(6) Water particle displacements.

(a) Another important aspect of linear wave theory deals with the displacement of individual water

particles within the wave. Water particles generally move in elliptical paths in shallow or transitional depth

water and in circular paths in deep water (Figure II-1-4). If the mean particle position is considered to be at

the center of the ellipse or circle, then vertical particle displacement with respect to the mean position cannot

exceed one-half the wave height. Thus, since the wave height is assumed to be small, the displacement of

any fluid particle from its mean position must be small. Integration of Equations II-1-22 and II-1-23 gives

the horizontal and vertical particle displacements from the mean position, respectively (Figure II-1-4).

(b) Fluid particle displacements are

2π(*z*%*d*)

cosh

2

sin θ

ξ'&

(II-1-26)

4π*L*

2π*d*

cosh

2π(*z *% *d*)

sinh

ζ'%

(II-1-27)

cos θ

4π*L*

2π*d*

cosh

Water Wave Mechanics

II-1-13

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