Page 225 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

214 Fundamentals of Ocean Renewable Energy

in a phase known as exponential wave growth. Wave growth can therefore be
described as a sum of linear (A) and exponential (BE) growth terms

S in (σ, θ) = A + BE(σ, θ) (8.40)
A drag coefficient is used to transform the wind speed (usually defined at 10 m
elevation) into a friction velocity U * , after which a linear expression can be used
to calculate A (e.g. [19]), and an exponential expression to calculate B (e.g. [20]).

Dissipation
In deep water, energy is dissipated from the wave field mainly through wave
breaking (whitecapping). In shallow water, it may also be dissipated through
interaction with the sea bed (bottom friction) and through depth-induced wave
breaking.
Whitecapping is active in wind-driven seas, and is the least understood of
all processes affecting waves [14]. A complicating factor is that there is no
generally accepted precise definition of breaking and, as you can imagine,
quantitative observations of deep water wave breaking are very difficult to
achieve. However, the whitecapping source term tends to be based on the theory
of Hasselmann [21], in which each white-cap acts as a pressure pulse on the sea
surface, just downwind of the wave crest.
In water of finite depth, wave energy is dissipated due to interaction with
the sea bed, and this tends to be dominated by bottom friction [22]. This can be
expressed as [23]
σ 2
S b =−C b 2 E(σ, θ) (8.41)
2
g sinh kd
where C b is a bottom friction coefficient.
As waves propagate from deep to shallow water, wave shoaling leads to an
increase in wave height. Waves tend to steepen at the front and to become more
gently sloping at the back, and at some point the waves will break. There are
various definitions of wave breaking; for example, breaking occurs when the
particle velocities at the crest exceed the phase speed, or when the free-surface
becomes vertical. Depth-induced wave breaking is included as a source term in
third-generation wave models.

Nonlinear Wave-Wave Interactions
Nonlinear wave-wave interactions redistribute wave energy over the spectrum,
due to an exchange of energy resulting from resonant sets of wave components.
There are two processes that are important for the inclusion of nonlinear wave-
wave interactions in wave models: four-wave interactions in deep and interme-
diate waters (known as quadruplets) and three-wave interactions in shallow
water (triads). A good explanation of the principal of nonlinear wave-wave
interactions is provided by Holthuijsen [14]. Two wave paddles, generating