Page 121 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

112 Fundamentals of Ocean Renewable Energy

FIG. 5.2 Simplifying the dispersion equation (5.13) in deep and shallow water conditions.

g
2 2
C = ⇒ σ = gk: deep water waves (5.14)
k
g
2 2
C = (kd) ⇒ C = gd: shallow water waves (5.15)
k
Note that the shallow water wave approximation is nondispersive, because it
does not relate the wave celerity to wave length.

5.1.3 Wave Energy and Wave Power

Assume that a regular wave, with a wave period T and wave height H,is
propagating in constant water depth d. Power (the rate of energy conversion) is
the product of velocity and force. In linear wave theory, the force is generated by
pressure (i.e. F = pA). Referring to Table 5.1, pressure depends on z. Therefore,
wave power can be evaluated by multiplying the pressure and velocity and
integrating over depth; the wave power, or more specifically the average energy
flux per unit width over a wave period, is given by
T η
1 2 1 2kh

P = p D udzdt = ρgH C 1 + = EC g = cst
0 −d 8 2 sinh 2kh
(5.16)
1 2kh

C g = C 1 + (5.17)
2 sinh 2kh