operational Oceanographic System
4046:Philosophical Transactions of the Royal Society A
3882:Philosophical Transactions of the Royal Society A
2230:. At infinite depth, the fluid is taken to be at
1086:forms a problem. Since a fluid parcel with label
2417:theory, the horizontal and vertical components,
5247:Deep-ocean Assessment and Reporting of Tsunamis
3941:Fluid Mechanics (A short course for physicists)
3805:. Cambridge University Press. pp. 197–229.
2210:direction). Further the fluid is assumed to be
2711:of the Eulerian horizontal velocity component
1184:{\displaystyle u={\hat {u}}\sin(kx-\omega t),}
4299:
4229:
4227:
4213:
4211:
4105:
4103:
4101:
2142:is a nonlinear quantity in terms of the wave
902:
867:
418:
383:
8:
4254:near bed and free surface, see for instance
3924:(2nd ed.). Cambridge University Press.
2157:/4, it is about 4% of its value at the mean
1934:and the wave propagation direction (meters),
1122:Example: A one-dimensional compressible flow
208:, who derived expressions for this drift in
74:Eulerian horizontal velocity below the wave
1976:As derived below, the horizontal component
164:. For instance, a particle floating at the
84:, experienced by a fluid particle near the
4306:
4292:
4284:
3802:Mathematical and Physical Papers, Volume I
2135:As can be seen, the Stokes drift velocity
4181:
4176:
4149:
4144:
3880:(1953). "Mass transport in water waves".
3686:
3681:
3674:
3613:
3576:
3555:
3550:
3543:
3530:
3473:
3468:
3412:
3407:
3395:
3338:
3333:
3274:
3269:
3254:
3228:
3214:
3204:
3197:
3182:
3172:
3153:
3139:
3129:
3122:
3107:
3097:
3067:
3058:
3051:
3007:
2998:
2988:
2973:
2938:
2929:
2919:
2904:
2880:
2871:
2860:
2830:
2821:
2814:
2791:
2782:
2775:
2762:
2751:
2750:
2745:
2743:
2640:
2635:
2614:
2613:
2593:
2571:
2524:
2519:
2498:
2497:
2477:
2455:
2447:
2445:
2431:respectively, of the Lagrangian position
2373:
2367:
2287:
2282:
2268:
2260:
2109:
2099:
2094:
2076:
2066:
2056:
2041:
2036:
2029:
2010:
1999:
1998:
1995:
1829:{\displaystyle \eta =a\cos(kx-\omega t),}
1785:
1675:
1669:
1658:
1657:
1641:
1639:
1603:
1592:
1591:
1584:
1574:
1553:
1526:
1515:
1504:
1503:
1496:
1486:
1465:
1434:
1432:
1423:
1401:
1389:
1332:
1331:
1296:
1295:
1293:
1259:
1241:
1217:
1206:
1205:
1200:
1140:
1139:
1131:
1115:
1050:
1039:
1037:
1036:
1026:
1015:
1013:
1012:
1002:
991:
989:
988:
985:
901:
900:
880:
872:
866:
865:
860:
857:
820:
812:
806:
800:
777:
763:
762:
759:
746:
735:
733:
732:
704:
696:
693:
680:
669:
667:
666:
661:
659:
612:
600:
588:
580:
578:
417:
416:
396:
388:
382:
381:
376:
357:
351:
337:
336:
334:
281:
4255:
326:in the Eulerian coordinates is given by
227:), as derived from a description in the
3992:
2792:
1080:to a corresponding Lagrangian position
881:
873:
861:
821:
813:
778:
765:
644:and average Lagrangian velocity vector
613:
589:
581:
397:
389:
358:
339:
4578:one-dimensional Saint-Venant equations
3779:10.1146/annurev.fluid.37.061903.175836
287:The Stokes drift is important for the
1758:in 1847. For simplicity, the case of
1096:of many different Eulerian positions
7:
5525:
2173:It is assumed that the waves are of
1750:The Stokes drift was formulated for
4082:Tables of progressive gravity waves
3735:Lagrangian and Eulerian coordinates
2206:(pointing downward in the negative
1228:{\displaystyle k{\hat {u}}/\omega }
229:Lagrangian and Eulerian coordinates
189:of a fluid parcel, and the average
5405:National Oceanographic Data Center
4832:World Ocean Circulation Experiment
4720:Global Ocean Data Analysis Project
3229:
3222:
3201:
3154:
3147:
3126:
3023:
2991:
2954:
2922:
2604:
2596:
2488:
2480:
2413:in (m/s). Within the framework of
1277:{\displaystyle x=\xi (\xi _{0},t)}
836:
809:
549:Often, the Lagrangian coordinates
364:
354:
14:
5252:Global Sea Level Observing System
4275:
4259:
4234:
4218:
4199:{\displaystyle +{\tfrac {1}{2}}.}
4110:
3860:Wave interactions and fluid flows
5535:
5524:
5515:
5514:
4710:Geochemical Ocean Sections Study
4626:
4615:
4164:{\displaystyle -{\tfrac {1}{4}}}
3960:Journal of Physical Oceanography
3759:Annual Review of Fluid Mechanics
3068:
3008:
2939:
2881:
2831:
1040:
1016:
992:
736:
705:
697:
670:
377:
62:. The light-blue line gives the
45:
23:
5440:Ocean thermal energy conversion
5163:Vine–Matthews–Morley hypothesis
4000:
3922:The dynamics of the upper ocean
1762:deep water is considered, with
1100:, it is not possible to assign
239:is obtained by integrating the
209:
38:of about twice the water depth.
4238:
4136:
4123:
4029:
4013:
3943:. Cambridge University Press.
3862:. Cambridge University Press.
3640:
3622:
3603:
3585:
3506:
3488:
3445:
3427:
3371:
3353:
3307:
3289:
3194:
3175:
3119:
3100:
3078:
3064:
3018:
3004:
2985:
2966:
2949:
2935:
2916:
2897:
2891:
2877:
2841:
2827:
2802:
2788:
2756:
2673:
2655:
2557:
2539:
2391:{\displaystyle \omega ^{2}=gk}
2320:
2302:
2004:
1820:
1802:
1663:
1597:
1568:
1543:
1509:
1480:
1455:
1439:
1413:
1394:
1367:
1349:
1337:
1325:
1313:
1271:
1252:
1211:
1175:
1157:
1145:
1044:
1020:
996:
891:
877:
831:
817:
788:
774:
740:
715:
701:
674:
606:
585:
531:is the position vector in the
519:is the position vector in the
407:
393:
160:parcel as it travels with the
118:. Stokes drift – besides e.g.
1:
933:Different definitions of the
4700:El Niño–Southern Oscillation
4670:Craik–Leibovich vortex force
4426:Luke's variational principle
3649:
3515:
3380:
3239:
3164:
3082:
3043:
2845:
2806:
908:
849:
792:
719:
533:Lagrangian coordinate system
282:Andrews and McIntyre in 1978
1733:Generalized Lagrangian Mean
1718:: instantaneous horizontal
1191:one readily obtains by the
1116:Andrews and McIntyre (1978)
1112:generalized Lagrangian mean
277:Generalized Lagrangian Mean
5584:
4765:Ocean dynamical thermostat
4613:
3823:Journal of Fluid Mechanics
1739:
970:The Stokes drift velocity
521:Eulerian coordinate system
251:in space. For instance in
231:. The end position in the
204:phenomenon is named after
200:at a fixed position. This
156:when following a specific
5510:
5300:Ocean acoustic tomography
5113:Mohorovičić discontinuity
4705:General circulation model
4341:Benjamin–Feir instability
3843:10.1017/S0022112078002773
2696:The horizontal component
1699:Example: Deep water waves
5430:Ocean surface topography
4805:Thermohaline circulation
4795:Subsurface ocean current
4735:Hydrothermal circulation
4568:Wave–current interaction
4346:Boussinesq approximation
2241:may be represented by a
1195: – with
1072:In many situations, the
303:Mathematical description
88:, is different from the
5467:Sea surface temperature
5450:Outline of oceanography
4645:Atmospheric circulation
4583:shallow water equations
4573:Waves and shallow water
4466:Significant wave height
311:of a fluid parcel with
5462:Sea surface microlayer
4827:Wind generated current
4256:Longuet-Higgins (1953)
4200:
4165:
4080:J.M. Williams (1985).
4066:10.1098/rsta.1981.0159
3902:10.1098/rsta.1953.0006
3709:
2687:
2392:
2330:
2184:oscillates around the
2126:
1830:
1737:
1690:
1625:
1377:
1278:
1229:
1185:
1063:
924:
624:
430:
268:Lagrangian description
233:Lagrangian description
131:
5295:Deep scattering layer
5277:World Geodetic System
4785:Princeton Ocean Model
4665:Coriolis–Stokes force
4315:Physical oceanography
4201:
4166:
3939:G. Falkovich (2011).
3858:A.D.D. Craik (1985).
3725:Coriolis–Stokes force
3710:
2688:
2393:
2331:
2127:
1831:
1756:George Gabriel Stokes
1706:
1691:
1626:
1378:
1279:
1230:
1186:
1064:
925:
625:
431:
293:Langmuir circulations
206:George Gabriel Stokes
147:Stokes drift velocity
105:
30:Stokes drift in deep
5315:Underwater acoustics
4875:Perigean spring tide
4740:Langmuir circulation
4451:Rossby-gravity waves
4175:
4143:
3878:M.S. Longuet-Higgins
3799:G.G. Stokes (1880).
2742:
2444:
2366:
2259:
1994:
1944:, with the positive
1784:
1638:
1388:
1292:
1240:
1199:
1130:
984:
658:
577:
559:at the initial time
333:
295:. For nonlinear and
237:Eulerian description
124:geostrophic currents
5477:Science On a Sphere
5083:Convergent boundary
4755:Modular Ocean Model
4715:Geostrophic current
4431:Mild-slope equation
4262:, pages 53–58.
4058:1981RSPTA.302..139W
3972:1994JPO....24.1059K
3894:1953RSPTA.245..535L
3835:1978JFM....89..609A
3817:D.G. Andrews &
3771:2005AnRFM..37...23C
3740:Material derivative
2343:solutions for this
1858:direction (meters),
1193:perturbation theory
110:along the northern
5133:Seafloor spreading
5123:Outer trench swell
5088:Divergent boundary
4988:Continental margin
4973:Carbonate platform
4870:Lunitidal interval
4196:
4191:
4161:
4159:
3705:
3703:
2683:
2681:
2388:
2326:
2243:velocity potential
2218:, with a constant
2122:
1930:is the horizontal
1826:
1777:of a fluid layer:
1738:
1686:
1651:
1621:
1373:
1274:
1225:
1181:
1092:traverses along a
1059:
920:
918:
620:
509:) is the Eulerian
473:) with respect to
455:partial derivative
426:
132:
5550:
5549:
5542:Oceans portal
5502:World Ocean Atlas
5492:Underwater glider
5435:Ocean temperature
5098:Hydrothermal vent
5063:Submarine volcano
4998:Continental shelf
4978:Coastal geography
4968:Bathymetric chart
4850:Amphidromic point
4538:Wave nonlinearity
4396:Infragravity wave
4190:
4158:
4091:978-0-273-08733-5
4052:(1466): 139–188.
3950:978-1-107-00575-4
3931:978-0-521-29801-8
3869:978-0-521-36829-2
3684:
3652:
3553:
3518:
3471:
3410:
3383:
3336:
3272:
3242:
3236:
3167:
3161:
3085:
3046:
3030:
2961:
2848:
2809:
2765:
2759:
2638:
2617:
2611:
2522:
2501:
2495:
2339:In order to have
2285:
2276:
2248:, satisfying the
2097:
2091:
2039:
2013:
2007:
1902:angular frequency
1666:
1650:
1613:
1600:
1582:
1532:
1512:
1494:
1447:
1442:
1340:
1304:
1214:
1148:
1053:
1047:
1029:
1023:
1005:
999:
911:
852:
843:
795:
771:
749:
743:
722:
683:
677:
371:
345:
309:Lagrangian motion
261:atmospheric waves
80:Observe that the
5575:
5540:
5539:
5528:
5527:
5518:
5517:
5457:Pelagic sediment
5395:Marine pollution
5189:Deep ocean water
5058:Submarine canyon
4993:Continental rise
4885:Rule of twelfths
4800:Sverdrup balance
4730:Humboldt Current
4655:Boundary current
4630:
4619:
4436:Radiation stress
4406:Iribarren number
4381:Equatorial waves
4336:Ballantine scale
4331:Airy wave theory
4308:
4301:
4294:
4285:
4279:
4269:
4263:
4248:
4242:
4231:
4222:
4215:
4206:
4205:
4203:
4202:
4197:
4192:
4183:
4170:
4168:
4167:
4162:
4160:
4151:
4137:Falkovich (2011)
4133:
4127:
4120:
4114:
4107:
4096:
4095:
4077:
4039:
4033:
4023:
4017:
4010:
4004:
3997:
3983:
3966:(5): 1059–1064.
3954:
3935:
3913:
3888:(903): 535–581.
3873:
3854:
3806:
3795:
3782:
3714:
3712:
3711:
3706:
3704:
3697:
3696:
3685:
3682:
3679:
3678:
3657:
3653:
3648:
3647:
3643:
3618:
3617:
3581:
3580:
3566:
3565:
3554:
3551:
3548:
3547:
3531:
3523:
3519:
3514:
3513:
3509:
3481:
3480:
3472:
3469:
3452:
3448:
3420:
3419:
3411:
3408:
3396:
3388:
3384:
3379:
3378:
3374:
3346:
3345:
3337:
3334:
3314:
3310:
3282:
3281:
3273:
3270:
3255:
3247:
3243:
3238:
3237:
3235:
3220:
3219:
3218:
3209:
3208:
3198:
3187:
3186:
3173:
3168:
3163:
3162:
3160:
3145:
3144:
3143:
3134:
3133:
3123:
3112:
3111:
3098:
3090:
3086:
3081:
3071:
3063:
3062:
3052:
3047:
3042:
3038:
3031:
3029:
3021:
3011:
3003:
3002:
2989:
2978:
2977:
2962:
2960:
2952:
2942:
2934:
2933:
2920:
2909:
2908:
2884:
2876:
2875:
2861:
2853:
2849:
2844:
2834:
2826:
2825:
2815:
2810:
2805:
2795:
2787:
2786:
2776:
2767:
2766:
2763:
2761:
2760:
2752:
2729:at the position
2705:Taylor expansion
2692:
2690:
2689:
2684:
2682:
2648:
2647:
2639:
2636:
2618:
2615:
2612:
2610:
2602:
2594:
2576:
2575:
2532:
2531:
2523:
2520:
2502:
2499:
2496:
2494:
2486:
2478:
2460:
2459:
2397:
2395:
2394:
2389:
2378:
2377:
2335:
2333:
2332:
2327:
2295:
2294:
2286:
2283:
2277:
2269:
2250:Laplace equation
2165: = 0.
2131:
2129:
2128:
2123:
2118:
2117:
2113:
2098:
2095:
2092:
2090:
2082:
2081:
2080:
2071:
2070:
2057:
2052:
2051:
2040:
2037:
2034:
2033:
2015:
2014:
2011:
2009:
2008:
2000:
1940:is the vertical
1835:
1833:
1832:
1827:
1767:wave propagation
1742:Airy wave theory
1695:
1693:
1692:
1687:
1679:
1674:
1673:
1668:
1667:
1659:
1652:
1643:
1630:
1628:
1627:
1622:
1614:
1609:
1608:
1607:
1602:
1601:
1593:
1585:
1583:
1575:
1558:
1557:
1533:
1531:
1530:
1521:
1520:
1519:
1514:
1513:
1505:
1497:
1495:
1487:
1470:
1469:
1448:
1443:
1435:
1433:
1428:
1427:
1406:
1405:
1382:
1380:
1379:
1374:
1342:
1341:
1333:
1306:
1305:
1297:
1285:
1283:
1281:
1280:
1275:
1264:
1263:
1234:
1232:
1231:
1226:
1221:
1216:
1215:
1207:
1190:
1188:
1187:
1182:
1150:
1149:
1141:
1068:
1066:
1065:
1060:
1055:
1054:
1051:
1049:
1048:
1043:
1038:
1031:
1030:
1027:
1025:
1024:
1019:
1014:
1007:
1006:
1003:
1001:
1000:
995:
990:
958:ensemble average
929:
927:
926:
921:
919:
912:
907:
906:
905:
884:
876:
871:
870:
864:
858:
853:
848:
844:
842:
834:
824:
816:
807:
801:
796:
791:
781:
773:
772:
764:
760:
751:
750:
747:
745:
744:
739:
734:
723:
718:
708:
700:
694:
685:
684:
681:
679:
678:
673:
668:
629:
627:
626:
621:
616:
605:
604:
592:
584:
435:
433:
432:
427:
422:
421:
400:
392:
387:
386:
380:
372:
370:
362:
361:
352:
347:
346:
338:
280:(GLM) theory of
174:wave propagation
116:Washington state
49:
27:
5583:
5582:
5578:
5577:
5576:
5574:
5573:
5572:
5553:
5552:
5551:
5546:
5534:
5506:
5345:
5319:
5281:
5262:Sea-level curve
5233:
5172:
5158:Transform fault
5108:Mid-ocean ridge
5074:
5067:
5033:Oceanic plateau
4939:
4925:Tidal resonance
4895:Theory of tides
4836:
4745:Longshore drift
4695:Ekman transport
4631:
4625:
4624:
4623:
4622:
4621:
4620:
4611:
4563:Wave turbulence
4496:Trochoidal wave
4421:Longshore drift
4317:
4312:
4282:
4276:Phillips (1977)
4270:
4266:
4260:Phillips (1977)
4252:boundary layers
4249:
4245:
4235:Phillips (1977)
4232:
4225:
4219:Phillips (1977)
4216:
4209:
4173:
4172:
4141:
4140:
4134:
4130:
4121:
4117:
4111:Phillips (1977)
4108:
4099:
4092:
4079:
4078:
4043:
4042:
4040:
4036:
4024:
4020:
4016:, page 105–113.
4011:
4007:
3998:
3994:
3990:
3957:
3951:
3938:
3932:
3916:
3876:
3870:
3857:
3816:
3813:
3798:
3796:
3785:
3756:
3753:
3748:
3721:
3702:
3701:
3680:
3670:
3655:
3654:
3609:
3572:
3571:
3567:
3549:
3539:
3532:
3521:
3520:
3467:
3457:
3453:
3406:
3402:
3398:
3397:
3386:
3385:
3332:
3319:
3315:
3268:
3261:
3257:
3256:
3245:
3244:
3221:
3210:
3200:
3199:
3178:
3174:
3146:
3135:
3125:
3124:
3103:
3099:
3088:
3087:
3054:
3053:
3022:
2994:
2990:
2969:
2953:
2925:
2921:
2900:
2867:
2866:
2862:
2851:
2850:
2817:
2816:
2778:
2777:
2768:
2749:
2740:
2739:
2723:
2716:
2702:
2680:
2679:
2634:
2603:
2595:
2577:
2567:
2564:
2563:
2518:
2487:
2479:
2461:
2451:
2442:
2441:
2429:
2422:
2369:
2364:
2363:
2281:
2257:
2256:
2171:
2141:
2093:
2083:
2072:
2062:
2058:
2035:
2025:
1997:
1992:
1991:
1982:
1782:
1781:
1748:
1720:flow velocities
1701:
1656:
1636:
1635:
1590:
1586:
1549:
1522:
1502:
1498:
1461:
1419:
1397:
1386:
1385:
1290:
1289:
1255:
1238:
1237:
1236:
1197:
1196:
1128:
1127:
1124:
1035:
1011:
987:
982:
981:
976:
917:
916:
859:
835:
808:
802:
761:
752:
731:
728:
727:
695:
686:
665:
656:
655:
650:
643:
596:
575:
574:
569:
363:
353:
331:
330:
313:position vector
305:
100:
99:
98:
97:
79:
55:
54:
53:
50:
41:
40:
39:
28:
17:
12:
11:
5:
5581:
5579:
5571:
5570:
5565:
5563:Fluid dynamics
5555:
5554:
5548:
5547:
5545:
5544:
5532:
5522:
5511:
5508:
5507:
5505:
5504:
5499:
5494:
5489:
5484:
5482:Stratification
5479:
5474:
5469:
5464:
5459:
5454:
5453:
5452:
5442:
5437:
5432:
5427:
5422:
5417:
5412:
5407:
5402:
5397:
5392:
5387:
5382:
5374:
5372:Color of water
5369:
5367:Benthic lander
5364:
5359:
5353:
5351:
5347:
5346:
5344:
5343:
5338:
5333:
5327:
5325:
5321:
5320:
5318:
5317:
5312:
5307:
5302:
5297:
5291:
5289:
5283:
5282:
5280:
5279:
5274:
5272:Sea level rise
5269:
5267:Sea level drop
5264:
5259:
5254:
5249:
5243:
5241:
5235:
5234:
5232:
5231:
5226:
5221:
5216:
5211:
5206:
5201:
5196:
5191:
5186:
5180:
5178:
5174:
5173:
5171:
5170:
5165:
5160:
5155:
5150:
5145:
5140:
5135:
5130:
5125:
5120:
5115:
5110:
5105:
5103:Marine geology
5100:
5095:
5090:
5085:
5079:
5077:
5069:
5068:
5066:
5065:
5060:
5055:
5050:
5045:
5043:Passive margin
5040:
5038:Oceanic trench
5035:
5030:
5025:
5020:
5015:
5010:
5005:
5000:
4995:
4990:
4985:
4980:
4975:
4970:
4965:
4960:
4955:
4949:
4947:
4941:
4940:
4938:
4937:
4932:
4927:
4922:
4917:
4912:
4907:
4902:
4897:
4892:
4887:
4882:
4877:
4872:
4867:
4862:
4857:
4852:
4846:
4844:
4838:
4837:
4835:
4834:
4829:
4824:
4819:
4814:
4813:
4812:
4802:
4797:
4792:
4787:
4782:
4777:
4772:
4770:Ocean dynamics
4767:
4762:
4757:
4752:
4747:
4742:
4737:
4732:
4727:
4722:
4717:
4712:
4707:
4702:
4697:
4692:
4687:
4682:
4677:
4672:
4667:
4662:
4660:Coriolis force
4657:
4652:
4647:
4641:
4639:
4633:
4632:
4614:
4612:
4610:
4609:
4608:
4607:
4597:
4592:
4587:
4586:
4585:
4580:
4570:
4565:
4560:
4555:
4550:
4545:
4540:
4535:
4530:
4525:
4520:
4515:
4510:
4509:
4508:
4498:
4493:
4488:
4483:
4481:Stokes problem
4478:
4473:
4468:
4463:
4458:
4453:
4448:
4443:
4438:
4433:
4428:
4423:
4418:
4416:Kinematic wave
4413:
4408:
4403:
4398:
4393:
4388:
4383:
4378:
4373:
4368:
4363:
4358:
4353:
4348:
4343:
4338:
4333:
4327:
4325:
4319:
4318:
4313:
4311:
4310:
4303:
4296:
4288:
4281:
4280:
4264:
4243:
4237:, page 44. Or
4223:
4207:
4195:
4189:
4186:
4180:
4157:
4154:
4148:
4128:
4115:
4097:
4090:
4034:
4018:
4005:
3991:
3989:
3986:
3985:
3984:
3955:
3949:
3936:
3930:
3918:Phillips, O.M.
3914:
3874:
3868:
3855:
3829:(4): 609–646.
3812:
3809:
3808:
3807:
3797:Reprinted in:
3783:
3752:
3749:
3747:
3744:
3743:
3742:
3737:
3732:
3727:
3720:
3717:
3716:
3715:
3700:
3695:
3692:
3689:
3677:
3673:
3669:
3666:
3663:
3660:
3658:
3656:
3651:
3646:
3642:
3639:
3636:
3633:
3630:
3627:
3624:
3621:
3616:
3612:
3608:
3605:
3602:
3599:
3596:
3593:
3590:
3587:
3584:
3579:
3575:
3570:
3564:
3561:
3558:
3546:
3542:
3538:
3535:
3529:
3526:
3524:
3522:
3517:
3512:
3508:
3505:
3502:
3499:
3496:
3493:
3490:
3487:
3484:
3479:
3476:
3466:
3463:
3460:
3456:
3451:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3426:
3423:
3418:
3415:
3405:
3401:
3394:
3391:
3389:
3387:
3382:
3377:
3373:
3370:
3367:
3364:
3361:
3358:
3355:
3352:
3349:
3344:
3341:
3331:
3328:
3325:
3322:
3318:
3313:
3309:
3306:
3303:
3300:
3297:
3294:
3291:
3288:
3285:
3280:
3277:
3267:
3264:
3260:
3253:
3250:
3248:
3246:
3241:
3234:
3231:
3227:
3224:
3217:
3213:
3207:
3203:
3196:
3193:
3190:
3185:
3181:
3177:
3171:
3166:
3159:
3156:
3152:
3149:
3142:
3138:
3132:
3128:
3121:
3118:
3115:
3110:
3106:
3102:
3096:
3093:
3091:
3089:
3084:
3080:
3077:
3074:
3070:
3066:
3061:
3057:
3050:
3045:
3041:
3037:
3034:
3028:
3025:
3020:
3017:
3014:
3010:
3006:
3001:
2997:
2993:
2987:
2984:
2981:
2976:
2972:
2968:
2965:
2959:
2956:
2951:
2948:
2945:
2941:
2937:
2932:
2928:
2924:
2918:
2915:
2912:
2907:
2903:
2899:
2896:
2893:
2890:
2887:
2883:
2879:
2874:
2870:
2865:
2859:
2856:
2854:
2852:
2847:
2843:
2840:
2837:
2833:
2829:
2824:
2820:
2813:
2808:
2804:
2801:
2798:
2794:
2790:
2785:
2781:
2774:
2771:
2769:
2758:
2755:
2748:
2747:
2721:
2714:
2700:
2694:
2693:
2678:
2675:
2672:
2669:
2666:
2663:
2660:
2657:
2654:
2651:
2646:
2643:
2633:
2630:
2627:
2624:
2621:
2609:
2606:
2601:
2598:
2592:
2589:
2586:
2583:
2580:
2578:
2574:
2570:
2566:
2565:
2562:
2559:
2556:
2553:
2550:
2547:
2544:
2541:
2538:
2535:
2530:
2527:
2517:
2514:
2511:
2508:
2505:
2493:
2490:
2485:
2482:
2476:
2473:
2470:
2467:
2464:
2462:
2458:
2454:
2450:
2449:
2427:
2420:
2399:
2398:
2387:
2384:
2381:
2376:
2372:
2337:
2336:
2325:
2322:
2319:
2316:
2313:
2310:
2307:
2304:
2301:
2298:
2293:
2290:
2280:
2275:
2272:
2267:
2264:
2216:incompressible
2170:
2167:
2139:
2133:
2132:
2121:
2116:
2112:
2108:
2105:
2102:
2089:
2086:
2079:
2075:
2069:
2065:
2061:
2055:
2050:
2047:
2044:
2032:
2028:
2024:
2021:
2018:
2006:
2003:
1980:
1974:
1973:
1959:
1949:
1935:
1925:
1895:
1869:
1859:
1837:
1836:
1825:
1822:
1819:
1816:
1813:
1810:
1807:
1804:
1801:
1798:
1795:
1792:
1789:
1700:
1697:
1685:
1682:
1678:
1672:
1665:
1662:
1655:
1649:
1646:
1632:
1631:
1620:
1617:
1612:
1606:
1599:
1596:
1589:
1581:
1578:
1573:
1570:
1567:
1564:
1561:
1556:
1552:
1548:
1545:
1542:
1539:
1536:
1529:
1525:
1518:
1511:
1508:
1501:
1493:
1490:
1485:
1482:
1479:
1476:
1473:
1468:
1464:
1460:
1457:
1454:
1451:
1446:
1441:
1438:
1431:
1426:
1422:
1418:
1415:
1412:
1409:
1404:
1400:
1396:
1393:
1383:
1372:
1369:
1366:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1339:
1336:
1330:
1327:
1324:
1321:
1318:
1315:
1312:
1309:
1303:
1300:
1273:
1270:
1267:
1262:
1258:
1254:
1251:
1248:
1245:
1224:
1220:
1213:
1210:
1204:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1147:
1144:
1138:
1135:
1123:
1120:
1070:
1069:
1058:
1046:
1042:
1034:
1022:
1018:
1010:
998:
994:
974:
968:
967:
961:
955:
949:
939:ergodic theory
931:
930:
915:
910:
904:
899:
896:
893:
890:
887:
883:
879:
875:
869:
863:
856:
851:
847:
841:
838:
833:
830:
827:
823:
819:
815:
811:
805:
799:
794:
790:
787:
784:
780:
776:
770:
767:
758:
755:
753:
742:
738:
730:
729:
726:
721:
717:
714:
711:
707:
703:
699:
692:
689:
687:
676:
672:
664:
663:
648:
641:
631:
630:
619:
615:
611:
608:
603:
599:
595:
591:
587:
583:
567:
547:
546:
536:
524:
514:
496:
478:
437:
436:
425:
420:
415:
412:
409:
406:
403:
399:
395:
391:
385:
379:
375:
369:
366:
360:
356:
350:
344:
341:
304:
301:
210:his 1847 study
143:fluid dynamics
106:An expanse of
57:
56:
51:
44:
43:
42:
29:
22:
21:
20:
19:
18:
15:
13:
10:
9:
6:
4:
3:
2:
5580:
5569:
5566:
5564:
5561:
5560:
5558:
5543:
5538:
5533:
5531:
5523:
5521:
5513:
5512:
5509:
5503:
5500:
5498:
5495:
5493:
5490:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5458:
5455:
5451:
5448:
5447:
5446:
5443:
5441:
5438:
5436:
5433:
5431:
5428:
5426:
5423:
5421:
5418:
5416:
5413:
5411:
5408:
5406:
5403:
5401:
5398:
5396:
5393:
5391:
5390:Marine energy
5388:
5386:
5383:
5381:
5380:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5357:Acidification
5355:
5354:
5352:
5348:
5342:
5339:
5337:
5334:
5332:
5329:
5328:
5326:
5322:
5316:
5313:
5311:
5310:SOFAR channel
5308:
5306:
5303:
5301:
5298:
5296:
5293:
5292:
5290:
5288:
5284:
5278:
5275:
5273:
5270:
5268:
5265:
5263:
5260:
5258:
5255:
5253:
5250:
5248:
5245:
5244:
5242:
5240:
5236:
5230:
5227:
5225:
5222:
5220:
5217:
5215:
5212:
5210:
5207:
5205:
5202:
5200:
5197:
5195:
5192:
5190:
5187:
5185:
5182:
5181:
5179:
5175:
5169:
5166:
5164:
5161:
5159:
5156:
5154:
5151:
5149:
5146:
5144:
5141:
5139:
5136:
5134:
5131:
5129:
5126:
5124:
5121:
5119:
5118:Oceanic crust
5116:
5114:
5111:
5109:
5106:
5104:
5101:
5099:
5096:
5094:
5093:Fracture zone
5091:
5089:
5086:
5084:
5081:
5080:
5078:
5076:
5070:
5064:
5061:
5059:
5056:
5054:
5051:
5049:
5046:
5044:
5041:
5039:
5036:
5034:
5031:
5029:
5028:Oceanic basin
5026:
5024:
5021:
5019:
5016:
5014:
5011:
5009:
5006:
5004:
5001:
4999:
4996:
4994:
4991:
4989:
4986:
4984:
4981:
4979:
4976:
4974:
4971:
4969:
4966:
4964:
4961:
4959:
4958:Abyssal plain
4956:
4954:
4951:
4950:
4948:
4946:
4942:
4936:
4933:
4931:
4928:
4926:
4923:
4921:
4918:
4916:
4913:
4911:
4908:
4906:
4903:
4901:
4898:
4896:
4893:
4891:
4888:
4886:
4883:
4881:
4878:
4876:
4873:
4871:
4868:
4866:
4865:Internal tide
4863:
4861:
4858:
4856:
4853:
4851:
4848:
4847:
4845:
4843:
4839:
4833:
4830:
4828:
4825:
4823:
4820:
4818:
4815:
4811:
4808:
4807:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4771:
4768:
4766:
4763:
4761:
4760:Ocean current
4758:
4756:
4753:
4751:
4748:
4746:
4743:
4741:
4738:
4736:
4733:
4731:
4728:
4726:
4723:
4721:
4718:
4716:
4713:
4711:
4708:
4706:
4703:
4701:
4698:
4696:
4693:
4691:
4688:
4686:
4683:
4681:
4678:
4676:
4673:
4671:
4668:
4666:
4663:
4661:
4658:
4656:
4653:
4651:
4648:
4646:
4643:
4642:
4640:
4638:
4634:
4629:
4618:
4606:
4603:
4602:
4601:
4598:
4596:
4593:
4591:
4588:
4584:
4581:
4579:
4576:
4575:
4574:
4571:
4569:
4566:
4564:
4561:
4559:
4558:Wave shoaling
4556:
4554:
4551:
4549:
4546:
4544:
4541:
4539:
4536:
4534:
4531:
4529:
4526:
4524:
4521:
4519:
4518:Ursell number
4516:
4514:
4511:
4507:
4504:
4503:
4502:
4499:
4497:
4494:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4462:
4459:
4457:
4454:
4452:
4449:
4447:
4444:
4442:
4439:
4437:
4434:
4432:
4429:
4427:
4424:
4422:
4419:
4417:
4414:
4412:
4409:
4407:
4404:
4402:
4401:Internal wave
4399:
4397:
4394:
4392:
4389:
4387:
4384:
4382:
4379:
4377:
4374:
4372:
4369:
4367:
4364:
4362:
4359:
4357:
4354:
4352:
4351:Breaking wave
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4332:
4329:
4328:
4326:
4324:
4320:
4316:
4309:
4304:
4302:
4297:
4295:
4290:
4289:
4286:
4277:
4274:
4268:
4265:
4261:
4257:
4253:
4247:
4244:
4240:
4236:
4230:
4228:
4224:
4220:
4214:
4212:
4208:
4193:
4187:
4184:
4178:
4155:
4152:
4146:
4138:
4132:
4129:
4125:
4119:
4116:
4112:
4106:
4104:
4102:
4098:
4093:
4087:
4083:
4075:
4071:
4067:
4063:
4059:
4055:
4051:
4047:
4038:
4035:
4031:
4028:
4022:
4019:
4015:
4009:
4006:
4002:
4001:Kubota (1994)
3996:
3993:
3987:
3981:
3977:
3973:
3969:
3965:
3961:
3956:
3952:
3946:
3942:
3937:
3933:
3927:
3923:
3919:
3915:
3911:
3907:
3903:
3899:
3895:
3891:
3887:
3883:
3879:
3875:
3871:
3865:
3861:
3856:
3852:
3848:
3844:
3840:
3836:
3832:
3828:
3824:
3820:
3819:M.E. McIntyre
3815:
3814:
3810:
3804:
3803:
3793:
3789:
3784:
3780:
3776:
3772:
3768:
3764:
3760:
3755:
3754:
3750:
3745:
3741:
3738:
3736:
3733:
3731:
3728:
3726:
3723:
3722:
3718:
3698:
3693:
3690:
3687:
3675:
3671:
3667:
3664:
3661:
3659:
3644:
3637:
3634:
3631:
3628:
3625:
3619:
3614:
3610:
3606:
3600:
3597:
3594:
3591:
3588:
3582:
3577:
3573:
3568:
3562:
3559:
3556:
3544:
3540:
3536:
3533:
3527:
3525:
3510:
3503:
3500:
3497:
3494:
3491:
3485:
3482:
3477:
3474:
3464:
3461:
3458:
3454:
3449:
3442:
3439:
3436:
3433:
3430:
3424:
3421:
3416:
3413:
3403:
3399:
3392:
3390:
3375:
3368:
3365:
3362:
3359:
3356:
3350:
3347:
3342:
3339:
3329:
3326:
3323:
3320:
3316:
3311:
3304:
3301:
3298:
3295:
3292:
3286:
3283:
3278:
3275:
3265:
3262:
3258:
3251:
3249:
3232:
3225:
3215:
3211:
3205:
3191:
3188:
3183:
3179:
3169:
3157:
3150:
3140:
3136:
3130:
3116:
3113:
3108:
3104:
3094:
3092:
3075:
3072:
3059:
3055:
3048:
3039:
3035:
3032:
3026:
3015:
3012:
2999:
2995:
2982:
2979:
2974:
2970:
2963:
2957:
2946:
2943:
2930:
2926:
2913:
2910:
2905:
2901:
2894:
2888:
2885:
2872:
2868:
2863:
2857:
2855:
2838:
2835:
2822:
2818:
2811:
2799:
2796:
2783:
2779:
2772:
2770:
2753:
2738:
2737:
2736:
2734:
2733:
2728:
2724:
2717:
2710:
2706:
2699:
2676:
2670:
2667:
2664:
2661:
2658:
2652:
2649:
2644:
2641:
2631:
2628:
2625:
2622:
2619:
2607:
2599:
2590:
2587:
2584:
2581:
2579:
2572:
2568:
2560:
2554:
2551:
2548:
2545:
2542:
2536:
2533:
2528:
2525:
2515:
2512:
2509:
2506:
2503:
2491:
2483:
2474:
2471:
2468:
2465:
2463:
2456:
2452:
2440:
2439:
2438:
2436:
2435:
2430:
2423:
2416:
2412:
2408:
2404:
2385:
2382:
2379:
2374:
2370:
2362:
2361:
2360:
2358:
2354:
2350:
2347:problem, the
2346:
2342:
2323:
2317:
2314:
2311:
2308:
2305:
2299:
2296:
2291:
2288:
2278:
2273:
2270:
2265:
2262:
2255:
2254:
2253:
2251:
2247:
2244:
2240:
2235:
2233:
2229:
2225:
2221:
2217:
2213:
2209:
2205:
2201:
2198:
2195:
2191:
2187:
2183:
2179:
2176:
2175:infinitesimal
2168:
2166:
2164:
2160:
2156:
2152:
2148:
2145:
2138:
2119:
2114:
2110:
2106:
2103:
2100:
2087:
2084:
2077:
2073:
2067:
2063:
2059:
2053:
2048:
2045:
2042:
2030:
2026:
2022:
2019:
2016:
2001:
1990:
1989:
1988:
1986:
1979:
1971:
1967:
1963:
1960:
1957:
1953:
1950:
1947:
1943:
1939:
1936:
1933:
1929:
1926:
1923:
1919:
1915:
1911:
1907:
1903:
1899:
1896:
1893:
1889:
1885:
1881:
1877:
1873:
1870:
1867:
1863:
1860:
1857:
1853:
1849:
1845:
1842:
1841:
1840:
1823:
1817:
1814:
1811:
1808:
1805:
1799:
1796:
1793:
1790:
1787:
1780:
1779:
1778:
1776:
1772:
1768:
1765:
1761:
1757:
1753:
1747:
1743:
1735:
1734:
1729:
1725:
1721:
1717:
1713:
1710:
1705:
1698:
1696:
1683:
1680:
1676:
1670:
1660:
1653:
1647:
1644:
1618:
1615:
1610:
1604:
1594:
1587:
1579:
1576:
1571:
1565:
1562:
1559:
1554:
1550:
1546:
1540:
1537:
1534:
1527:
1523:
1516:
1506:
1499:
1491:
1488:
1483:
1477:
1474:
1471:
1466:
1462:
1458:
1452:
1449:
1444:
1436:
1429:
1424:
1420:
1416:
1410:
1407:
1402:
1398:
1391:
1384:
1370:
1364:
1361:
1358:
1355:
1352:
1346:
1343:
1334:
1328:
1322:
1319:
1316:
1310:
1307:
1301:
1298:
1288:
1287:
1286:
1268:
1265:
1260:
1256:
1249:
1246:
1243:
1222:
1218:
1208:
1202:
1194:
1178:
1172:
1169:
1166:
1163:
1160:
1154:
1151:
1142:
1136:
1133:
1121:
1119:
1117:
1113:
1109:
1105:
1104:
1099:
1095:
1091:
1090:
1085:
1084:
1079:
1075:
1056:
1032:
1008:
980:
979:
978:
973:
965:
962:
959:
956:
953:
950:
947:
944:
943:
942:
940:
936:
913:
897:
894:
888:
885:
854:
845:
839:
828:
825:
803:
797:
785:
782:
768:
756:
754:
724:
712:
709:
690:
688:
654:
653:
652:
647:
640:
636:
617:
609:
601:
597:
593:
573:
572:
571:
566:
562:
558:
554:
553:
544:
540:
537:
534:
530:
529:
525:
522:
518:
515:
512:
508:
504:
500:
497:
494:
490:
489:
484:
483:
479:
476:
472:
468:
467:
462:
461:
456:
452:
448:
447:
442:
441:
440:
423:
413:
410:
404:
401:
373:
367:
348:
342:
329:
328:
327:
325:
323:
319:
314:
310:
302:
300:
298:
294:
290:
289:mass transfer
285:
283:
279:
278:
273:
269:
264:
262:
258:
254:
250:
249:inhomogeneous
244:
242:
241:flow velocity
238:
234:
230:
226:
222:
217:
215:
211:
207:
203:
199:
195:
194:flow velocity
192:
188:
187:flow velocity
185:
182:
177:
175:
171:
167:
163:
159:
155:
152:
148:
144:
140:
137:
129:
128:marine debris
125:
121:
117:
113:
109:
104:
95:
94:Doppler shift
91:
87:
83:
77:
73:
69:
65:
61:
60:flow velocity
48:
37:
33:
26:
5497:Water column
5445:Oceanography
5420:Observations
5415:Explorations
5385:Marginal sea
5378:
5336:OSTM/Jason-2
5168:Volcanic arc
5143:Slab suction
4860:Head of tide
4750:Loop Current
4690:Ekman spiral
4476:Stokes drift
4475:
4386:Gravity wave
4361:Cnoidal wave
4272:
4267:
4246:
4239:Craik (1985)
4131:
4124:Craik (1985)
4118:
4081:
4049:
4045:
4037:
4030:Craik (1985)
4026:
4021:
4014:Craik (1985)
4008:
3995:
3963:
3959:
3940:
3921:
3885:
3881:
3859:
3826:
3822:
3801:
3791:
3787:
3765:(1): 23–42.
3762:
3758:
3730:Darwin drift
2731:
2730:
2726:
2719:
2712:
2708:
2697:
2695:
2433:
2432:
2425:
2418:
2407:acceleration
2402:
2400:
2338:
2245:
2236:
2228:irrotational
2222:. The fluid
2220:mass density
2207:
2197:acceleration
2189:
2182:free surface
2172:
2162:
2159:free surface
2154:
2150:
2146:
2136:
2134:
1984:
1977:
1975:
1961:
1951:
1945:
1937:
1927:
1913:
1909:
1905:
1897:
1887:
1883:
1879:
1871:
1864:is the wave
1861:
1855:
1852:free surface
1843:
1838:
1775:free surface
1773:wave on the
1749:
1731:
1723:
1715:
1711:
1633:
1125:
1107:
1106:to a unique
1102:
1101:
1097:
1088:
1087:
1082:
1081:
1077:
1071:
971:
969:
932:
645:
638:
632:
564:
560:
556:
551:
550:
548:
538:
527:
526:
516:
506:
502:
498:
492:
487:
486:
481:
480:
474:
470:
465:
464:
459:
458:
450:
445:
444:
438:
321:
317:
315:
306:
286:
275:
265:
245:
221:Stokes drift
220:
218:
178:
166:free surface
146:
133:
86:free surface
5568:Water waves
5487:Thermocline
5204:Mesopelagic
5177:Ocean zones
5148:Slab window
5013:Hydrography
4953:Abyssal fan
4920:Tidal range
4910:Tidal power
4905:Tidal force
4790:Rip current
4725:Gulf Stream
4685:Ekman layer
4675:Downwelling
4650:Baroclinity
4637:Circulation
4533:Wave height
4523:Wave action
4506:megatsunami
4486:Stokes wave
4446:Rossby wave
4411:Kelvin wave
4391:Green's law
4241:, page 110.
4171:instead of
4032:, page 120.
2353:wave period
2349:wave length
2341:non-trivial
1966:wave period
1956:wave length
1894:per meter),
1876:wave number
1752:water waves
1746:Stokes wave
253:water waves
225:wave period
214:water waves
170:water waves
134:For a pure
120:Ekman drift
90:wave period
82:wave period
68:wave period
36:wave length
32:water waves
5557:Categories
5425:Reanalysis
5324:Satellites
5305:Sofar bomb
5153:Subduction
5128:Ridge push
5023:Ocean bank
5003:Contourite
4930:Tide gauge
4915:Tidal race
4900:Tidal bore
4890:Slack tide
4855:Earth tide
4775:Ocean gyre
4595:Wind setup
4590:Wind fetch
4553:Wave setup
4548:Wave radar
4543:Wave power
4441:Rogue wave
4371:Dispersion
4278:, page 38.
4221:, page 37.
4126:, page 84.
4113:, page 43.
4084:. Pitman.
3794:: 441–455.
3751:Historical
3746:References
2359:relation:
2357:dispersion
2345:eigenvalue
2169:Derivation
1942:coordinate
1932:coordinate
1771:sinusoidal
1760:infinitely
1740:See also:
184:Lagrangian
162:fluid flow
5287:Acoustics
5239:Sea level
5138:Slab pull
5075:tectonics
4983:Cold seep
4945:Landforms
4822:Whirlpool
4817:Upwelling
4600:Wind wave
4528:Wave base
4456:Sea state
4376:Edge wave
4366:Cross sea
4217:See e.g.
4147:−
4122:See e.g.
4074:122673867
3910:120420719
3665:ω
3650:¯
3635:ω
3632:−
3620:
3598:ω
3595:−
3583:
3534:ω
3516:¯
3501:ω
3498:−
3486:
3459:ω
3440:ω
3437:−
3425:
3381:¯
3366:ω
3363:−
3351:
3324:ω
3321:−
3302:ω
3299:−
3287:
3263:−
3240:¯
3230:∂
3223:∂
3212:ξ
3202:∂
3189:−
3180:ξ
3165:¯
3155:∂
3148:∂
3137:ξ
3127:∂
3114:−
3105:ξ
3095:≈
3083:¯
3049:−
3044:¯
3036:⋯
3024:∂
2992:∂
2980:−
2971:ξ
2955:∂
2923:∂
2911:−
2902:ξ
2846:¯
2812:−
2807:¯
2793:ξ
2757:¯
2668:ω
2665:−
2653:
2605:∂
2600:φ
2597:∂
2591:∫
2569:ξ
2552:ω
2549:−
2537:
2513:−
2489:∂
2484:φ
2481:∂
2475:∫
2453:ξ
2371:ω
2315:ω
2312:−
2300:
2271:ω
2263:φ
2178:amplitude
2144:amplitude
2115:λ
2104:π
2085:λ
2064:π
2020:ω
2017:≈
2005:¯
1958:(meters),
1868:(meters),
1866:amplitude
1848:elevation
1815:ω
1812:−
1800:
1788:η
1681:ω
1664:^
1611:ω
1598:^
1563:ω
1560:−
1551:ξ
1538:
1524:ω
1510:^
1484:−
1475:ω
1472:−
1463:ξ
1453:
1445:ω
1440:^
1421:ξ
1417:≈
1399:ξ
1392:ξ
1362:ω
1359:−
1356:ξ
1347:
1338:^
1317:ξ
1302:˙
1299:ξ
1257:ξ
1250:ξ
1223:ω
1212:^
1170:ω
1167:−
1155:
1146:^
1114:(GLM) by
1045:¯
1033:−
1021:¯
997:¯
909:¯
882:α
874:ξ
850:¯
837:∂
822:α
814:ξ
810:∂
793:¯
779:α
769:˙
766:ξ
741:¯
720:¯
675:¯
614:α
590:α
582:ξ
398:α
390:ξ
365:∂
359:ξ
355:∂
343:˙
340:ξ
324:, t)
202:nonlinear
108:driftwood
34:, with a
5520:Category
5472:Seawater
5199:Littoral
5194:Deep sea
5053:Seamount
4935:Tideline
4880:Rip tide
4810:shutdown
4780:Overflow
4513:Undertow
4356:Clapotis
3920:(1977).
3719:See also
2237:Now the
2212:inviscid
2194:constant
2180:and the
966:average.
954:average,
948:average,
511:velocity
297:periodic
191:Eulerian
154:velocity
78:is zero.
5530:Commons
5400:Mooring
5350:Related
5341:Jason-3
5331:Jason-1
5214:Pelagic
5209:Oceanic
5184:Benthic
4501:Tsunami
4471:Soliton
4054:Bibcode
3968:Bibcode
3890:Bibcode
3851:4988274
3831:Bibcode
3767:Bibcode
2707:around
2411:gravity
2204:gravity
1970:seconds
1964:is the
1954:is the
1918:radians
1900:is the
1892:radians
1874:is the
1854:in the
1850:of the
1846:is the
1728:average
1074:mapping
935:average
635:average
633:If the
453:is the
272:average
266:In the
196:of the
181:average
151:average
149:is the
5219:Photic
5048:Seabed
4461:Seiche
4088:
4072:
3947:
3928:
3908:
3866:
3849:
2415:linear
2200:vector
2188:level
1922:second
1839:where
1764:linear
1736:(GLM).
1709:period
439:where
145:, the
139:motion
76:trough
5410:Ocean
5379:Alvin
5229:Swash
5073:Plate
5018:Knoll
5008:Guyot
4963:Atoll
4842:Tides
4605:model
4491:Swell
4323:Waves
4258:. Or
4070:S2CID
3988:Notes
3906:S2CID
3847:S2CID
3811:Other
2401:with
1769:of a
1724:Right
964:phase
952:space
257:tides
198:fluid
158:fluid
112:coast
5377:DSV
5362:Argo
5224:Surf
4680:Eddy
4273:e.g.
4271:See
4233:See
4135:See
4109:See
4086:ISBN
4027:e.g.
4025:See
4012:See
3999:See
3945:ISBN
3926:ISBN
3864:ISBN
2437:are
2424:and
2405:the
2351:and
2252:and
2239:flow
2232:rest
2224:flow
2214:and
2186:mean
1920:per
1744:and
1716:Left
1094:path
946:time
651:are
543:time
316:x =
307:The
259:and
219:The
136:wave
122:and
72:mean
64:path
4062:doi
4050:302
3976:doi
3898:doi
3886:245
3839:doi
3775:doi
3611:cos
3574:sin
3483:cos
3422:cos
3348:sin
3284:sin
2725:/ ∂
2718:= ∂
2650:cos
2534:sin
2409:by
2297:sin
2226:is
2202:by
2153:= −
1908:= 2
1882:= 2
1797:cos
1754:by
1535:sin
1450:cos
1344:sin
1152:sin
941:):
541:is
457:of
212:of
168:of
141:in
114:of
5559::
4226:^
4210:^
4100:^
4068:.
4060:.
4048:.
3974:.
3964:24
3962:.
3904:.
3896:.
3884:.
3845:.
3837:.
3827:89
3825:.
3790:.
3773:.
3763:37
3761:.
2735::
2234:.
2161:,
1972:).
1924:),
1904::
1878::
1726::
1722:.
1118:.
570::
563:=
505:,
491:,
469:,
449:/∂
284:.
263:.
255:,
216:.
176:.
4307:e
4300:t
4293:v
4194:.
4188:2
4185:1
4179:+
4156:4
4153:1
4094:.
4076:.
4064::
4056::
4003:.
3982:.
3978::
3970::
3953:.
3934:.
3912:.
3900::
3892::
3872:.
3853:.
3841::
3833::
3792:8
3781:.
3777::
3769::
3699:.
3694:z
3691:k
3688:2
3683:e
3676:2
3672:a
3668:k
3662:=
3645:]
3641:)
3638:t
3629:x
3626:k
3623:(
3615:2
3607:+
3604:)
3601:t
3592:x
3589:k
3586:(
3578:2
3569:[
3563:z
3560:k
3557:2
3552:e
3545:2
3541:a
3537:k
3528:=
3511:]
3507:)
3504:t
3495:x
3492:k
3489:(
3478:z
3475:k
3470:e
3465:a
3462:k
3455:[
3450:]
3446:)
3443:t
3434:x
3431:k
3428:(
3417:z
3414:k
3409:e
3404:a
3400:[
3393:+
3376:]
3372:)
3369:t
3360:x
3357:k
3354:(
3343:z
3340:k
3335:e
3330:a
3327:k
3317:[
3312:]
3308:)
3305:t
3296:x
3293:k
3290:(
3279:z
3276:k
3271:e
3266:a
3259:[
3252:=
3233:t
3226:z
3216:x
3206:2
3195:)
3192:z
3184:z
3176:(
3170:+
3158:t
3151:x
3141:x
3131:2
3120:)
3117:x
3109:x
3101:(
3079:)
3076:t
3073:,
3069:x
3065:(
3060:x
3056:u
3040:]
3033:+
3027:z
3019:)
3016:t
3013:,
3009:x
3005:(
3000:x
2996:u
2986:)
2983:z
2975:z
2967:(
2964:+
2958:x
2950:)
2947:t
2944:,
2940:x
2936:(
2931:x
2927:u
2917:)
2914:x
2906:x
2898:(
2895:+
2892:)
2889:t
2886:,
2882:x
2878:(
2873:x
2869:u
2864:[
2858:=
2842:)
2839:t
2836:,
2832:x
2828:(
2823:x
2819:u
2803:)
2800:t
2797:,
2789:(
2784:x
2780:u
2773:=
2764:S
2754:u
2732:ξ
2727:t
2722:x
2720:ξ
2715:x
2713:u
2709:x
2701:S
2698:ū
2677:.
2674:)
2671:t
2662:x
2659:k
2656:(
2645:z
2642:k
2637:e
2632:a
2629:+
2626:z
2623:=
2620:t
2616:d
2608:z
2588:+
2585:z
2582:=
2573:z
2561:,
2558:)
2555:t
2546:x
2543:k
2540:(
2529:z
2526:k
2521:e
2516:a
2510:x
2507:=
2504:t
2500:d
2492:x
2472:+
2469:x
2466:=
2457:x
2434:ξ
2428:z
2426:ξ
2421:x
2419:ξ
2403:g
2386:k
2383:g
2380:=
2375:2
2324:.
2321:)
2318:t
2309:x
2306:k
2303:(
2292:z
2289:k
2284:e
2279:a
2274:k
2266:=
2246:φ
2208:z
2190:z
2163:z
2155:λ
2151:z
2147:a
2140:S
2137:ū
2120:.
2111:/
2107:z
2101:4
2096:e
2088:T
2078:2
2074:a
2068:2
2060:4
2054:=
2049:z
2046:k
2043:2
2038:e
2031:2
2027:a
2023:k
2012:S
2002:u
1985:z
1983:(
1981:S
1978:ū
1968:(
1962:T
1952:λ
1946:z
1938:z
1928:x
1916:(
1914:T
1912:/
1910:π
1906:ω
1898:ω
1890:(
1888:λ
1886:/
1884:π
1880:k
1872:k
1862:a
1856:z
1844:η
1824:,
1821:)
1818:t
1809:x
1806:k
1803:(
1794:a
1791:=
1712:T
1684:.
1677:/
1671:2
1661:u
1654:k
1648:2
1645:1
1619:.
1616:t
1605:2
1595:u
1588:k
1580:2
1577:1
1572:+
1569:)
1566:t
1555:0
1547:k
1544:(
1541:2
1528:2
1517:2
1507:u
1500:k
1492:4
1489:1
1481:)
1478:t
1467:0
1459:k
1456:(
1437:u
1430:+
1425:0
1414:)
1411:t
1408:,
1403:0
1395:(
1371:,
1368:)
1365:t
1353:k
1350:(
1335:u
1329:=
1326:)
1323:t
1320:,
1314:(
1311:u
1308:=
1284::
1272:)
1269:t
1266:,
1261:0
1253:(
1247:=
1244:x
1219:/
1209:u
1203:k
1179:,
1176:)
1173:t
1164:x
1161:k
1158:(
1143:u
1137:=
1134:u
1108:x
1103:α
1098:x
1089:α
1083:α
1078:x
1057:.
1052:E
1041:u
1028:L
1017:u
1009:=
1004:S
993:u
975:S
972:ū
960:,
914:.
903:)
898:t
895:,
892:)
889:t
886:,
878:(
868:(
862:u
855:=
846:)
840:t
832:)
829:t
826:,
818:(
804:(
798:=
789:)
786:t
783:,
775:(
757:=
748:L
737:u
725:,
716:)
713:t
710:,
706:x
702:(
698:u
691:=
682:E
671:u
649:L
646:ū
642:E
639:ū
618:.
610:=
607:)
602:0
598:t
594:,
586:(
568:0
565:t
561:t
557:x
552:α
545:.
539:t
535:,
528:α
523:,
517:x
513:,
507:t
503:x
501:(
499:u
493:t
488:α
485:(
482:ξ
477:,
475:t
471:t
466:α
463:(
460:ξ
451:t
446:ξ
443:∂
424:,
419:)
414:t
411:,
408:)
405:t
402:,
394:(
384:(
378:u
374:=
368:t
349:=
322:α
320:(
318:ξ
130:.
96:.
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