By Gordon David Crapper

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1 03), the vector equivalent of kc = w when there is no current; now, of course, kc = a. Note also that with no current the phase speed c is parallel to k, perpendicular to the crests, but once a current appears the convected speed C can be in any direction. 104) rather than (2. 32). 7 COMBINATION OF WAVES: GROUP VELOCITY Some important ideas emerge if we consider the surface produced by the addition of two trains of waves. w . w)t). (2. 1 l l ) The second cosine i s a wave with the mean wave number and frequency o f the two originals.

9] k1 k kr k = = cos X , kz = cos (x - 8) , k ke k sin X = 61 , (2. 149) sin (x - 8) Fig. 12. 1 50) so that a

On each ray. The numerical method uses a standard library routine com­ puter program for systems of ordinary differential equations. 162). Clearly they are remarkably accurate in this simple configuration. 1 Show that

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