1

j *j B*j

M*u*

cosh *jk*(*z*%*d*)

2

2

(II-1-109)

sin *jkx*

'&

M*x*

cosh *jkd*

1

j *j B*j

M*u*

sinh *jk*(*z*%*d*)

2

2

cos *jkx*

(II-1-110)

'

M*z*

cosh *jkd*

(t)

The instantaneous water surface elevation η(x) and water particle pressure are given by

η(*x*) ' * a*N cos *Nkx *% j *a*j cos *jkx*

1

2

(II-1-111)

1

ρ(*u * 2 % *w * 2)

2

(u) Integral properties of periodic gravity waves, including wave potential and kinetic energy, wave

momentum and impulse, wave energy flux and wave power, and wave radiation stresses obtained by

Klopman (1990) and Sobey et al. (1987) are listed in the Leenknecht, Szuwalski, and Sherlock (1992)

documentation.

(v) A computer program developed by Fenton (1988) has recently been implemented in the ACES

package. The ACES implementation facilitates use of Fenton's theory to applications in deep water and

finite-depth water. It uses Fourier series of up to 25 terms to describe a wave train and provides information

about various wave quantities. The output includes wave estimates for common engineering parameters

including water surface elevation, wave particle kinematics, and wave integral properties as functions of wave

height, period, water depth, and position in the wave form.

(w) The wave is assumed to co-exist on a uniform co-flowing current, taken either as the mean Eulerian

current or mean mass transport velocity. At a given point in the water column, wave kinematics are tabulated

over two wavelengths, and vertical distribution of the selected kinematics under the wave crest are graphically

displayed. ACES implementation of Fenton's theory and its input/output requirements, computations, and

examples are described in detail in the ACES documentation manual (Leenknecht, Szuwalski, and Sherlock

1992).

(x) Figure II-1-18 illustrates the application of Fenton's theory. This case represents shallow-water

(10-m) conditions and wave height and period of 5 m and 10 sec, respectively. Surface elevation, horizontal

velocity, and pressure over two wavelengths is shown graphically in Figure II-1-18. The ACES

documentation includes guidance on proper use of Fenton's theory.

II-1-54

Water Wave Mechanics

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