of the breaker crest. Since it is this wave-induced water particle motion
that causes the sédiment to move, it is useful to know the length of the
elliptical path traveled by the water particles and the maximum velocity
and accélération attained during this orbit.
The basic équations for water-wave motion before breaking are discussed in Chapter 2. Quantitative estimâtes of water motion are possible
from small-amplitude wave theory (Section 2.23), even near breaking where
assumptions of the theory are not valid. (Dean, 1970; Eagleson, 1956.)
Equations 2-13 and 2-14, in Section 2.234 give the fluid-particle velocity
components u, w in a wave where small-amplitude theory is applicable.
(See Figure 2-3 for relation to wave phase and water particle accélération.)
For sédiment transport, the conditions of most interest are those
when the wave is in shallow water. For this condition, and making the
small-amplitude assumption, the horizontal length 2A, of the path moved
by the water particle as a wave passes in shallow water is approximately
HTVgT
2A = ——----- ,
(4-10)
2îrd
and the maximum horizontal water velocity is
Hv/p~'
umax =
•
(4-11)
Ilie term under the radical is the wave speed in shallow water.
************** EXAMPLE problem ***************
GIVEN: A wave 1 foot high with a period of 5 seconds is progressing shore
ward in a depth of 2 feet.
FIND:
(a) Calculate the maximum horizontal distance 2A the water particle
moves during the passing of a wave.
(b) Détermine the maximum horizontal velocity un,
of a water
particle.
(c) Compare the maximum horizontal distance 2A with the wavelength
in the 2-foot depth.
(d) speed™ Che
horizontal velocity u^æ, with the wave
4-40
that causes the sédiment to move, it is useful to know the length of the
elliptical path traveled by the water particles and the maximum velocity
and accélération attained during this orbit.
The basic équations for water-wave motion before breaking are discussed in Chapter 2. Quantitative estimâtes of water motion are possible
from small-amplitude wave theory (Section 2.23), even near breaking where
assumptions of the theory are not valid. (Dean, 1970; Eagleson, 1956.)
Equations 2-13 and 2-14, in Section 2.234 give the fluid-particle velocity
components u, w in a wave where small-amplitude theory is applicable.
(See Figure 2-3 for relation to wave phase and water particle accélération.)
For sédiment transport, the conditions of most interest are those
when the wave is in shallow water. For this condition, and making the
small-amplitude assumption, the horizontal length 2A, of the path moved
by the water particle as a wave passes in shallow water is approximately
HTVgT
2A = ——----- ,
(4-10)
2îrd
and the maximum horizontal water velocity is
Hv/p~'
umax =
•
(4-11)
Ilie term under the radical is the wave speed in shallow water.
************** EXAMPLE problem ***************
GIVEN: A wave 1 foot high with a period of 5 seconds is progressing shore
ward in a depth of 2 feet.
FIND:
(a) Calculate the maximum horizontal distance 2A the water particle
moves during the passing of a wave.
(b) Détermine the maximum horizontal velocity un,
of a water
particle.
(c) Compare the maximum horizontal distance 2A with the wavelength
in the 2-foot depth.
(d) speed™ Che
horizontal velocity u^æ, with the wave
4-40