1

ρ *g H*2 L

(II-1-56)

16

(c) According to the Airy theory, if the potential energy is determined relative to SWL, and all waves

are propagated in the same direction, potential and kinetic energy components are equal, and the total wave

energy in one wavelength per unit crest width is given by

ρ*gH * 2L

ρ*gH * 2L

ρ*gH * 2L

(II-1-57)

%

'

16

16

8

where subscripts *k *and *p *refer to kinetic and potential energies. Total average wave energy per unit surface

area, termed the *specific energy *or *energy density*, is given by

2

' *E *' ρ*gH*

(II-1-58)

8

(d) *Wave energy flux *is the rate at which energy is transmitted in the direction of wave propagation across

a vertical plan perpendicular to the direction of wave advance and extending down the entire depth.

Assuming linear theory holds, the average energy flux per unit wave crest width transmitted across a vertical

plane perpendicular to the direction of wave advance is

1 t%*r*

m&*d*

η

(II-1-59)

which, upon integration, gives

(II-1-60)

where P is frequently called *wave power*, and the variable *n *has been defined earlier in Equation II-1-50.

(e) If a vertical plane is taken other than perpendicular to the direction of wave advance, = E Cg sin

P

θ, where θ is the angle between the plane across which the energy is being transmitted and the direction of

wave advance.

(f) For deep and shallow water, Equation II-1-60 becomes

1

(II-1-61)

2 0* o*

(II-1-62)

(g) An energy balance for a region through which waves are passing will reveal that, for steady state, the

amount of energy entering the region will equal the amount leaving the region provided no energy is added

or removed. Therefore, when the waves are moving so that their crests are parallel to the bottom contours

(II-1-63)

or since

II-1-28

Water Wave Mechanics

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