EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-1-2.
Local fluid velocities and accelerations
(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
HgT
L
sin θ
ξ'&
(II-1-26)
4πL
2πd
cosh
L
2π(z % d)
sinh
HgT 2
L
ζ'%
(II-1-27)
cos θ
4πL
2πd
cosh
L
Water Wave Mechanics
II-1-13
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