A Variational Principle for Periodic Waves of Infinite Depth
A Variational Principle for Periodic Waves of Infinite Depth
Ellen R Gottlieb
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Is equivalent to proving that -^. > 1 ° (6l^)^dx the two constraints that A and E are held fixed. o In order to evaluate g/c and to investigate our con- straints, we consider the flat case as the limit of the classi- cal linearized soluti whlnh the amplitude h is small. We the.. , ..... , . , ^. , .^3 this 1. , . -. -. ... D case briefly (cf. \9]). 5^4 Let ^(x, y) be the velocity potential. For the linearized case we may redefine ^ by the expression J(x, y) = ex +(t)(x, y), where the gradient o...f ^ will be inf initesimally small. We may write Vf = (c, 0) +(^^, where H is a constant. Expanding, we obtain c^+ 2c(t) +
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