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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(1):1-12; doi:10.1093/qjmam/10.1.1
© 1957 by Oxford University Press
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THE THEORY OF SYMMETRICAL GRAVITY WAVES OF FINITE AMPLITUDE

IV.{dagger} STEADY, SYMMETRICAL, PERIODIC WAVES IN A CHANNEL OF FINITE DEPTH

A. J. GOODY and T. V. DAVIES

( King's College London )

The perfect fluid problem of two-dimensional finite amplitude gravity waves in a channel of finite depth has been investigated and the four quantities, wave velocity (c), wave amplitude (a), wavelength ({lambda}), and depth of the liquid (h), are shown to depend upon two parameters u and k, where O ≤ u ≤ umax and O ≤ k ≤ 1. When u = umax the wave is on the point of breaking. Tables have been prepared of four combination of c, a, {lambda} and h against u and k from which it is possible to deternine (say) the wave velocity when the three quantities a, h and {lambda} are given. An analytical formula is also derived for the relation between a, h, and {lambda} when the wave is on the point of breaking.


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