5813:
4890:
1556:
5265:
3990:
1118:
5808:{\displaystyle {\begin{aligned}{\frac {\partial E}{\partial t}}&+{\frac {\partial }{\partial x}}\left+{\frac {\partial }{\partial y}}\left\\&+S_{xx}{\frac {\partial {\overline {u}}_{x}}{\partial x}}+S_{xy}\left({\frac {\partial {\overline {u}}_{y}}{\partial x}}+{\frac {\partial {\overline {u}}_{x}}{\partial y}}\right)+S_{yy}{\frac {\partial {\overline {u}}_{y}}{\partial y}}\\&=\left(\tau _{w,x}-\tau _{b,x}\right){\overline {u}}_{x}+\left(\tau _{w,y}-\tau _{b,y}\right){\overline {u}}_{y}-\varepsilon .\end{aligned}}}
4885:{\displaystyle {\begin{aligned}{\frac {\partial }{\partial t}}\left&+{\frac {\partial }{\partial x}}\left+{\frac {\partial }{\partial y}}\left\\&=\rho g\left(h+{\overline {\eta }}\right){\frac {\partial }{\partial x}}h+\tau _{w,x}-\tau _{b,x},\\{\frac {\partial }{\partial t}}\left&+{\frac {\partial }{\partial x}}\left+{\frac {\partial }{\partial y}}\left\\&=\rho g\left(h+{\overline {\eta }}\right){\frac {\partial }{\partial y}}h+\tau _{w,y}-\tau _{b,y}.\end{aligned}}}
20:
6677:
1551:{\displaystyle {\begin{aligned}S_{xx}&={\overline {\int _{-h}^{\eta }\left(p+\rho {\tilde {u}}^{2}\right)\;{\text{d}}z}}-{\frac {1}{2}}\rho g\left(h+{\overline {\eta }}\right)^{2},\\S_{xy}&={\overline {\int _{-h}^{\eta }\left(\rho {\tilde {u}}{\tilde {v}}\right)\;{\text{d}}z}}=S_{yx},\\S_{yy}&={\overline {\int _{-h}^{\eta }\left(p+\rho {\tilde {v}}^{2}\right)\;{\text{d}}z}}-{\frac {1}{2}}\rho g\left(h+{\overline {\eta }}\right)^{2},\end{aligned}}}
3699:
7565:
5118:
7586:
6666:
3401:
7575:
2830:
4927:
2622:
2120:
3315:
441:
2250:
The radiation stress tensor is an important quantity in the description of the phase-averaged dynamical interaction between waves and mean flows. Here, the depth-integrated dynamical conservation equations are given, but ā in order to model three-dimensional mean flows forced by or interacting with
3694:{\displaystyle {\begin{aligned}&{\frac {\partial }{\partial t}}\left+\nabla \cdot {\boldsymbol {M}}=0,\\&{\frac {\partial {\boldsymbol {M}}}{\partial t}}+\nabla \cdot \left=\rho g\left(h+{\overline {\eta }}\right)\nabla h+{\boldsymbol {\tau }}_{w}-{\boldsymbol {\tau }}_{b}.\end{aligned}}}
2699:
2434:
5113:{\displaystyle {\frac {\partial E}{\partial t}}+\nabla \cdot \left+\mathbf {S} :\left(\nabla \otimes {\overline {\boldsymbol {u}}}\right)={\boldsymbol {\tau }}_{w}\cdot {\overline {\boldsymbol {u}}}-{\boldsymbol {\tau }}_{b}\cdot {\overline {\boldsymbol {u}}}-\varepsilon ,}
3942:
2496:
1696:
3032:
1091:
4908:
of the total flow ā that is the sum of the energy of the mean flow and the fluctuating motion ā is conserved. However, the mean energy of the fluctuating motion itself is not conserved, nor is the energy of the mean flow. The mean energy
284:
5184:
2337:
2825:{\displaystyle {\overline {\boldsymbol {u}}}={\frac {\boldsymbol {M}}{\rho \,\left(h+{\overline {\eta }}\right)}}={\overline {\boldsymbol {v}}}+{\frac {{\boldsymbol {M}}_{w}}{\rho \,\left(h+{\overline {\eta }}\right)}}.}
735:
3001:
860:
2359:
3719:
2617:{\displaystyle {\boldsymbol {M}}={\overline {\int _{-h}^{\eta }\rho \,{\boldsymbol {v}}\;{\text{d}}z}}=\rho \,\left(h+{\overline {\eta }}\right){\overline {\boldsymbol {v}}}+{\boldsymbol {M}}_{w},}
5270:
3995:
3406:
1701:
1123:
2115:{\displaystyle {\begin{aligned}S_{xx}&=\leftE,\\S_{xy}&=\left({\frac {k_{x}k_{y}}{k^{2}}}{\frac {c_{g}}{c_{p}}}\right)E=S_{yx},\quad {\text{and}}\\S_{yy}&=\leftE,\end{aligned}}}
1681:
175:
in the surf zone ā for oblique incidence of waves on a beach, the reduction in wave height inside the surf zone (by breaking) introduces a variation of the shear-stress component
514:
3310:{\displaystyle {\frac {\partial }{\partial t}}\left+\nabla \cdot \left=\rho g\left(h+{\overline {\eta }}\right)\nabla h+{\boldsymbol {\tau }}_{w}-{\boldsymbol {\tau }}_{b},}
1617:
1588:
980:
134:
The radiation stress ā mean excess momentum-flux due to the presence of the waves ā plays an important role in the explanation and modeling of various coastal processes:
7305:
992:
111:
The radiation stress tensor, as well as several of its implications on the physics of surface gravity waves and mean flows, were formulated in a series of papers by
7295:
6354:
436:{\displaystyle S_{xx}={\overline {\int _{-h}^{\eta }\left(p+\rho {\tilde {u}}^{2}\right)\;{\text{d}}z}}-{\frac {1}{2}}\rho g\left(h+{\overline {\eta }}\right)^{2},}
5138:
2280:
7211:
165:, this results in changes of the mean surface elevation called wave setup (in case of an increased level) and setdown (for a decreased water level);
651:
184:
of the radiation stress over the width of the surf zone. This provides the forcing of a wave-driven longshore current, which is of importance for
2868:
6626:
6394:
249:, the energy exchanges between the waves and the mean flow, as well as the mean-flow forcing, can be modeled by means of the radiation stress.
5965:
784:
6858:
2429:{\displaystyle c_{p}={\frac {\sigma }{k}}\qquad {\text{with}}\qquad \sigma =\omega -{\boldsymbol {k}}\cdot {\overline {\boldsymbol {v}}},}
6748:
6219:
Longuet-Higgins, M. S.; Stewart, R. W. (1962), "Radiation stress and mass transport in gravity waves, with application to 'surf beats'",
2673:
is also the mean of the depth-integrated horizontal mass flux, and consists of two contributions: one by the mean current and the other (
6347:
5986:
7453:
6880:
6768:
7300:
6571:
6323:
6302:
6718:
6758:
6183:
Longuet-Higgins, M. S.; Stewart, R. W. (1961), "The changes in amplitude of short gravity waves on steady non-uniform currents",
3937:{\displaystyle {\frac {\partial }{\partial t}}\left+{\frac {\partial }{\partial x}}\left+{\frac {\partial }{\partial y}}\left=0,}
528:
7578:
7488:
6474:
7161:
6255:
Longuet-Higgins, M. S.; Stewart, R. W. (1964), "Radiation stresses in water waves; a physical discussion, with applications",
6147:
Longuet-Higgins, M. S.; Stewart, R. W. (1960), "Changes in the form of short gravity waves on long waves and tidal currents",
7611:
7568:
6340:
214:
the radiation stress varies along the group. As a result, a non-linear long wave propagates together with the group, at the
5823:
6616:
5981:
Walstra, D. J. R.; Roelvink, J. A.; Groeneweg, J. (2000), "Calculation of wave-driven currents in a 3D mean flow model",
5187:
238:
6676:
3710:
2835:
Observe that first the depth-integrated horizontal momentum is averaged, before the division by the mean water depth (
1097:
5882:
6813:
112:
6713:
7348:
6753:
123:
7478:
6853:
6843:
6783:
6419:
6389:
219:
774:) per unit of horizontal area. From the results of Airy wave theory, to second order, the mean energy density
7515:
7498:
7335:
6828:
6693:
6631:
6621:
6514:
929:
1630:
7510:
7448:
6875:
6561:
81:
in the fluid layer. As a result, varying radiation stresses induce changes in the mean surface elevation (
469:
7343:
7325:
6833:
6728:
6363:
2251:
surface waves ā a three-dimensional description of the radiation stress over the fluid layer is needed.
26:
on beaches induce variations in radiation stress, driving longshore currents. The resulting longshore
7616:
7530:
7363:
7066:
6923:
6788:
6499:
6311:
6264:
6228:
6192:
6156:
6095:
6019:
624:
268:
97:
59:
7525:
7410:
7405:
7131:
6803:
6763:
6479:
6007:
1593:
1564:
963:
7468:
7181:
7171:
7136:
7036:
7021:
6918:
6244:
6208:
6172:
6035:
185:
146:
119:
27:
1086:{\displaystyle \mathbf {S} ={\begin{pmatrix}S_{xx}&S_{xy}\\S_{yx}&S_{yy}\end{pmatrix}}.}
580:
19:
7550:
7540:
7483:
7463:
7146:
7111:
7046:
7026:
7016:
6898:
6586:
6444:
6319:
6298:
5961:
4905:
2490:, also per unit of horizontal area, is the mean value of the integral of momentum over depth:
2343:
207:
5884:
Computation of set-up, longshore currents, run-up and overtopping due to wind-generated waves
7505:
7473:
7443:
7252:
7237:
7106:
7041:
6933:
6848:
6778:
6703:
6454:
6384:
6379:
6272:
6236:
6200:
6164:
6027:
5990:
4918:
890:
771:
642:
231:
6110:) not a constant ā results in non-conservation of the depth-integrated horizontal momentum.
7310:
7206:
7156:
7121:
7081:
6973:
6943:
6793:
6743:
6653:
6611:
6544:
6469:
6429:
3379:
3371:
2859:
2193:
246:
189:
105:
6665:
6268:
6232:
6196:
6160:
6023:
153:
elevation of the mean flow. If the radiation stress varies spatially, as it does in the
7420:
7415:
7320:
7315:
7151:
7091:
7086:
6818:
6708:
6529:
6464:
6439:
5878:
5240:
4914:
3382:
of the momentum equation provides the non-conservative contributions of the bed slope ā
3337:
886:
767:
223:
215:
89:
39:
5179:{\displaystyle \mathbf {S} :\left(\nabla \otimes {\overline {\boldsymbol {u}}}\right)}
7605:
7590:
7438:
7358:
7247:
7166:
7141:
7076:
7006:
6913:
6808:
6685:
6606:
6566:
6539:
6449:
6399:
6290:
6276:
6248:
6212:
6176:
5132:
4901:
2478:
2332:{\displaystyle {\boldsymbol {M}}_{w}={\frac {\boldsymbol {k}}{k}}{\frac {E}{c_{p}}},}
638:
584:
525:
193:
162:
101:
77:
due to the presence of the waves, which changes the mean depth-integrated horizontal
47:
31:
23:
6039:
1690:ā the components of the radiation stress tensor for progressive periodic waves are:
7585:
7545:
7493:
7433:
7384:
7262:
7257:
7232:
7216:
7191:
6908:
6798:
6738:
6524:
6434:
6409:
3356:
150:
7535:
7267:
7196:
7061:
7001:
6968:
6958:
6953:
6838:
6773:
6733:
6723:
6698:
6581:
6554:
6534:
6494:
6459:
882:
759:
748:
521:
158:
93:
7353:
7201:
7176:
7071:
7051:
6978:
6963:
6948:
6938:
6903:
6823:
6643:
6638:
6601:
6596:
6591:
6489:
6240:
6204:
6168:
6031:
2148:
82:
5994:
7425:
7287:
7272:
7186:
7031:
6870:
6865:
6648:
6576:
6504:
6424:
6414:
6371:
2260:
870:
730:{\displaystyle S_{xx}=\left(2{\frac {c_{g}}{c_{p}}}-{\frac {1}{2}}\right)E,}
641:
can be determined from the properties of surface gravity waves according to
243:
227:
154:
63:
2996:{\displaystyle {\frac {\partial }{\partial t}}\left+\nabla \cdot \left=0,}
7520:
7242:
7101:
6993:
6983:
6928:
6404:
5255:
In a
Cartesian coordinate system, the above equation for the mean energy
2264:
620:
463:
78:
6332:
267:-coordinate direction ā the component of the radiation stress tensor of
7389:
7379:
6549:
6519:
6297:, Advanced series on ocean engineering, vol. 1, World Scientific,
5983:
Proceedings of the 27th
International Conference on Coastal Engineering
5124:
2447:, as seen by an observer moving with the mean horizontal flow-velocity
2210:
respectively, are the lengths of the phase and group velocity vectors:
960:
For wave propagation in two horizontal dimensions the radiation stress
587:
572:
218:
of the modulated short waves within the group. While, according to the
51:
5956:
Dean, R.G.; Walton, T.L. (2009), "Wave setup", in Young C. Kim (ed.),
855:{\displaystyle E={\frac {1}{2}}\rho ga^{2}={\frac {1}{8}}\rho gH^{2},}
96:
of the fluid motion, the radiation stress tensor is important for its
7096:
6509:
983:
67:
5239: : the mean energy transport by the waves themselves, with the
222:, a long wave of this length should propagate at its own ā higher ā
5131:
denotes the dissipation of mean mechanical energy (for instance by
7458:
7277:
7056:
7011:
3026:
The equation for the conservation of horizontal mean momentum is:
74:
18:
2463:
of an observer at rest (with respect to 'Earth'). The difference
2263:
in the wave propagation direction, also called the wave (pseudo)
766:
is the mean depth-integrated wave energy density (the sum of the
6890:
211:
55:
6336:
6098:, an inhomogeneous medium ā in this case a non-horizontal bed,
118:
Radiation stress derives its name from the analogous effect of
2647:) the total flow velocity at any point below the free surface
234:
of the wave height, and is only significant in shallow water;
5224: : the transport of wave energy by the mean flow, and
2342:
which is exact for progressive waves of permanent form in
3386:, as well the forcing by the wind and the bed friction.
5186:
is the exchange of energy with the mean motion, due to
1009:
254:
Definitions and values derived from linear wave theory
5268:
5141:
4930:
3993:
3722:
3404:
3370:
is the identity tensor, with components given by the
3035:
2871:
2702:
2499:
2362:
2283:
2259:
Propagating waves induce a ā relatively small ā mean
1699:
1633:
1596:
1567:
1121:
995:
966:
787:
654:
472:
287:
73:
The radiation stress tensor describes the additional
7398:
7372:
7334:
7286:
7225:
7120:
6992:
6889:
6684:
6370:
5807:
5178:
5112:
4884:
3936:
3693:
3309:
2995:
2824:
2616:
2428:
2331:
2114:
1675:
1611:
1582:
1550:
1085:
974:
854:
729:
508:
435:
263:For uni-directional wave propagation ā say in the
66:. The radiation stresses behave as a second-order
7306:North West Shelf Operational Oceanographic System
6072:
6070:
6068:
6066:
5818:So the radiation stress changes the wave energy
3014:including the contribution of the wave momentum
7296:Deep-ocean Assessment and Reporting of Tsunamis
885:. Note this equation is for periodic waves: in
630:To lowest (second) order, the radiation stress
551:) is the bed elevation of the fluid layer, and
2858:The equation of mean mass conservation is, in
2353:is the phase speed relative to the mean flow:
6348:
5190:. The mean horizontal wave-energy transport (
145:ā the radiation stress consists in part of a
85:) and the mean flow (wave-induced currents).
8:
6318:(2nd ed.), Cambridge University Press,
6295:The applied dynamics of ocean surface waves
6355:
6341:
6333:
5859:Longuet-Higgins & Stewart (1964,1962).
4913:of the fluctuating motion (the sum of the
3973:components of the mass transport velocity
3713:, the mass conservation equation becomes:
2538:
1474:
1357:
1205:
363:
5958:Handbook of Coastal and Ocean Engineering
5903:
5901:
5786:
5776:
5758:
5739:
5721:
5711:
5693:
5674:
5638:
5628:
5621:
5612:
5583:
5573:
5566:
5546:
5536:
5529:
5515:
5491:
5481:
5474:
5465:
5426:
5413:
5403:
5377:
5349:
5336:
5326:
5300:
5273:
5269:
5267:
5161:
5142:
5140:
5091:
5082:
5077:
5063:
5054:
5049:
5030:
5011:
4989:
4984:
4970:
4931:
4929:
4863:
4844:
4819:
4804:
4766:
4752:
4727:
4715:
4702:
4692:
4685:
4675:
4659:
4625:
4608:
4595:
4585:
4578:
4568:
4552:
4518:
4500:
4490:
4474:
4440:
4421:
4402:
4377:
4362:
4321:
4308:
4298:
4291:
4281:
4265:
4231:
4217:
4203:
4178:
4166:
4153:
4143:
4136:
4126:
4110:
4076:
4058:
4048:
4032:
3998:
3994:
3992:
3914:
3904:
3888:
3854:
3840:
3830:
3814:
3780:
3757:
3723:
3721:
3678:
3673:
3663:
3658:
3633:
3603:
3602:
3596:
3582:
3557:
3549:
3541:
3528:
3498:
3492:
3473:
3444:
3410:
3405:
3403:
3298:
3293:
3283:
3278:
3253:
3223:
3222:
3216:
3202:
3177:
3169:
3156:
3143:
3128:
3085:
3070:
3036:
3034:
2969:
2954:
2906:
2872:
2870:
2801:
2789:
2779:
2774:
2771:
2758:
2737:
2725:
2716:
2703:
2701:
2605:
2600:
2586:
2571:
2559:
2539:
2533:
2532:
2523:
2515:
2508:
2500:
2498:
2413:
2405:
2387:
2376:
2367:
2361:
2318:
2309:
2299:
2290:
2285:
2282:
2082:
2071:
2061:
2055:
2039:
2029:
2023:
2015:
2005:
2000:
1994:
1973:
1960:
1947:
1924:
1914:
1908:
1900:
1889:
1879:
1872:
1851:
1817:
1806:
1796:
1790:
1774:
1764:
1758:
1750:
1740:
1735:
1729:
1708:
1700:
1698:
1635:
1634:
1632:
1598:
1597:
1595:
1569:
1568:
1566:
1535:
1520:
1492:
1475:
1463:
1452:
1451:
1430:
1422:
1415:
1399:
1379:
1358:
1341:
1340:
1329:
1328:
1314:
1306:
1299:
1283:
1266:
1251:
1223:
1206:
1194:
1183:
1182:
1161:
1153:
1146:
1130:
1122:
1120:
1063:
1048:
1031:
1016:
1004:
996:
994:
967:
965:
843:
823:
814:
794:
786:
706:
695:
685:
679:
659:
653:
474:
473:
471:
424:
409:
381:
364:
352:
341:
340:
319:
311:
304:
292:
286:
46:is the depth-integrated ā and thereafter
5915:
5913:
5887:(Thesis). Delft University of Technology
590:. The last term on the right-hand side,
230:of this bound long wave varies with the
6010:(1981), "On the 'wave momentum' myth",
5852:
5163:
5093:
5078:
5065:
5050:
5032:
4985:
4972:
3984:The horizontal momentum equations are:
3705:Component form in Cartesian coordinates
3674:
3659:
3542:
3530:
3499:
3474:
3294:
3279:
3158:
3145:
3087:
2971:
2775:
2760:
2718:
2705:
2601:
2588:
2534:
2501:
2415:
2406:
2301:
2286:
6627:one-dimensional Saint-Venant equations
5251:as the wave-energy transport velocity.
30:shapes the beaches, and may result in
5946:Longuet-Higgins & Stewart (1961).
2267:. To lowest order, the wave momentum
1676:{\displaystyle {\tilde {u}}(x,y,z,t)}
7:
7574:
3389:In terms of the horizontal momentum
1686:To second order ā in wave amplitude
1627:-components of the oscillatory part
567:) is the surface elevation. Further
5960:, World Scientific, pp. 1ā23,
509:{\displaystyle {\tilde {u}}(x,z,t)}
7454:National Oceanographic Data Center
6881:World Ocean Circulation Experiment
6769:Global Ocean Data Analysis Project
5646:
5624:
5591:
5569:
5554:
5532:
5499:
5477:
5383:
5379:
5306:
5302:
5284:
5276:
5259:of the flow fluctuations becomes:
5155:
5024:
4954:
4942:
4934:
4825:
4821:
4631:
4627:
4524:
4520:
4446:
4442:
4383:
4379:
4237:
4233:
4082:
4078:
4004:
4000:
3860:
3856:
3786:
3782:
3729:
3725:
3648:
3517:
3505:
3495:
3467:
3416:
3412:
3268:
3103:
3042:
3038:
2929:
2878:
2874:
14:
7301:Global Sea Level Observing System
3366:is the bed shear stress. Further
2274:is, per unit of horizontal area:
7584:
7573:
7564:
7563:
6759:Geochemical Ocean Sections Study
6675:
6664:
5143:
5012:
3604:
3550:
3224:
3170:
2685:Now the mass transport velocity
2667:). The mean horizontal momentum
997:
968:
956:Two-dimensional wave propagation
259:One-dimensional wave propagation
7489:Ocean thermal energy conversion
7212:VineāMatthewsāMorley hypothesis
6316:The dynamics of the upper ocean
5209:consists of two contributions:
2392:
2386:
1959:
4763:
4743:
4214:
4194:
3593:
3573:
3213:
3193:
2849:Mass and momentum conservation
2196:. The phase and group speeds,
1670:
1646:
1640:
1603:
1574:
1457:
1346:
1334:
1188:
503:
485:
479:
346:
58:caused by the presence of the
1:
2484:The mean horizontal momentum
1683:of the flow velocity vector.
16:Term in physical oceanography
6749:El NiƱoāSouthern Oscillation
6719:CraikāLeibovich vortex force
6475:Luke's variational principle
6277:10.1016/0011-7471(64)90001-4
5781:
5716:
5633:
5578:
5541:
5486:
5408:
5331:
5166:
5096:
5068:
5035:
4975:
4809:
4757:
4697:
4680:
4664:
4590:
4573:
4557:
4495:
4479:
4367:
4303:
4286:
4270:
4208:
4148:
4131:
4115:
4053:
4037:
3909:
3893:
3835:
3819:
3762:
3638:
3587:
3533:
3449:
3395:the above equations become:
3258:
3207:
3161:
3148:
3133:
3090:
3075:
2974:
2959:
2911:
2806:
2763:
2742:
2708:
2591:
2576:
2548:
2418:
1612:{\displaystyle {\tilde {v}}}
1583:{\displaystyle {\tilde {u}}}
1525:
1484:
1367:
1256:
1215:
975:{\displaystyle \mathbf {S} }
627:over the still-water depth.
535:is the vertical coordinate,
414:
373:
192:) and the resulting coastal
6128:Phillips (1977), pp. 65ā66.
6119:Phillips (1977), pp. 63ā65.
6076:Phillips (1977), pp. 61ā63.
6060:Phillips (1977), pp. 23ā24.
5868:Phillips (1977), pp. 70ā81.
3711:Cartesian coordinate system
3359:at the free surface, while
2445:intrinsic angular frequency
1098:Cartesian coordinate system
583:, while an overbar denotes
7633:
6814:Ocean dynamical thermostat
6662:
6221:Journal of Fluid Mechanics
6185:Journal of Fluid Mechanics
6149:Journal of Fluid Mechanics
6012:Journal of Fluid Mechanics
5822:only in case of a spatial-
2461:apparent angular frequency
2192:perpendicular to the wave
115:and Stewart in 1960ā1964.
62:, which is exerted on the
7559:
7349:Ocean acoustic tomography
7162:MohoroviÄiÄ discontinuity
6754:General circulation model
6390:BenjamināFeir instability
6241:10.1017/S0022112062000877
6205:10.1017/S0022112061000342
6169:10.1017/S0022112060000803
6032:10.1017/S0022112081001626
124:electromagnetic radiation
7479:Ocean surface topography
6854:Thermohaline circulation
6844:Subsurface ocean current
6784:Hydrothermal circulation
6617:Waveācurrent interaction
6395:Boussinesq approximation
5188:waveācurrent interaction
239:Waveācurrent interaction
7516:Sea surface temperature
7499:Outline of oceanography
6694:Atmospheric circulation
6632:shallow water equations
6622:Waves and shallow water
6515:Significant wave height
6051:Phillips (1977), p. 40.
5937:Phillips (1977), p. 39.
5928:Phillips (1977), p. 68.
2682:) is due to the waves.
2255:Mass transport velocity
930:significant wave height
581:acceleration by gravity
7511:Sea surface microlayer
6876:Wind generated current
5989:, pp. 1050ā1063,
5809:
5180:
5123:where ":" denotes the
5114:
4886:
3938:
3695:
3311:
2997:
2826:
2618:
2430:
2333:
2246:Dynamical significance
2116:
1677:
1613:
1584:
1552:
1087:
976:
856:
762:of the waves. Further
731:
510:
437:
35:
7612:Physical oceanography
7344:Deep scattering layer
7326:World Geodetic System
6834:Princeton Ocean Model
6714:CoriolisāStokes force
6364:Physical oceanography
5810:
5181:
5115:
4887:
3939:
3696:
3312:
2998:
2827:
2619:
2431:
2334:
2117:
1678:
1614:
1585:
1553:
1088:
977:
857:
732:
511:
438:
130:Physical significance
60:surface gravity waves
22:
7364:Underwater acoustics
6924:Perigean spring tide
6789:Langmuir circulation
6500:Rossby-gravity waves
5995:10.1061/40549(276)81
5266:
5139:
4928:
3991:
3720:
3402:
3033:
2869:
2700:
2497:
2360:
2281:
1697:
1631:
1594:
1565:
1119:
993:
964:
900:should be used with
785:
652:
625:hydrostatic pressure
470:
285:
278:. It is defined as:
7526:Science On a Sphere
7132:Convergent boundary
6804:Modular Ocean Model
6764:Geostrophic current
6480:Mild-slope equation
6269:1964DSRA...11..529L
6233:1962JFM....13..481L
6197:1961JFM....10..529L
6161:1960JFM.....8..565L
6085:Mei (2003), p. 453.
6024:1981JFM...106..331M
5907:Mei (2003), p. 457.
4896:Energy conservation
2528:
2147:-components of the
2010:
1745:
1619:are the horizontal
1435:
1319:
1166:
324:
220:dispersion relation
169:Wave-driven current
7182:Seafloor spreading
7172:Outer trench swell
7137:Divergent boundary
7037:Continental margin
7022:Carbonate platform
6919:Lunitidal interval
5919:Mei (2003), p. 97.
5805:
5803:
5176:
5125:double-dot product
5110:
4919:potential energies
4882:
4880:
3934:
3691:
3689:
3307:
2993:
2822:
2614:
2511:
2426:
2329:
2112:
2110:
1996:
1731:
1673:
1609:
1580:
1548:
1546:
1418:
1302:
1149:
1083:
1074:
982:is a second-order
972:
852:
727:
520:-component of the
516:is the horizontal
506:
433:
307:
208:infragravity waves
186:sediment transport
147:radiation pressure
120:radiation pressure
36:
28:sediment transport
7599:
7598:
7591:Oceans portal
7551:World Ocean Atlas
7541:Underwater glider
7484:Ocean temperature
7147:Hydrothermal vent
7112:Submarine volcano
7047:Continental shelf
7027:Coastal geography
7017:Bathymetric chart
6899:Amphidromic point
6587:Wave nonlinearity
6445:Infragravity wave
6257:Deep-Sea Research
6096:Noether's theorem
5967:978-981-281-929-1
5784:
5719:
5653:
5636:
5598:
5581:
5561:
5544:
5506:
5489:
5411:
5390:
5334:
5313:
5291:
5169:
5099:
5071:
5038:
4978:
4949:
4906:mechanical energy
4832:
4812:
4760:
4735:
4700:
4683:
4667:
4638:
4593:
4576:
4560:
4531:
4498:
4482:
4453:
4390:
4370:
4306:
4289:
4273:
4244:
4211:
4186:
4151:
4134:
4118:
4089:
4056:
4040:
4011:
3965:respectively the
3912:
3896:
3867:
3838:
3822:
3793:
3765:
3736:
3641:
3590:
3565:
3536:
3512:
3452:
3423:
3355:is the mean wind
3348:with itself, and
3261:
3210:
3185:
3164:
3151:
3136:
3093:
3078:
3049:
2977:
2962:
2914:
2885:
2817:
2809:
2766:
2753:
2745:
2711:
2594:
2579:
2551:
2542:
2421:
2390:
2384:
2344:irrotational flow
2324:
2307:
2090:
2077:
2045:
2021:
1963:
1930:
1906:
1825:
1812:
1780:
1756:
1643:
1606:
1577:
1528:
1500:
1487:
1478:
1460:
1370:
1361:
1349:
1337:
1259:
1231:
1218:
1209:
1191:
986:with components:
831:
802:
714:
701:
482:
417:
389:
376:
367:
349:
204:forced long waves
173:longshore current
149:, exerted at the
7624:
7589:
7588:
7577:
7576:
7567:
7566:
7506:Pelagic sediment
7444:Marine pollution
7238:Deep ocean water
7107:Submarine canyon
7042:Continental rise
6934:Rule of twelfths
6849:Sverdrup balance
6779:Humboldt Current
6704:Boundary current
6679:
6668:
6485:Radiation stress
6455:Iribarren number
6430:Equatorial waves
6385:Ballantine scale
6380:Airy wave theory
6357:
6350:
6343:
6334:
6328:
6307:
6279:
6251:
6215:
6179:
6129:
6126:
6120:
6117:
6111:
6092:
6086:
6083:
6077:
6074:
6061:
6058:
6052:
6049:
6043:
6042:
6004:
5998:
5997:
5978:
5972:
5971:
5953:
5947:
5944:
5938:
5935:
5929:
5926:
5920:
5917:
5908:
5905:
5896:
5895:
5893:
5892:
5875:
5869:
5866:
5860:
5857:
5840:
5831:
5814:
5812:
5811:
5806:
5804:
5791:
5790:
5785:
5777:
5774:
5770:
5769:
5768:
5750:
5749:
5726:
5725:
5720:
5712:
5709:
5705:
5704:
5703:
5685:
5684:
5658:
5654:
5652:
5644:
5643:
5642:
5637:
5629:
5622:
5620:
5619:
5604:
5600:
5599:
5597:
5589:
5588:
5587:
5582:
5574:
5567:
5562:
5560:
5552:
5551:
5550:
5545:
5537:
5530:
5523:
5522:
5507:
5505:
5497:
5496:
5495:
5490:
5482:
5475:
5473:
5472:
5454:
5450:
5446:
5442:
5438:
5437:
5436:
5418:
5417:
5412:
5404:
5391:
5389:
5378:
5373:
5369:
5365:
5361:
5360:
5359:
5341:
5340:
5335:
5327:
5314:
5312:
5301:
5292:
5290:
5282:
5274:
5219:
5197:
5185:
5183:
5182:
5177:
5175:
5171:
5170:
5162:
5146:
5119:
5117:
5116:
5111:
5100:
5092:
5087:
5086:
5081:
5072:
5064:
5059:
5058:
5053:
5044:
5040:
5039:
5031:
5015:
5007:
5003:
4999:
4995:
4994:
4993:
4988:
4979:
4971:
4950:
4948:
4940:
4932:
4891:
4889:
4888:
4883:
4881:
4874:
4873:
4855:
4854:
4833:
4831:
4820:
4818:
4814:
4813:
4805:
4780:
4776:
4772:
4771:
4770:
4761:
4753:
4736:
4728:
4723:
4722:
4707:
4706:
4701:
4693:
4690:
4689:
4684:
4676:
4673:
4669:
4668:
4660:
4639:
4637:
4626:
4621:
4617:
4616:
4615:
4600:
4599:
4594:
4586:
4583:
4582:
4577:
4569:
4566:
4562:
4561:
4553:
4532:
4530:
4519:
4510:
4506:
4505:
4504:
4499:
4491:
4488:
4484:
4483:
4475:
4454:
4452:
4441:
4432:
4431:
4413:
4412:
4391:
4389:
4378:
4376:
4372:
4371:
4363:
4338:
4334:
4330:
4329:
4328:
4313:
4312:
4307:
4299:
4296:
4295:
4290:
4282:
4279:
4275:
4274:
4266:
4245:
4243:
4232:
4227:
4223:
4222:
4221:
4212:
4204:
4187:
4179:
4174:
4173:
4158:
4157:
4152:
4144:
4141:
4140:
4135:
4127:
4124:
4120:
4119:
4111:
4090:
4088:
4077:
4068:
4064:
4063:
4062:
4057:
4049:
4046:
4042:
4041:
4033:
4012:
4010:
3999:
3980:
3961:
3952:
3943:
3941:
3940:
3935:
3924:
3920:
3919:
3918:
3913:
3905:
3902:
3898:
3897:
3889:
3868:
3866:
3855:
3850:
3846:
3845:
3844:
3839:
3831:
3828:
3824:
3823:
3815:
3794:
3792:
3781:
3776:
3772:
3771:
3767:
3766:
3758:
3737:
3735:
3724:
3700:
3698:
3697:
3692:
3690:
3683:
3682:
3677:
3668:
3667:
3662:
3647:
3643:
3642:
3634:
3612:
3608:
3607:
3601:
3600:
3591:
3583:
3566:
3558:
3553:
3545:
3537:
3529:
3513:
3511:
3503:
3502:
3493:
3490:
3477:
3463:
3459:
3458:
3454:
3453:
3445:
3424:
3422:
3411:
3408:
3378:. Note that the
3347:
3335:
3327:
3316:
3314:
3313:
3308:
3303:
3302:
3297:
3288:
3287:
3282:
3267:
3263:
3262:
3254:
3232:
3228:
3227:
3221:
3220:
3211:
3203:
3186:
3178:
3173:
3165:
3157:
3152:
3144:
3142:
3138:
3137:
3129:
3099:
3095:
3094:
3086:
3084:
3080:
3079:
3071:
3050:
3048:
3037:
3013:
3002:
3000:
2999:
2994:
2983:
2979:
2978:
2970:
2968:
2964:
2963:
2955:
2925:
2921:
2920:
2916:
2915:
2907:
2886:
2884:
2873:
2843:
2831:
2829:
2828:
2823:
2818:
2816:
2815:
2811:
2810:
2802:
2784:
2783:
2778:
2772:
2767:
2759:
2754:
2752:
2751:
2747:
2746:
2738:
2717:
2712:
2704:
2692:
2623:
2621:
2620:
2615:
2610:
2609:
2604:
2595:
2587:
2585:
2581:
2580:
2572:
2552:
2547:
2543:
2540:
2537:
2527:
2522:
2509:
2504:
2476:
2454:
2435:
2433:
2432:
2427:
2422:
2414:
2409:
2391:
2388:
2385:
2377:
2372:
2371:
2338:
2336:
2335:
2330:
2325:
2323:
2322:
2310:
2308:
2300:
2295:
2294:
2289:
2185:
2184:
2121:
2119:
2118:
2113:
2111:
2101:
2097:
2096:
2092:
2091:
2083:
2078:
2076:
2075:
2066:
2065:
2056:
2046:
2044:
2043:
2034:
2033:
2024:
2022:
2020:
2019:
2009:
2004:
1995:
1981:
1980:
1964:
1961:
1955:
1954:
1936:
1932:
1931:
1929:
1928:
1919:
1918:
1909:
1907:
1905:
1904:
1895:
1894:
1893:
1884:
1883:
1873:
1859:
1858:
1836:
1832:
1831:
1827:
1826:
1818:
1813:
1811:
1810:
1801:
1800:
1791:
1781:
1779:
1778:
1769:
1768:
1759:
1757:
1755:
1754:
1744:
1739:
1730:
1716:
1715:
1682:
1680:
1679:
1674:
1645:
1644:
1636:
1618:
1616:
1615:
1610:
1608:
1607:
1599:
1589:
1587:
1586:
1581:
1579:
1578:
1570:
1557:
1555:
1554:
1549:
1547:
1540:
1539:
1534:
1530:
1529:
1521:
1501:
1493:
1488:
1483:
1479:
1476:
1473:
1469:
1468:
1467:
1462:
1461:
1453:
1434:
1429:
1416:
1407:
1406:
1387:
1386:
1371:
1366:
1362:
1359:
1356:
1352:
1351:
1350:
1342:
1339:
1338:
1330:
1318:
1313:
1300:
1291:
1290:
1271:
1270:
1265:
1261:
1260:
1252:
1232:
1224:
1219:
1214:
1210:
1207:
1204:
1200:
1199:
1198:
1193:
1192:
1184:
1165:
1160:
1147:
1138:
1137:
1092:
1090:
1089:
1084:
1079:
1078:
1071:
1070:
1056:
1055:
1039:
1038:
1024:
1023:
1000:
981:
979:
978:
973:
971:
945:
944:
940:
920:
919:
891:root-mean-square
861:
859:
858:
853:
848:
847:
832:
824:
819:
818:
803:
795:
772:potential energy
736:
734:
733:
728:
720:
716:
715:
707:
702:
700:
699:
690:
689:
680:
667:
666:
643:Airy wave theory
617:
605:
603:
602:
599:
596:
522:oscillatory part
515:
513:
512:
507:
484:
483:
475:
442:
440:
439:
434:
429:
428:
423:
419:
418:
410:
390:
382:
377:
372:
368:
365:
362:
358:
357:
356:
351:
350:
342:
323:
318:
305:
300:
299:
200:Bound long waves
100:, in case of an
94:oscillatory part
44:radiation stress
7632:
7631:
7627:
7626:
7625:
7623:
7622:
7621:
7602:
7601:
7600:
7595:
7583:
7555:
7394:
7368:
7330:
7311:Sea-level curve
7282:
7221:
7207:Transform fault
7157:Mid-ocean ridge
7123:
7116:
7082:Oceanic plateau
6988:
6974:Tidal resonance
6944:Theory of tides
6885:
6794:Longshore drift
6744:Ekman transport
6680:
6674:
6673:
6672:
6671:
6670:
6669:
6660:
6612:Wave turbulence
6545:Trochoidal wave
6470:Longshore drift
6366:
6361:
6331:
6326:
6312:Phillips, O. M.
6310:
6305:
6289:
6284:Further reading
6254:
6218:
6182:
6146:
6141:Primary sources
6137:
6132:
6127:
6123:
6118:
6114:
6093:
6089:
6084:
6080:
6075:
6064:
6059:
6055:
6050:
6046:
6008:Mcintyre, M. E.
6006:
6005:
6001:
5980:
5979:
5975:
5968:
5955:
5954:
5950:
5945:
5941:
5936:
5932:
5927:
5923:
5918:
5911:
5906:
5899:
5890:
5888:
5877:
5876:
5872:
5867:
5863:
5858:
5854:
5850:
5843:
5836:
5834:
5827:
5826:current field (
5802:
5801:
5775:
5754:
5735:
5734:
5730:
5710:
5689:
5670:
5669:
5665:
5656:
5655:
5645:
5627:
5623:
5608:
5590:
5572:
5568:
5553:
5535:
5531:
5528:
5524:
5511:
5498:
5480:
5476:
5461:
5452:
5451:
5422:
5402:
5401:
5397:
5396:
5392:
5382:
5345:
5325:
5324:
5320:
5319:
5315:
5305:
5293:
5283:
5275:
5264:
5263:
5250:
5234:
5213:
5204:
5191:
5154:
5150:
5137:
5136:
5076:
5048:
5023:
5019:
4983:
4969:
4965:
4964:
4960:
4941:
4933:
4926:
4925:
4898:
4879:
4878:
4859:
4840:
4824:
4797:
4793:
4778:
4777:
4762:
4711:
4691:
4674:
4652:
4648:
4644:
4640:
4630:
4604:
4584:
4567:
4545:
4541:
4537:
4533:
4523:
4511:
4489:
4467:
4463:
4459:
4455:
4445:
4437:
4436:
4417:
4398:
4382:
4355:
4351:
4336:
4335:
4317:
4297:
4280:
4258:
4254:
4250:
4246:
4236:
4213:
4162:
4142:
4125:
4103:
4099:
4095:
4091:
4081:
4069:
4047:
4025:
4021:
4017:
4013:
4003:
3989:
3988:
3974:
3964:
3957:
3955:
3948:
3903:
3881:
3877:
3873:
3869:
3859:
3829:
3807:
3803:
3799:
3795:
3785:
3750:
3746:
3742:
3738:
3728:
3718:
3717:
3707:
3688:
3687:
3672:
3657:
3626:
3622:
3592:
3527:
3523:
3504:
3494:
3488:
3487:
3437:
3433:
3429:
3425:
3415:
3400:
3399:
3380:right hand side
3377:
3372:Kronecker delta
3365:
3354:
3341:
3329:
3321:
3292:
3277:
3246:
3242:
3212:
3121:
3117:
3113:
3109:
3063:
3059:
3055:
3051:
3041:
3031:
3030:
3022:
3007:
2947:
2943:
2939:
2935:
2899:
2895:
2891:
2887:
2877:
2867:
2866:
2860:vector notation
2856:
2854:Vector notation
2851:
2841:
2794:
2790:
2785:
2773:
2730:
2726:
2721:
2698:
2697:
2693:is defined as:
2686:
2681:
2599:
2564:
2560:
2510:
2495:
2494:
2470:
2448:
2363:
2358:
2357:
2352:
2314:
2284:
2279:
2278:
2273:
2257:
2248:
2241:
2232:
2225:
2216:
2209:
2202:
2186:and the vector
2183:
2176:
2170:
2168:
2138:
2131:
2109:
2108:
2067:
2057:
2054:
2050:
2035:
2025:
2011:
1993:
1989:
1982:
1969:
1966:
1965:
1943:
1920:
1910:
1896:
1885:
1875:
1874:
1871:
1867:
1860:
1847:
1844:
1843:
1802:
1792:
1789:
1785:
1770:
1760:
1746:
1728:
1724:
1717:
1704:
1695:
1694:
1629:
1628:
1592:
1591:
1563:
1562:
1545:
1544:
1513:
1509:
1508:
1450:
1440:
1436:
1417:
1408:
1395:
1392:
1391:
1375:
1324:
1320:
1301:
1292:
1279:
1276:
1275:
1244:
1240:
1239:
1181:
1171:
1167:
1148:
1139:
1126:
1117:
1116:
1073:
1072:
1059:
1057:
1044:
1041:
1040:
1027:
1025:
1012:
1005:
991:
990:
962:
961:
958:
951:
942:
938:
937:
927:
917:
915:
913:
906:
899:
839:
810:
783:
782:
757:
746:
691:
681:
675:
671:
655:
650:
649:
636:
615:
600:
597:
594:
593:
591:
468:
467:
462:) is the fluid
402:
398:
397:
339:
329:
325:
306:
288:
283:
282:
277:
261:
256:
190:longshore drift
183:
171:, especially a
132:
113:Longuet-Higgins
17:
12:
11:
5:
7630:
7628:
7620:
7619:
7614:
7604:
7603:
7597:
7596:
7594:
7593:
7581:
7571:
7560:
7557:
7556:
7554:
7553:
7548:
7543:
7538:
7533:
7531:Stratification
7528:
7523:
7518:
7513:
7508:
7503:
7502:
7501:
7491:
7486:
7481:
7476:
7471:
7466:
7461:
7456:
7451:
7446:
7441:
7436:
7431:
7423:
7421:Color of water
7418:
7416:Benthic lander
7413:
7408:
7402:
7400:
7396:
7395:
7393:
7392:
7387:
7382:
7376:
7374:
7370:
7369:
7367:
7366:
7361:
7356:
7351:
7346:
7340:
7338:
7332:
7331:
7329:
7328:
7323:
7321:Sea level rise
7318:
7316:Sea level drop
7313:
7308:
7303:
7298:
7292:
7290:
7284:
7283:
7281:
7280:
7275:
7270:
7265:
7260:
7255:
7250:
7245:
7240:
7235:
7229:
7227:
7223:
7222:
7220:
7219:
7214:
7209:
7204:
7199:
7194:
7189:
7184:
7179:
7174:
7169:
7164:
7159:
7154:
7152:Marine geology
7149:
7144:
7139:
7134:
7128:
7126:
7118:
7117:
7115:
7114:
7109:
7104:
7099:
7094:
7092:Passive margin
7089:
7087:Oceanic trench
7084:
7079:
7074:
7069:
7064:
7059:
7054:
7049:
7044:
7039:
7034:
7029:
7024:
7019:
7014:
7009:
7004:
6998:
6996:
6990:
6989:
6987:
6986:
6981:
6976:
6971:
6966:
6961:
6956:
6951:
6946:
6941:
6936:
6931:
6926:
6921:
6916:
6911:
6906:
6901:
6895:
6893:
6887:
6886:
6884:
6883:
6878:
6873:
6868:
6863:
6862:
6861:
6851:
6846:
6841:
6836:
6831:
6826:
6821:
6819:Ocean dynamics
6816:
6811:
6806:
6801:
6796:
6791:
6786:
6781:
6776:
6771:
6766:
6761:
6756:
6751:
6746:
6741:
6736:
6731:
6726:
6721:
6716:
6711:
6709:Coriolis force
6706:
6701:
6696:
6690:
6688:
6682:
6681:
6663:
6661:
6659:
6658:
6657:
6656:
6646:
6641:
6636:
6635:
6634:
6629:
6619:
6614:
6609:
6604:
6599:
6594:
6589:
6584:
6579:
6574:
6569:
6564:
6559:
6558:
6557:
6547:
6542:
6537:
6532:
6530:Stokes problem
6527:
6522:
6517:
6512:
6507:
6502:
6497:
6492:
6487:
6482:
6477:
6472:
6467:
6465:Kinematic wave
6462:
6457:
6452:
6447:
6442:
6437:
6432:
6427:
6422:
6417:
6412:
6407:
6402:
6397:
6392:
6387:
6382:
6376:
6374:
6368:
6367:
6362:
6360:
6359:
6352:
6345:
6337:
6330:
6329:
6324:
6308:
6303:
6291:Mei, Chiang C.
6286:
6285:
6281:
6280:
6263:(4): 529ā562,
6252:
6227:(4): 481ā504,
6216:
6191:(4): 529ā549,
6180:
6155:(4): 565ā583,
6143:
6142:
6138:
6136:
6133:
6131:
6130:
6121:
6112:
6087:
6078:
6062:
6053:
6044:
5999:
5973:
5966:
5948:
5939:
5930:
5921:
5909:
5897:
5879:Battjes, J. A.
5870:
5861:
5851:
5849:
5846:
5841:
5832:
5816:
5815:
5800:
5797:
5794:
5789:
5783:
5780:
5773:
5767:
5764:
5761:
5757:
5753:
5748:
5745:
5742:
5738:
5733:
5729:
5724:
5718:
5715:
5708:
5702:
5699:
5696:
5692:
5688:
5683:
5680:
5677:
5673:
5668:
5664:
5661:
5659:
5657:
5651:
5648:
5641:
5635:
5632:
5626:
5618:
5615:
5611:
5607:
5603:
5596:
5593:
5586:
5580:
5577:
5571:
5565:
5559:
5556:
5549:
5543:
5540:
5534:
5527:
5521:
5518:
5514:
5510:
5504:
5501:
5494:
5488:
5485:
5479:
5471:
5468:
5464:
5460:
5457:
5455:
5453:
5449:
5445:
5441:
5435:
5432:
5429:
5425:
5421:
5416:
5410:
5407:
5400:
5395:
5388:
5385:
5381:
5376:
5372:
5368:
5364:
5358:
5355:
5352:
5348:
5344:
5339:
5333:
5330:
5323:
5318:
5311:
5308:
5304:
5299:
5296:
5294:
5289:
5286:
5281:
5278:
5272:
5271:
5253:
5252:
5248:
5241:group velocity
5232:
5225:
5202:
5174:
5168:
5165:
5160:
5157:
5153:
5149:
5145:
5121:
5120:
5109:
5106:
5103:
5098:
5095:
5090:
5085:
5080:
5075:
5070:
5067:
5062:
5057:
5052:
5047:
5043:
5037:
5034:
5029:
5026:
5022:
5018:
5014:
5010:
5006:
5002:
4998:
4992:
4987:
4982:
4977:
4974:
4968:
4963:
4959:
4956:
4953:
4947:
4944:
4939:
4936:
4897:
4894:
4893:
4892:
4877:
4872:
4869:
4866:
4862:
4858:
4853:
4850:
4847:
4843:
4839:
4836:
4830:
4827:
4823:
4817:
4811:
4808:
4803:
4800:
4796:
4792:
4789:
4786:
4783:
4781:
4779:
4775:
4769:
4765:
4759:
4756:
4751:
4748:
4745:
4742:
4739:
4734:
4731:
4726:
4721:
4718:
4714:
4710:
4705:
4699:
4696:
4688:
4682:
4679:
4672:
4666:
4663:
4658:
4655:
4651:
4647:
4643:
4636:
4633:
4629:
4624:
4620:
4614:
4611:
4607:
4603:
4598:
4592:
4589:
4581:
4575:
4572:
4565:
4559:
4556:
4551:
4548:
4544:
4540:
4536:
4529:
4526:
4522:
4517:
4514:
4512:
4509:
4503:
4497:
4494:
4487:
4481:
4478:
4473:
4470:
4466:
4462:
4458:
4451:
4448:
4444:
4439:
4438:
4435:
4430:
4427:
4424:
4420:
4416:
4411:
4408:
4405:
4401:
4397:
4394:
4388:
4385:
4381:
4375:
4369:
4366:
4361:
4358:
4354:
4350:
4347:
4344:
4341:
4339:
4337:
4333:
4327:
4324:
4320:
4316:
4311:
4305:
4302:
4294:
4288:
4285:
4278:
4272:
4269:
4264:
4261:
4257:
4253:
4249:
4242:
4239:
4235:
4230:
4226:
4220:
4216:
4210:
4207:
4202:
4199:
4196:
4193:
4190:
4185:
4182:
4177:
4172:
4169:
4165:
4161:
4156:
4150:
4147:
4139:
4133:
4130:
4123:
4117:
4114:
4109:
4106:
4102:
4098:
4094:
4087:
4084:
4080:
4075:
4072:
4070:
4067:
4061:
4055:
4052:
4045:
4039:
4036:
4031:
4028:
4024:
4020:
4016:
4009:
4006:
4002:
3997:
3996:
3962:
3953:
3945:
3944:
3933:
3930:
3927:
3923:
3917:
3911:
3908:
3901:
3895:
3892:
3887:
3884:
3880:
3876:
3872:
3865:
3862:
3858:
3853:
3849:
3843:
3837:
3834:
3827:
3821:
3818:
3813:
3810:
3806:
3802:
3798:
3791:
3788:
3784:
3779:
3775:
3770:
3764:
3761:
3756:
3753:
3749:
3745:
3741:
3734:
3731:
3727:
3706:
3703:
3702:
3701:
3686:
3681:
3676:
3671:
3666:
3661:
3656:
3653:
3650:
3646:
3640:
3637:
3632:
3629:
3625:
3621:
3618:
3615:
3611:
3606:
3599:
3595:
3589:
3586:
3581:
3578:
3575:
3572:
3569:
3564:
3561:
3556:
3552:
3548:
3544:
3540:
3535:
3532:
3526:
3522:
3519:
3516:
3510:
3507:
3501:
3497:
3491:
3489:
3486:
3483:
3480:
3476:
3472:
3469:
3466:
3462:
3457:
3451:
3448:
3443:
3440:
3436:
3432:
3428:
3421:
3418:
3414:
3409:
3407:
3375:
3363:
3352:
3338:tensor product
3318:
3317:
3306:
3301:
3296:
3291:
3286:
3281:
3276:
3273:
3270:
3266:
3260:
3257:
3252:
3249:
3245:
3241:
3238:
3235:
3231:
3226:
3219:
3215:
3209:
3206:
3201:
3198:
3195:
3192:
3189:
3184:
3181:
3176:
3172:
3168:
3163:
3160:
3155:
3150:
3147:
3141:
3135:
3132:
3127:
3124:
3120:
3116:
3112:
3108:
3105:
3102:
3098:
3092:
3089:
3083:
3077:
3074:
3069:
3066:
3062:
3058:
3054:
3047:
3044:
3040:
3020:
3004:
3003:
2992:
2989:
2986:
2982:
2976:
2973:
2967:
2961:
2958:
2953:
2950:
2946:
2942:
2938:
2934:
2931:
2928:
2924:
2919:
2913:
2910:
2905:
2902:
2898:
2894:
2890:
2883:
2880:
2876:
2855:
2852:
2850:
2847:
2833:
2832:
2821:
2814:
2808:
2805:
2800:
2797:
2793:
2788:
2782:
2777:
2770:
2765:
2762:
2757:
2750:
2744:
2741:
2736:
2733:
2729:
2724:
2720:
2715:
2710:
2707:
2679:
2625:
2624:
2613:
2608:
2603:
2598:
2593:
2590:
2584:
2578:
2575:
2570:
2567:
2563:
2558:
2555:
2550:
2546:
2536:
2531:
2526:
2521:
2518:
2514:
2507:
2503:
2437:
2436:
2425:
2420:
2417:
2412:
2408:
2404:
2401:
2398:
2395:
2383:
2380:
2375:
2370:
2366:
2350:
2340:
2339:
2328:
2321:
2317:
2313:
2306:
2303:
2298:
2293:
2288:
2271:
2261:mass transport
2256:
2253:
2247:
2244:
2239:
2233: = |
2230:
2223:
2217: = |
2214:
2207:
2200:
2181:
2174:
2167:| =
2161: = |
2157:, with length
2136:
2129:
2123:
2122:
2107:
2104:
2100:
2095:
2089:
2086:
2081:
2074:
2070:
2064:
2060:
2053:
2049:
2042:
2038:
2032:
2028:
2018:
2014:
2008:
2003:
1999:
1992:
1988:
1985:
1983:
1979:
1976:
1972:
1968:
1967:
1958:
1953:
1950:
1946:
1942:
1939:
1935:
1927:
1923:
1917:
1913:
1903:
1899:
1892:
1888:
1882:
1878:
1870:
1866:
1863:
1861:
1857:
1854:
1850:
1846:
1845:
1842:
1839:
1835:
1830:
1824:
1821:
1816:
1809:
1805:
1799:
1795:
1788:
1784:
1777:
1773:
1767:
1763:
1753:
1749:
1743:
1738:
1734:
1727:
1723:
1720:
1718:
1714:
1711:
1707:
1703:
1702:
1672:
1669:
1666:
1663:
1660:
1657:
1654:
1651:
1648:
1642:
1639:
1605:
1602:
1576:
1573:
1559:
1558:
1543:
1538:
1533:
1527:
1524:
1519:
1516:
1512:
1507:
1504:
1499:
1496:
1491:
1486:
1482:
1472:
1466:
1459:
1456:
1449:
1446:
1443:
1439:
1433:
1428:
1425:
1421:
1414:
1411:
1409:
1405:
1402:
1398:
1394:
1393:
1390:
1385:
1382:
1378:
1374:
1369:
1365:
1355:
1348:
1345:
1336:
1333:
1327:
1323:
1317:
1312:
1309:
1305:
1298:
1295:
1293:
1289:
1286:
1282:
1278:
1277:
1274:
1269:
1264:
1258:
1255:
1250:
1247:
1243:
1238:
1235:
1230:
1227:
1222:
1217:
1213:
1203:
1197:
1190:
1187:
1180:
1177:
1174:
1170:
1164:
1159:
1156:
1152:
1145:
1142:
1140:
1136:
1133:
1129:
1125:
1124:
1094:
1093:
1082:
1077:
1069:
1066:
1062:
1058:
1054:
1051:
1047:
1043:
1042:
1037:
1034:
1030:
1026:
1022:
1019:
1015:
1011:
1010:
1008:
1003:
999:
970:
957:
954:
949:
925:
911:
904:
897:
877: = 2
863:
862:
851:
846:
842:
838:
835:
830:
827:
822:
817:
813:
809:
806:
801:
798:
793:
790:
755:
744:
738:
737:
726:
723:
719:
713:
710:
705:
698:
694:
688:
684:
678:
674:
670:
665:
662:
658:
639:periodic waves
637:for traveling
634:
543: = ā
505:
502:
499:
496:
493:
490:
487:
481:
478:
444:
443:
432:
427:
422:
416:
413:
408:
405:
401:
396:
393:
388:
385:
380:
375:
371:
361:
355:
348:
345:
338:
335:
332:
328:
322:
317:
314:
310:
303:
298:
295:
291:
275:
271:importance is
260:
257:
255:
252:
251:
250:
235:
224:phase velocity
216:group velocity
206:, part of the
197:
179:
166:
131:
128:
90:energy density
40:fluid dynamics
24:Breaking waves
15:
13:
10:
9:
6:
4:
3:
2:
7629:
7618:
7615:
7613:
7610:
7609:
7607:
7592:
7587:
7582:
7580:
7572:
7570:
7562:
7561:
7558:
7552:
7549:
7547:
7544:
7542:
7539:
7537:
7534:
7532:
7529:
7527:
7524:
7522:
7519:
7517:
7514:
7512:
7509:
7507:
7504:
7500:
7497:
7496:
7495:
7492:
7490:
7487:
7485:
7482:
7480:
7477:
7475:
7472:
7470:
7467:
7465:
7462:
7460:
7457:
7455:
7452:
7450:
7447:
7445:
7442:
7440:
7439:Marine energy
7437:
7435:
7432:
7430:
7429:
7424:
7422:
7419:
7417:
7414:
7412:
7409:
7407:
7406:Acidification
7404:
7403:
7401:
7397:
7391:
7388:
7386:
7383:
7381:
7378:
7377:
7375:
7371:
7365:
7362:
7360:
7359:SOFAR channel
7357:
7355:
7352:
7350:
7347:
7345:
7342:
7341:
7339:
7337:
7333:
7327:
7324:
7322:
7319:
7317:
7314:
7312:
7309:
7307:
7304:
7302:
7299:
7297:
7294:
7293:
7291:
7289:
7285:
7279:
7276:
7274:
7271:
7269:
7266:
7264:
7261:
7259:
7256:
7254:
7251:
7249:
7246:
7244:
7241:
7239:
7236:
7234:
7231:
7230:
7228:
7224:
7218:
7215:
7213:
7210:
7208:
7205:
7203:
7200:
7198:
7195:
7193:
7190:
7188:
7185:
7183:
7180:
7178:
7175:
7173:
7170:
7168:
7167:Oceanic crust
7165:
7163:
7160:
7158:
7155:
7153:
7150:
7148:
7145:
7143:
7142:Fracture zone
7140:
7138:
7135:
7133:
7130:
7129:
7127:
7125:
7119:
7113:
7110:
7108:
7105:
7103:
7100:
7098:
7095:
7093:
7090:
7088:
7085:
7083:
7080:
7078:
7077:Oceanic basin
7075:
7073:
7070:
7068:
7065:
7063:
7060:
7058:
7055:
7053:
7050:
7048:
7045:
7043:
7040:
7038:
7035:
7033:
7030:
7028:
7025:
7023:
7020:
7018:
7015:
7013:
7010:
7008:
7007:Abyssal plain
7005:
7003:
7000:
6999:
6997:
6995:
6991:
6985:
6982:
6980:
6977:
6975:
6972:
6970:
6967:
6965:
6962:
6960:
6957:
6955:
6952:
6950:
6947:
6945:
6942:
6940:
6937:
6935:
6932:
6930:
6927:
6925:
6922:
6920:
6917:
6915:
6914:Internal tide
6912:
6910:
6907:
6905:
6902:
6900:
6897:
6896:
6894:
6892:
6888:
6882:
6879:
6877:
6874:
6872:
6869:
6867:
6864:
6860:
6857:
6856:
6855:
6852:
6850:
6847:
6845:
6842:
6840:
6837:
6835:
6832:
6830:
6827:
6825:
6822:
6820:
6817:
6815:
6812:
6810:
6809:Ocean current
6807:
6805:
6802:
6800:
6797:
6795:
6792:
6790:
6787:
6785:
6782:
6780:
6777:
6775:
6772:
6770:
6767:
6765:
6762:
6760:
6757:
6755:
6752:
6750:
6747:
6745:
6742:
6740:
6737:
6735:
6732:
6730:
6727:
6725:
6722:
6720:
6717:
6715:
6712:
6710:
6707:
6705:
6702:
6700:
6697:
6695:
6692:
6691:
6689:
6687:
6683:
6678:
6667:
6655:
6652:
6651:
6650:
6647:
6645:
6642:
6640:
6637:
6633:
6630:
6628:
6625:
6624:
6623:
6620:
6618:
6615:
6613:
6610:
6608:
6607:Wave shoaling
6605:
6603:
6600:
6598:
6595:
6593:
6590:
6588:
6585:
6583:
6580:
6578:
6575:
6573:
6570:
6568:
6567:Ursell number
6565:
6563:
6560:
6556:
6553:
6552:
6551:
6548:
6546:
6543:
6541:
6538:
6536:
6533:
6531:
6528:
6526:
6523:
6521:
6518:
6516:
6513:
6511:
6508:
6506:
6503:
6501:
6498:
6496:
6493:
6491:
6488:
6486:
6483:
6481:
6478:
6476:
6473:
6471:
6468:
6466:
6463:
6461:
6458:
6456:
6453:
6451:
6450:Internal wave
6448:
6446:
6443:
6441:
6438:
6436:
6433:
6431:
6428:
6426:
6423:
6421:
6418:
6416:
6413:
6411:
6408:
6406:
6403:
6401:
6400:Breaking wave
6398:
6396:
6393:
6391:
6388:
6386:
6383:
6381:
6378:
6377:
6375:
6373:
6369:
6365:
6358:
6353:
6351:
6346:
6344:
6339:
6338:
6335:
6327:
6325:0-521-29801-6
6321:
6317:
6313:
6309:
6306:
6304:9971-5-0789-7
6300:
6296:
6292:
6288:
6287:
6283:
6282:
6278:
6274:
6270:
6266:
6262:
6258:
6253:
6250:
6246:
6242:
6238:
6234:
6230:
6226:
6222:
6217:
6214:
6210:
6206:
6202:
6198:
6194:
6190:
6186:
6181:
6178:
6174:
6170:
6166:
6162:
6158:
6154:
6150:
6145:
6144:
6140:
6139:
6134:
6125:
6122:
6116:
6113:
6109:
6105:
6101:
6097:
6091:
6088:
6082:
6079:
6073:
6071:
6069:
6067:
6063:
6057:
6054:
6048:
6045:
6041:
6037:
6033:
6029:
6025:
6021:
6017:
6013:
6009:
6003:
6000:
5996:
5992:
5988:
5984:
5977:
5974:
5969:
5963:
5959:
5952:
5949:
5943:
5940:
5934:
5931:
5925:
5922:
5916:
5914:
5910:
5904:
5902:
5898:
5886:
5885:
5880:
5874:
5871:
5865:
5862:
5856:
5853:
5847:
5845:
5839:
5830:
5825:
5824:inhomogeneous
5821:
5798:
5795:
5792:
5787:
5778:
5771:
5765:
5762:
5759:
5755:
5751:
5746:
5743:
5740:
5736:
5731:
5727:
5722:
5713:
5706:
5700:
5697:
5694:
5690:
5686:
5681:
5678:
5675:
5671:
5666:
5662:
5660:
5649:
5639:
5630:
5616:
5613:
5609:
5605:
5601:
5594:
5584:
5575:
5563:
5557:
5547:
5538:
5525:
5519:
5516:
5512:
5508:
5502:
5492:
5483:
5469:
5466:
5462:
5458:
5456:
5447:
5443:
5439:
5433:
5430:
5427:
5423:
5419:
5414:
5405:
5398:
5393:
5386:
5374:
5370:
5366:
5362:
5356:
5353:
5350:
5346:
5342:
5337:
5328:
5321:
5316:
5309:
5297:
5295:
5287:
5279:
5262:
5261:
5260:
5258:
5247:
5246:
5242:
5238:
5231:
5230:
5226:
5223:
5218:
5217:
5212:
5211:
5210:
5208:
5201:
5198: +
5196:
5195:
5189:
5172:
5158:
5151:
5147:
5134:
5133:wave breaking
5130:
5126:
5107:
5104:
5101:
5088:
5083:
5073:
5060:
5055:
5045:
5041:
5027:
5020:
5016:
5008:
5004:
5000:
4996:
4990:
4980:
4966:
4961:
4957:
4951:
4945:
4937:
4924:
4923:
4922:
4920:
4916:
4912:
4907:
4903:
4902:inviscid flow
4895:
4875:
4870:
4867:
4864:
4860:
4856:
4851:
4848:
4845:
4841:
4837:
4834:
4828:
4815:
4806:
4801:
4798:
4794:
4790:
4787:
4784:
4782:
4773:
4767:
4754:
4749:
4746:
4740:
4737:
4732:
4729:
4724:
4719:
4716:
4712:
4708:
4703:
4694:
4686:
4677:
4670:
4661:
4656:
4653:
4649:
4645:
4641:
4634:
4622:
4618:
4612:
4609:
4605:
4601:
4596:
4587:
4579:
4570:
4563:
4554:
4549:
4546:
4542:
4538:
4534:
4527:
4515:
4513:
4507:
4501:
4492:
4485:
4476:
4471:
4468:
4464:
4460:
4456:
4449:
4433:
4428:
4425:
4422:
4418:
4414:
4409:
4406:
4403:
4399:
4395:
4392:
4386:
4373:
4364:
4359:
4356:
4352:
4348:
4345:
4342:
4340:
4331:
4325:
4322:
4318:
4314:
4309:
4300:
4292:
4283:
4276:
4267:
4262:
4259:
4255:
4251:
4247:
4240:
4228:
4224:
4218:
4205:
4200:
4197:
4191:
4188:
4183:
4180:
4175:
4170:
4167:
4163:
4159:
4154:
4145:
4137:
4128:
4121:
4112:
4107:
4104:
4100:
4096:
4092:
4085:
4073:
4071:
4065:
4059:
4050:
4043:
4034:
4029:
4026:
4022:
4018:
4014:
4007:
3987:
3986:
3985:
3982:
3979:
3978:
3972:
3968:
3960:
3951:
3931:
3928:
3925:
3921:
3915:
3906:
3899:
3890:
3885:
3882:
3878:
3874:
3870:
3863:
3851:
3847:
3841:
3832:
3825:
3816:
3811:
3808:
3804:
3800:
3796:
3789:
3777:
3773:
3768:
3759:
3754:
3751:
3747:
3743:
3739:
3732:
3716:
3715:
3714:
3712:
3704:
3684:
3679:
3669:
3664:
3654:
3651:
3644:
3635:
3630:
3627:
3623:
3619:
3616:
3613:
3609:
3597:
3584:
3579:
3576:
3570:
3567:
3562:
3559:
3554:
3546:
3538:
3524:
3520:
3514:
3508:
3484:
3481:
3478:
3470:
3464:
3460:
3455:
3446:
3441:
3438:
3434:
3430:
3426:
3419:
3398:
3397:
3396:
3394:
3393:
3387:
3385:
3381:
3373:
3369:
3362:
3358:
3351:
3346:
3345:
3339:
3334:
3333:
3328: ā
3326:
3325:
3304:
3299:
3289:
3284:
3274:
3271:
3264:
3255:
3250:
3247:
3243:
3239:
3236:
3233:
3229:
3217:
3204:
3199:
3196:
3190:
3187:
3182:
3179:
3174:
3166:
3153:
3139:
3130:
3125:
3122:
3118:
3114:
3110:
3106:
3100:
3096:
3081:
3072:
3067:
3064:
3060:
3056:
3052:
3045:
3029:
3028:
3027:
3024:
3019:
3018:
3012:
3011:
2990:
2987:
2984:
2980:
2965:
2956:
2951:
2948:
2944:
2940:
2936:
2932:
2926:
2922:
2917:
2908:
2903:
2900:
2896:
2892:
2888:
2881:
2865:
2864:
2863:
2861:
2853:
2848:
2846:
2844:
2838:
2819:
2812:
2803:
2798:
2795:
2791:
2786:
2780:
2768:
2755:
2748:
2739:
2734:
2731:
2727:
2722:
2713:
2696:
2695:
2694:
2691:
2690:
2683:
2678:
2677:
2672:
2671:
2666:
2662:
2658:
2654:
2651: =
2650:
2646:
2642:
2638:
2634:
2630:
2611:
2606:
2596:
2582:
2573:
2568:
2565:
2561:
2556:
2553:
2544:
2529:
2524:
2519:
2516:
2512:
2505:
2493:
2492:
2491:
2489:
2488:
2482:
2480:
2479:Doppler shift
2475:
2474:
2468:
2467:
2462:
2458:
2453:
2452:
2446:
2442:
2423:
2410:
2402:
2399:
2396:
2393:
2381:
2378:
2373:
2368:
2364:
2356:
2355:
2354:
2349:
2345:
2326:
2319:
2315:
2311:
2304:
2296:
2291:
2277:
2276:
2275:
2270:
2266:
2262:
2254:
2252:
2245:
2243:
2238:
2237:
2229:
2222:
2221:
2213:
2206:
2199:
2195:
2191:
2190:
2180:
2173:
2166:
2165:
2160:
2156:
2155:
2150:
2146:
2142:
2135:
2128:
2105:
2102:
2098:
2093:
2087:
2084:
2079:
2072:
2068:
2062:
2058:
2051:
2047:
2040:
2036:
2030:
2026:
2016:
2012:
2006:
2001:
1997:
1990:
1986:
1984:
1977:
1974:
1970:
1956:
1951:
1948:
1944:
1940:
1937:
1933:
1925:
1921:
1915:
1911:
1901:
1897:
1890:
1886:
1880:
1876:
1868:
1864:
1862:
1855:
1852:
1848:
1840:
1837:
1833:
1828:
1822:
1819:
1814:
1807:
1803:
1797:
1793:
1786:
1782:
1775:
1771:
1765:
1761:
1751:
1747:
1741:
1736:
1732:
1725:
1721:
1719:
1712:
1709:
1705:
1693:
1692:
1691:
1689:
1684:
1667:
1664:
1661:
1658:
1655:
1652:
1649:
1637:
1626:
1622:
1600:
1571:
1541:
1536:
1531:
1522:
1517:
1514:
1510:
1505:
1502:
1497:
1494:
1489:
1480:
1470:
1464:
1454:
1447:
1444:
1441:
1437:
1431:
1426:
1423:
1419:
1412:
1410:
1403:
1400:
1396:
1388:
1383:
1380:
1376:
1372:
1363:
1353:
1343:
1331:
1325:
1321:
1315:
1310:
1307:
1303:
1296:
1294:
1287:
1284:
1280:
1272:
1267:
1262:
1253:
1248:
1245:
1241:
1236:
1233:
1228:
1225:
1220:
1211:
1201:
1195:
1185:
1178:
1175:
1172:
1168:
1162:
1157:
1154:
1150:
1143:
1141:
1134:
1131:
1127:
1115:
1114:
1113:
1111:
1107:
1103:
1099:
1080:
1075:
1067:
1064:
1060:
1052:
1049:
1045:
1035:
1032:
1028:
1020:
1017:
1013:
1006:
1001:
989:
988:
987:
985:
955:
953:
948:
936: =
935:
931:
924:
914: /
910:
907: =
903:
896:
892:
888:
884:
880:
876:
872:
868:
849:
844:
840:
836:
833:
828:
825:
820:
815:
811:
807:
804:
799:
796:
791:
788:
781:
780:
779:
777:
773:
769:
765:
761:
754:
750:
743:
724:
721:
717:
711:
708:
703:
696:
692:
686:
682:
676:
672:
668:
663:
660:
656:
648:
647:
646:
644:
640:
633:
628:
626:
622:
618:
612:
608:
589:
586:
582:
578:
574:
571:is the fluid
570:
566:
562:
558:
555: =
554:
550:
546:
542:
538:
534:
530:
527:
526:flow velocity
523:
519:
500:
497:
494:
491:
488:
476:
465:
461:
457:
453:
449:
430:
425:
420:
411:
406:
403:
399:
394:
391:
386:
383:
378:
369:
359:
353:
343:
336:
333:
330:
326:
320:
315:
312:
308:
301:
296:
293:
289:
281:
280:
279:
274:
270:
266:
258:
253:
248:
245:
242:ā in varying
241:
240:
236:
233:
229:
225:
221:
217:
213:
209:
205:
201:
198:
195:
191:
187:
182:
178:
174:
170:
167:
164:
163:wave breaking
160:
156:
152:
148:
144:
140:
137:
136:
135:
129:
127:
125:
121:
116:
114:
109:
107:
103:
102:inhomogeneous
99:
95:
91:
88:For the mean
86:
84:
80:
76:
71:
69:
65:
61:
57:
56:momentum flux
53:
49:
45:
41:
34:or accretion.
33:
32:beach erosion
29:
25:
21:
7546:Water column
7494:Oceanography
7469:Observations
7464:Explorations
7434:Marginal sea
7427:
7385:OSTM/Jason-2
7217:Volcanic arc
7192:Slab suction
6909:Head of tide
6799:Loop Current
6739:Ekman spiral
6525:Stokes drift
6484:
6435:Gravity wave
6410:Cnoidal wave
6315:
6294:
6260:
6256:
6224:
6220:
6188:
6184:
6152:
6148:
6124:
6115:
6107:
6103:
6099:
6090:
6081:
6056:
6047:
6015:
6011:
6002:
5982:
5976:
5957:
5951:
5942:
5933:
5924:
5889:. Retrieved
5883:
5873:
5864:
5855:
5837:
5828:
5819:
5817:
5256:
5254:
5244:
5243:
5236:
5228:
5227:
5221:
5215:
5214:
5206:
5199:
5193:
5192:
5135:). The term
5128:
5122:
4910:
4899:
3983:
3976:
3975:
3970:
3966:
3958:
3949:
3946:
3708:
3391:
3390:
3388:
3383:
3367:
3360:
3357:shear stress
3349:
3343:
3342:
3336:denotes the
3331:
3330:
3323:
3322:
3319:
3025:
3016:
3015:
3009:
3008:
3005:
2857:
2840:
2836:
2834:
2688:
2687:
2684:
2675:
2674:
2669:
2668:
2664:
2660:
2656:
2652:
2648:
2644:
2640:
2636:
2632:
2628:
2626:
2486:
2485:
2483:
2472:
2471:
2465:
2464:
2460:
2456:
2450:
2449:
2444:
2440:
2438:
2347:
2341:
2268:
2258:
2249:
2235:
2234:
2227:
2219:
2218:
2211:
2204:
2197:
2188:
2187:
2178:
2171:
2163:
2162:
2158:
2153:
2152:
2144:
2140:
2133:
2126:
2124:
1687:
1685:
1624:
1620:
1560:
1109:
1105:
1101:
1095:
959:
946:
933:
922:
908:
901:
894:
893:wave height
887:random waves
878:
874:
866:
864:
775:
763:
752:
741:
739:
631:
629:
614:
610:
606:
576:
568:
564:
560:
556:
552:
548:
544:
540:
536:
532:
517:
459:
455:
451:
447:
445:
272:
264:
262:
237:
203:
199:
180:
176:
172:
168:
151:free surface
142:
138:
133:
117:
110:
87:
72:
43:
37:
7617:Water waves
7536:Thermocline
7253:Mesopelagic
7226:Ocean zones
7197:Slab window
7062:Hydrography
7002:Abyssal fan
6969:Tidal range
6959:Tidal power
6954:Tidal force
6839:Rip current
6774:Gulf Stream
6734:Ekman layer
6724:Downwelling
6699:Baroclinity
6686:Circulation
6582:Wave height
6572:Wave action
6555:megatsunami
6535:Stokes wave
6495:Rossby wave
6460:Kelvin wave
6440:Green's law
6018:: 331ā347,
4921:satisfies:
2845:) is made.
1096:With, in a
883:wave height
760:group speed
749:phase speed
212:wave groups
161:reduces by
159:wave height
7606:Categories
7474:Reanalysis
7373:Satellites
7354:Sofar bomb
7202:Subduction
7177:Ridge push
7072:Ocean bank
7052:Contourite
6979:Tide gauge
6964:Tidal race
6949:Tidal bore
6939:Slack tide
6904:Earth tide
6824:Ocean gyre
6644:Wind setup
6639:Wind fetch
6602:Wave setup
6597:Wave radar
6592:Wave power
6490:Rogue wave
6420:Dispersion
6135:References
5985:, Sydney:
5891:2010-11-25
2149:wavenumber
619:), is the
194:morphology
157:where the
139:Wave setup
104:mean-flow
83:wave setup
7336:Acoustics
7288:Sea level
7187:Slab pull
7124:tectonics
7032:Cold seep
6994:Landforms
6871:Whirlpool
6866:Upwelling
6649:Wind wave
6577:Wave base
6505:Sea state
6425:Edge wave
6415:Cross sea
6249:117932573
6213:120585538
6177:124628167
5796:ε
5793:−
5782:¯
5756:τ
5752:−
5737:τ
5717:¯
5691:τ
5687:−
5672:τ
5647:∂
5634:¯
5625:∂
5592:∂
5579:¯
5570:∂
5555:∂
5542:¯
5533:∂
5500:∂
5487:¯
5478:∂
5409:¯
5384:∂
5380:∂
5332:¯
5307:∂
5303:∂
5285:∂
5277:∂
5167:¯
5159:⊗
5156:∇
5105:ε
5102:−
5097:¯
5089:⋅
5079:τ
5074:−
5069:¯
5061:⋅
5051:τ
5036:¯
5028:⊗
5025:∇
4976:¯
4958:⋅
4955:∇
4943:∂
4935:∂
4904:the mean
4861:τ
4857:−
4842:τ
4826:∂
4822:∂
4810:¯
4807:η
4788:ρ
4758:¯
4755:η
4738:ρ
4698:¯
4681:¯
4665:¯
4662:η
4646:ρ
4632:∂
4628:∂
4591:¯
4574:¯
4558:¯
4555:η
4539:ρ
4525:∂
4521:∂
4496:¯
4480:¯
4477:η
4461:ρ
4447:∂
4443:∂
4419:τ
4415:−
4400:τ
4384:∂
4380:∂
4368:¯
4365:η
4346:ρ
4304:¯
4287:¯
4271:¯
4268:η
4252:ρ
4238:∂
4234:∂
4209:¯
4206:η
4189:ρ
4149:¯
4132:¯
4116:¯
4113:η
4097:ρ
4083:∂
4079:∂
4054:¯
4038:¯
4035:η
4019:ρ
4005:∂
4001:∂
3910:¯
3894:¯
3891:η
3875:ρ
3861:∂
3857:∂
3836:¯
3820:¯
3817:η
3801:ρ
3787:∂
3783:∂
3763:¯
3760:η
3744:ρ
3730:∂
3726:∂
3675:τ
3670:−
3660:τ
3649:∇
3639:¯
3636:η
3617:ρ
3588:¯
3585:η
3568:ρ
3539:⊗
3534:¯
3521:⋅
3518:∇
3506:∂
3496:∂
3471:⋅
3468:∇
3450:¯
3447:η
3431:ρ
3417:∂
3413:∂
3295:τ
3290:−
3280:τ
3269:∇
3259:¯
3256:η
3237:ρ
3208:¯
3205:η
3188:ρ
3162:¯
3154:⊗
3149:¯
3134:¯
3131:η
3115:ρ
3107:⋅
3104:∇
3091:¯
3076:¯
3073:η
3057:ρ
3043:∂
3039:∂
2975:¯
2960:¯
2957:η
2941:ρ
2933:⋅
2930:∇
2912:¯
2909:η
2893:ρ
2879:∂
2875:∂
2807:¯
2804:η
2787:ρ
2764:¯
2743:¯
2740:η
2723:ρ
2709:¯
2592:¯
2577:¯
2574:η
2557:ρ
2549:¯
2530:ρ
2525:η
2517:−
2513:∫
2419:¯
2411:⋅
2403:−
2400:ω
2394:σ
2379:σ
2346:. Above,
2080:−
1815:−
1641:~
1604:~
1575:~
1526:¯
1523:η
1503:ρ
1490:−
1485:¯
1458:~
1448:ρ
1432:η
1424:−
1420:∫
1368:¯
1347:~
1335:~
1326:ρ
1316:η
1308:−
1304:∫
1257:¯
1254:η
1234:ρ
1221:−
1216:¯
1189:~
1179:ρ
1163:η
1155:−
1151:∫
871:amplitude
869:the wave
834:ρ
805:ρ
704:−
588:averaging
539:is time,
480:~
415:¯
412:η
392:ρ
379:−
374:¯
347:~
337:ρ
321:η
313:−
309:∫
269:dynamical
244:mean-flow
228:amplitude
155:surf zone
64:mean flow
54:ā excess
7569:Category
7521:Seawater
7248:Littoral
7243:Deep sea
7102:Seamount
6984:Tideline
6929:Rip tide
6859:shutdown
6829:Overflow
6562:Undertow
6405:Clapotis
6314:(1977),
6293:(2003),
6040:18232994
5881:(1974).
2265:momentum
2139:are the
921:, where
778:equals:
621:integral
464:pressure
98:dynamics
79:momentum
52:averaged
7579:Commons
7449:Mooring
7399:Related
7390:Jason-3
7380:Jason-1
7263:Pelagic
7258:Oceanic
7233:Benthic
6550:Tsunami
6520:Soliton
6265:Bibcode
6229:Bibcode
6193:Bibcode
6157:Bibcode
6020:Bibcode
5205:)
4915:kinetic
4900:For an
2477:is the
2459:is the
2226:| and
2169:√
2151:vector
941:⁄
932:. Then
928:is the
916:√
768:kinetic
758:is the
747:is the
623:of the
604:
592:
579:is the
573:density
524:of the
143:setdown
92:in the
75:forcing
7268:Photic
7097:Seabed
6510:Seiche
6322:
6301:
6247:
6211:
6175:
6038:
5964:
5235:
5220:
5127:, and
3320:where
2455:while
2194:crests
2143:- and
2125:where
1623:- and
1561:where
984:tensor
740:where
529:vector
446:where
247:fields
232:square
226:. The
210:ā for
68:tensor
42:, the
7459:Ocean
7428:Alvin
7278:Swash
7122:Plate
7067:Knoll
7057:Guyot
7012:Atoll
6891:Tides
6654:model
6540:Swell
6372:Waves
6245:S2CID
6209:S2CID
6173:S2CID
6036:S2CID
5848:Notes
3947:with
3709:In a
3006:with
2627:with
2439:with
865:with
585:phase
106:field
48:phase
7426:DSV
7411:Argo
7273:Surf
6729:Eddy
6320:ISBN
6299:ISBN
5987:ASCE
5962:ISBN
4917:and
3969:and
3956:and
2443:the
2389:with
2203:and
2132:and
1590:and
889:the
881:the
873:and
770:and
751:and
575:and
141:and
122:for
6273:doi
6237:doi
6201:doi
6165:doi
6094:By
6028:doi
6016:106
5991:doi
5844:).
3340:of
2242:|.
1962:and
1112:):
947:ĻgH
905:rms
898:rms
202:or
38:In
7608::
6271:,
6261:11
6259:,
6243:,
6235:,
6225:13
6223:,
6207:,
6199:,
6189:10
6187:,
6171:,
6163:,
6151:,
6065:^
6034:,
6026:,
6014:,
5912:^
5900:^
3981:.
3376:ij
3023:.
2862::
2481:.
952:.
950:m0
943:16
926:m0
912:m0
645::
635:xx
607:Ļg
531:,
466:,
276:xx
181:xy
126:.
108:.
70:.
6356:e
6349:t
6342:v
6275::
6267::
6239::
6231::
6203::
6195::
6167::
6159::
6153:8
6108:y
6106:,
6104:x
6102:(
6100:h
6030::
6022::
5993::
5970:.
5894:.
5842:y
5838:u
5835:,
5833:x
5829:u
5820:E
5799:.
5788:y
5779:u
5772:)
5766:y
5763:,
5760:b
5747:y
5744:,
5741:w
5732:(
5728:+
5723:x
5714:u
5707:)
5701:x
5698:,
5695:b
5682:x
5679:,
5676:w
5667:(
5663:=
5650:y
5640:y
5631:u
5617:y
5614:y
5610:S
5606:+
5602:)
5595:y
5585:x
5576:u
5564:+
5558:x
5548:y
5539:u
5526:(
5520:y
5517:x
5513:S
5509:+
5503:x
5493:x
5484:u
5470:x
5467:x
5463:S
5459:+
5448:]
5444:E
5440:)
5434:y
5431:,
5428:g
5424:c
5420:+
5415:y
5406:u
5399:(
5394:[
5387:y
5375:+
5371:]
5367:E
5363:)
5357:x
5354:,
5351:g
5347:c
5343:+
5338:x
5329:u
5322:(
5317:[
5310:x
5298:+
5288:t
5280:E
5257:E
5249:g
5245:c
5237:E
5233:g
5229:c
5222:E
5216:u
5207:E
5203:g
5200:c
5194:u
5173:)
5164:u
5152:(
5148::
5144:S
5129:Īµ
5108:,
5094:u
5084:b
5066:u
5056:w
5046:=
5042:)
5033:u
5021:(
5017::
5013:S
5009:+
5005:]
5001:E
4997:)
4991:g
4986:c
4981:+
4973:u
4967:(
4962:[
4952:+
4946:t
4938:E
4911:E
4876:.
4871:y
4868:,
4865:b
4852:y
4849:,
4846:w
4838:+
4835:h
4829:y
4816:)
4802:+
4799:h
4795:(
4791:g
4785:=
4774:]
4768:2
4764:)
4750:+
4747:h
4744:(
4741:g
4733:2
4730:1
4725:+
4720:y
4717:y
4713:S
4709:+
4704:y
4695:u
4687:y
4678:u
4671:)
4657:+
4654:h
4650:(
4642:[
4635:y
4623:+
4619:]
4613:x
4610:y
4606:S
4602:+
4597:x
4588:u
4580:y
4571:u
4564:)
4550:+
4547:h
4543:(
4535:[
4528:x
4516:+
4508:]
4502:y
4493:u
4486:)
4472:+
4469:h
4465:(
4457:[
4450:t
4434:,
4429:x
4426:,
4423:b
4410:x
4407:,
4404:w
4396:+
4393:h
4387:x
4374:)
4360:+
4357:h
4353:(
4349:g
4343:=
4332:]
4326:y
4323:x
4319:S
4315:+
4310:y
4301:u
4293:x
4284:u
4277:)
4263:+
4260:h
4256:(
4248:[
4241:y
4229:+
4225:]
4219:2
4215:)
4201:+
4198:h
4195:(
4192:g
4184:2
4181:1
4176:+
4171:x
4168:x
4164:S
4160:+
4155:x
4146:u
4138:x
4129:u
4122:)
4108:+
4105:h
4101:(
4093:[
4086:x
4074:+
4066:]
4060:x
4051:u
4044:)
4030:+
4027:h
4023:(
4015:[
4008:t
3977:u
3971:y
3967:x
3963:y
3959:u
3954:x
3950:u
3932:,
3929:0
3926:=
3922:]
3916:y
3907:u
3900:)
3886:+
3883:h
3879:(
3871:[
3864:y
3852:+
3848:]
3842:x
3833:u
3826:)
3812:+
3809:h
3805:(
3797:[
3790:x
3778:+
3774:]
3769:)
3755:+
3752:h
3748:(
3740:[
3733:t
3685:.
3680:b
3665:w
3655:+
3652:h
3645:)
3631:+
3628:h
3624:(
3620:g
3614:=
3610:]
3605:I
3598:2
3594:)
3580:+
3577:h
3574:(
3571:g
3563:2
3560:1
3555:+
3551:S
3547:+
3543:M
3531:u
3525:[
3515:+
3509:t
3500:M
3485:,
3482:0
3479:=
3475:M
3465:+
3461:]
3456:)
3442:+
3439:h
3435:(
3427:[
3420:t
3392:M
3384:h
3374:Ī“
3368:I
3364:b
3361:Ļ
3353:w
3350:Ļ
3344:u
3332:u
3324:u
3305:,
3300:b
3285:w
3275:+
3272:h
3265:)
3251:+
3248:h
3244:(
3240:g
3234:=
3230:]
3225:I
3218:2
3214:)
3200:+
3197:h
3194:(
3191:g
3183:2
3180:1
3175:+
3171:S
3167:+
3159:u
3146:u
3140:)
3126:+
3123:h
3119:(
3111:[
3101:+
3097:]
3088:u
3082:)
3068:+
3065:h
3061:(
3053:[
3046:t
3021:w
3017:M
3010:u
2991:,
2988:0
2985:=
2981:]
2972:u
2966:)
2952:+
2949:h
2945:(
2937:[
2927:+
2923:]
2918:)
2904:+
2901:h
2897:(
2889:[
2882:t
2842:Ī·
2839:+
2837:h
2820:.
2813:)
2799:+
2796:h
2792:(
2781:w
2776:M
2769:+
2761:v
2756:=
2749:)
2735:+
2732:h
2728:(
2719:M
2714:=
2706:u
2689:u
2680:w
2676:M
2670:M
2665:t
2663:,
2661:y
2659:,
2657:x
2655:(
2653:Ī·
2649:z
2645:t
2643:,
2641:z
2639:,
2637:y
2635:,
2633:x
2631:(
2629:v
2612:,
2607:w
2602:M
2597:+
2589:v
2583:)
2569:+
2566:h
2562:(
2554:=
2545:z
2541:d
2535:v
2520:h
2506:=
2502:M
2487:M
2473:v
2469:ā
2466:k
2457:Ļ
2451:v
2441:Ļ
2424:,
2416:v
2407:k
2397:=
2382:k
2374:=
2369:p
2365:c
2351:p
2348:c
2327:,
2320:p
2316:c
2312:E
2305:k
2302:k
2297:=
2292:w
2287:M
2272:w
2269:M
2240:g
2236:c
2231:g
2228:c
2224:p
2220:c
2215:p
2212:c
2208:g
2205:c
2201:p
2198:c
2189:k
2182:y
2179:k
2177:+
2175:x
2172:k
2164:k
2159:k
2154:k
2145:y
2141:x
2137:y
2134:k
2130:x
2127:k
2106:,
2103:E
2099:]
2094:)
2088:2
2085:1
2073:p
2069:c
2063:g
2059:c
2052:(
2048:+
2041:p
2037:c
2031:g
2027:c
2017:2
2013:k
2007:2
2002:y
1998:k
1991:[
1987:=
1978:y
1975:y
1971:S
1957:,
1952:x
1949:y
1945:S
1941:=
1938:E
1934:)
1926:p
1922:c
1916:g
1912:c
1902:2
1898:k
1891:y
1887:k
1881:x
1877:k
1869:(
1865:=
1856:y
1853:x
1849:S
1841:,
1838:E
1834:]
1829:)
1823:2
1820:1
1808:p
1804:c
1798:g
1794:c
1787:(
1783:+
1776:p
1772:c
1766:g
1762:c
1752:2
1748:k
1742:2
1737:x
1733:k
1726:[
1722:=
1713:x
1710:x
1706:S
1688:a
1671:)
1668:t
1665:,
1662:z
1659:,
1656:y
1653:,
1650:x
1647:(
1638:u
1625:y
1621:x
1601:v
1572:u
1542:,
1537:2
1532:)
1518:+
1515:h
1511:(
1506:g
1498:2
1495:1
1481:z
1477:d
1471:)
1465:2
1455:v
1445:+
1442:p
1438:(
1427:h
1413:=
1404:y
1401:y
1397:S
1389:,
1384:x
1381:y
1377:S
1373:=
1364:z
1360:d
1354:)
1344:v
1332:u
1322:(
1311:h
1297:=
1288:y
1285:x
1281:S
1273:,
1268:2
1263:)
1249:+
1246:h
1242:(
1237:g
1229:2
1226:1
1212:z
1208:d
1202:)
1196:2
1186:u
1176:+
1173:p
1169:(
1158:h
1144:=
1135:x
1132:x
1128:S
1110:z
1108:,
1106:y
1104:,
1102:x
1100:(
1081:.
1076:)
1068:y
1065:y
1061:S
1053:x
1050:y
1046:S
1036:y
1033:x
1029:S
1021:x
1018:x
1014:S
1007:(
1002:=
998:S
969:S
939:1
934:E
923:H
918:2
909:H
902:H
895:H
879:a
875:H
867:a
850:,
845:2
841:H
837:g
829:8
826:1
821:=
816:2
812:a
808:g
800:2
797:1
792:=
789:E
776:E
764:E
756:g
753:c
745:p
742:c
725:,
722:E
718:)
712:2
709:1
697:p
693:c
687:g
683:c
677:2
673:(
669:=
664:x
661:x
657:S
632:S
616:Ī·
613:+
611:h
609:(
601:2
598:/
595:1
577:g
569:Ļ
565:t
563:,
561:x
559:(
557:Ī·
553:z
549:x
547:(
545:h
541:z
537:t
533:z
518:x
504:)
501:t
498:,
495:z
492:,
489:x
486:(
477:u
460:t
458:,
456:z
454:,
452:x
450:(
448:p
431:,
426:2
421:)
407:+
404:h
400:(
395:g
387:2
384:1
370:z
366:d
360:)
354:2
344:u
334:+
331:p
327:(
316:h
302:=
297:x
294:x
290:S
273:S
265:x
196:;
188:(
177:S
50:-
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