Page 224 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Ocean Modelling for Resource Characterization Chapter | 8 213

such models could be useful for wave resource characterization, they are not
generally used due to very high computational cost; therefore, the remainder of
this section concentrates on the more widely applied phase-averaged models.

8.4.1 Phase-Averaged Wave Models

As discussed in Chapter 5, a wave field can be considered as a wave spectrum,
which can be represented by a large number of regular sinusoidal wave
components. Wave models work by predicting each of these independent wave
components individually, and how they vary in space and time, through the
energy balance equation, which has the form (e.g. [14])
dE(σ, θ; x, y, t)
= S(σ, θ; x, y, t) (8.38)
dt
where E is the spectral energy density, σ is the angular wave frequency, θ is
wave direction, x and y are the horizontal dimensions, t is time, and S are the
source terms, comprising generation, wave-wave interaction, and dissipation.
Energy density E is not preserved in the presence of ambient currents, and
so wave models tend to solve the action density (N) balance equation, where
N = E/σ. In spherical coordinates, this can be written as [15]
∂N ∂c λ N ∂c φ N ∂c σ N ∂c θ N S tot
+ + + + = (8.39)
∂t ∂λ ∂φ ∂σ ∂θ σ
where c λ and c φ are the propagation velocities in the zonal (λ) and meridional
(φ) directions, and c σ and c θ are the propagation velocities in spectral space.
The numerical solution of Eq. (8.39), without any prior assumption about
the spectral shape, is what is known as a third-generation wave model [16], and
is the most popular type of wave model in use today for resource assessment,
including the models SWAN [15], WAM [16], and WAVEWATCH III [17].

8.4.2 Source Terms

Central to third-generation wave models is the calculation of the source terms
(RHS of Eq. 8.39), and the key processes are introduced briefly as follows.

Wind Input
There are two mechanisms that describe the transfer of wind energy and
momentum into the wave field. Small pressure fluctuations associated with
turbulence in the airflow above the water surface are sufficient to induce small
perturbations on the sea surface, and to support a subsequent linear growth as the
wavelets move in resonance with the pressure fluctuations [18]. This mechanism
is only significant early in the growth of waves on a relatively calm sea. When
the wavelets have grown to a sufficient size to start affecting the flow of air
above them, most of the development commences. The wind now pushes and
drags the waves with a vigour that depends on the size of the waves themselves,