# On three-dimensional packets of surface waves

##### Citations

1,318 citations

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### Cites background from "On three-dimensional packets of sur..."

...Later, Davey & Stewartson (1974) extended this to waves on finite depth....

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495 citations

### Cites background from "On three-dimensional packets of sur..."

...Patterns of the sort contemplated do arise in wind-generated seas (Kinsman 1965, p. 543), and a possible theoretical basis for bimodal directional spectra has been advanced by Longuet-Higgins (1976) and Fox (976), based on the resonant interaction theory of Davey & Stewartson (1974)....

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474 citations

##### References

2,109 citations

### "On three-dimensional packets of sur..." refers background in this paper

...Hasimoto & Ono (1972) established th a t this solution is stable to relatively small disturbances only if Xv > 0 , a condition which leads to kh 1.363 and is the same as tha t found by Benjamin & Feir (1967)....

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...I f the depth is h and if the wavelength of this train is 2tz/1c, Benjamin & Feir (1967) proved theoretically and Feir (1967) demonstrated experimentally that it is unstable if kh > 1.363 approximately....

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510 citations

### "On three-dimensional packets of sur..." refers background or methods in this paper

...Hasimoto & Ono (1972) established th a t this solution is stable to relatively small disturbances only if Xv > 0 , a condition which leads to kh 1.363 and is the same as tha t found by Benjamin & Feir (1967)....

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...…= kg-lhAj*, A = 0O1 = krtyh fy Moreover if A and ^ 01 are independent of 7] then (2.19), (2.20) reduce to b w ^ A - ~ W \A\*A (2 21)gihtdr kh~ 2 ( Hasimoto & Ono (1972) have pointed out th a t the nonlinear plane wave solution of (2.21) corresponds to the weak cnoidal wave solution of the…...

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...…° ’ \ 4wcr2 2cr2 9 - 10cr> + 9<r* - {4c * + 4c, c«( 1 - <t») + (rj( 1 - <r*)«} 1>1 = —{2cp + cg( l - c r 2)}, A, = > 0, /t, °g > (2.25) and ghcg 2Cp + cg( 1 — o'2) g h -c 2 The principal equation (4.5) of Hasimoto & Ono (1972) is now recovered on assum ing A to be independent of tj and putting = 0....

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...Our aim in this paper is to develop a theory for threedimensional wave-packets parallel to tha t of Hasimoto & Ono (1972)....

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...At first sight the form of the equations for A and 0O1 look rather different from those obtained by Hasimoto & Ono (1972) for the two-dimensional problem but it is possible to write (2.14), (2.15) in an alternative way which makes the connexion obvious....

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440 citations

### "On three-dimensional packets of sur..." refers methods in this paper

...We observe also tha t Stewartson & Stuart (1971), using the method of multiple scales, have developed a theory for the evolution of small two-dimensional dis turbances in marginally unstable plane Poiseuille flow, where dissipative effects are important....

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...I t is the same scaling as used by Stewartson & Stuart (1971) in the first stage of their theory which led to a first order equation for A ....

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141 citations

### "On three-dimensional packets of sur..." refers methods in this paper

...Whitham (1970) has discussed the equivalence of his variational method with a particular multiple scale theory for dissipationless systems....

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131 citations