Radiation stresses in water waves; a physical discussion, with applications

Longuet‐Higgins, M. S.; Stewart, R. W.

doi:10.1016/0011-7471(64)90001-4

Cited by 973 publications

(844 citation statements)

References 18 publications

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“…This non-linear behavior has been noted before in channel models by and is in accordance with the concept of a radiation stress (Longuet-Higgins and Stewart, 1964). The greater the dissipation of the tide, the larger the set-up in mean sea level at the channel interior boundary.…”

Section: I I Isupporting

confidence: 89%

Tidal distortion in shallow estuaries

Speer¹

1984

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The offshore tide becomes distorted as it propagates into shallow inlet/ estuarine systems. Time asymmetries develop in the rise and fall of sea surface with consequent time and magnitude asymmetries in tidal currents. Flood-dominant estuaries are characterized by longer falling tides and stronger flood currents while ebb-dominant estuaries have longer rising tides and stronger ebb currents. The asymmetries are reflected in the nonlinear growth of harmonics and compound tides of the principal equilibrium tidal constituents. This dissertation consists of three papers which examine the development of tidal asymmetries in shallow estuarine systems: a study of the recent migration history of Nauset Inlet (MA), a shallow estuarine system located on Cape Cod; an analysis of the results of a series of field experiments conducted at Nauset; a numerical model study of the types of estuarine characteristics controlling tidal asymmetry. The analysis of field results focuses on sea surface measurements. Non-linear distortion of the tide at Nauset is characterized by the strong growth of harmonics and compound constituents particularly in the quarter-diurnal band. Phase relationships between the forced constituents and their parents produce a flood-dominant estuary. Numerical modeling of M 2 tidal propagation in shallow estuarine channels utilizes the one-dimensional equations of motion. Shallow, frictionally dominated channels with moderate tidal flat area develop a flood-dominant asymmetry while deeper channels with extensive tidal flats develop an ebb-dominant asymmetry. Model results are supported by observations of tidal asymmetry in natural estuaries. Implications of non-linear tidal distortion on bedload and suspended material transport are profound. Flood-dominant estuaries tend to import sediment if the supply is adequate whereas ebb-dominant estuaries can flush entering sediment effectively. Over long time periods, flood-dominant estuaries may eventually fill. Ebb-dominant estuaries may represent more stable long-term configurations. Coastal geologists have focused on the velocity asymmetries frequently observed in the tidal inlet channel and classified inlets as either "ebb dominant" or "flood dominant" (eg., Hayes, 1975). Many inlet channels are termed "ebb dominant" because it is observed that ebb currents continue to flow even after the ocean tide has turned to rise. As a result, flood currents are confined to shallow channels on either side of the main inlet channel during early stages of rising tide (see figure 1 for inlet morphology). This situation is caused by lags in low water from the ocean to the far reaches of the estuary. The terms "ebb dominant" and "flood dominant" stability. An estuary characterized by a longer falling tide and hence stronger flood currents may show a pattern of net up-estuary sediment transport. Such an estuary may be unable to flush effectively sediments entering the system through the inlet. As a result, the estuary could be expected to gradually fill, with consequent re...

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Section: I I Isupporting

confidence: 89%

Tidal distortion in shallow estuaries

Speer¹

1984

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“…For linear waves S yy 5S ff n sin 2 h11 ð Þ 2 1 2 Â Ã , and S xy 5S yx 5 1 2 S ff nsin 2h, were computed spectrally and integrated over 1/5 to 1/25 Hz, where n5C g =C, with group velocity C g and phase speed C [Longuet- Higgins and Stewart, 1964]. To evaluate @S xy =@x, h m at the B stations was assumed equal to the corresponding A station.…”

Section: Discussionmentioning

confidence: 99%

Field observations of wave‐driven circulation over spur and groove formations on a coral reef

et al. 2015

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Spur and groove (SAG) formations are found on the forereefs of many coral reefs worldwide.Modeling results have shown that SAG formations together with shoaling waves induce a nearshore Lagrangian circulation pattern of counter-rotating circulation cells, but these have never been observed in the field. We present results from two separate field studies of SAG formations on Palmyra Atoll which show their effect on waves to be small, but reveal a persistent order 1 cm/s depth-averaged Lagrangian offshore flow over the spur and onshore flow over the grooves. This circulation was stronger for larger, directly incident waves and low alongshore flow conditions, consistent with predictions from modeling. Favorable forcing conditions must be maintained on the order of 1 h to accelerate and develop the SAG circulation cells. The primary cross and alongshore depth-averaged momentum balances were between the pressure gradient, radiation stress gradient, and nonlinear convective terms, and the bottom drag was similar to values found on other reefs. The vertical structure of these circulation cells was previously unknown and the results show a complex horizontal offshore Lagrangian flow over the spurs near the surface driven by alongshore variability in radiation stress gradients. Vertical flow was downward over the spur and upward over the groove, likely driven by alongshore differences in bottom stress and not by vortex forcing.

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“…wave equations and boundary cond'itions, by the method of The coupling coefficients . C and .C (at vertical distance z Stokes, to second order in the wave slope [Diesel, 1952;Longuet-measured from the sea surface) are given by [llasselhanmn, 1962;Higgins and Stewart, 1960, 1964Ilasselmann. 1962;and Sand.…”

Section: 4s4mentioning

confidence: 99%

Bound infragravity waves

Okihiro¹,

Guza²,

Seymour³

1992

J. Geophys. Res.

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Model predictions of bound (i.e,, nonlinearly forced by and coupled to wave groups) infragravity wave enryaecompared with about 2 years of observations in 8-to 13-rn depths at Imperial Beach. California, and r-% Barbers Pointm Hawaii. Frequency-directional spectra of free waves at sea and swell frequencies, estimated with a small array of four pressure sensors, are used to predict the bound wave spectra below 0.04 Hz. The predicted S• total bound wave energy is always less than the observed infragravity energy, and the underprediction increases c with increasing water depth and especially with decreasing swell energy. At most half, and usually much less. of the observed infragravity energy is bound. Bound wave spectra are also predicted with data from a single wave gage in 183-m depth at Point Conception. California, and the assumption of unidirectional sea and swell. Even with energetic swell, less than 10% of the total observed infragravity energy in 183-m depth is bound Free waves, either leaky or edge waves, are more energetic than bound waves at both the shallow and deep sites. The low level of infragravity energy observed in 183-m depth compared with 8-to 13-m depths, with similarly moderate sea and swell energy, suggests that leaky (and very high-mode edge) waves contribute less than 10% of the infragravity energy in 8-13 m. Most of the free infragravity energy in shallow water is refractively 98 sra andnriaý cTeea4 INTRODUC171ONFollowing the early observations by Munk [1949] and Tucker Infragravity waves are believed to be an important factnr in [19501 suggesting that the seaward propagating infragravity wave several nearshore processes. The purpose of this paper is to estiamplitude was at least as large as the amplitudes of the shoreward mate the contribution of bound waves to infragravity energy propagating bound wave, Longuet-Higgins and Stewart 11962] observed well outside the surf zone in depths of both -10 and speculated that the incoming bound wave somehow reflects from -200 m. Infragravity motions (typical periods of 25-200 s on the shoreline and radiates seaward as a free wave. Numerical Pacific coasts) coupled to incident wave (typical periods of models [Symonds et al., 1982) suggest that slow modulation of the 4-25 s) groups were first observed in roughly 15 m depth by breakpoint position at the group frequency results i, long-wave Munk [1949] and Tucker [19501, who showed suggestive correlaradiation seaward from the breakpoint, but laboratory results are tions between wave groups and low-frequency motions. In both inconclusive. Kosten~se [1984] measured the amplitudes of cases the infragravity wave heights were about 10% of the infragravity waves in shallow water induced by wave grouping in incident wave heights. a long wave channel with a plane beach at one end. The observed Weak nonlinear interactions between first-order free waves (sea and theoretical bound wave amplitudes agreed, but there were and swell) of nearly equal frequency is one possible mechanism of significant differences b...

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Radiation stresses in water waves; a physical discussion, with applications

Cited by 973 publications

References 18 publications

Tidal distortion in shallow estuaries

Tidal distortion in shallow estuaries

Field observations of wave‐driven circulation over spur and groove formations on a coral reef

Bound infragravity waves

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