Page 311 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

296 Fundamentals of Ocean Renewable Energy

some regions [57]. Using simple mathematics, it can easily be shown that the
nature of tidal asymmetry is related to the phase difference between semidiurnal
and quarterdiurnal tidal constituents. Further, Speer et al. [58] showed that
(10.10)
2φ M 2 − φ M 4 ≈ φ M 2 + φ S 2 − φ MS 4 ≈ φ M 2 + φ N 2 − φ MN 4
It is generally the phase relationship between the principal semidiurnal tidal
current (M 2 ) and its first harmonic (M 4 ) that dominates tidal asymmetry [59,60].
Although the combination of M 2 and M 4 tidal currents in Fig. 10.12A results in
a distorted tide (Fig. 10.12B), the flood and ebb tides are equal in magnitude,
as is the net power (a function of velocity cubed) generated during the flood
and ebb phases of the tidal cycle. By combining M 2 and M 4 tidal currents as
in Fig. 10.12C, however, the flood tide is stronger than the ebb (Fig. 10.12D).
3
Although there is no net residual flow, the integrated cube of the velocity (U )
is greater during the flood phase of the tide. Hence, there will be a strong bias
of power production in favour of the flood phase of the tidal cycle. In the case
where the flood and ebb currents are equal
+ 90 degrees (10.11)
2φ M 2 = φ M 4
and where there is a maximum asymmetry
(10.12)
2φ M 2 = φ M 4
are the phases (in degrees) of the M 2 and M 4 tidal currents,
where φ M 2 and φ M 4
respectively. Hence, tidal asymmetry can be quantified by
(10.13)
2φ M 2 − φ M 4
Calculations of peak bed shear stress due to M 2 and M 4 tidal interactions can
be used to infer sediment transport pathways (e.g. Fig. 10.13). Regions where
bed shear stress vectors diverge are known as bed load partings, for example,
the region in the middle of the Irish Sea (between Ireland and Wales) and in the
English Channel (between England and France).
Morphological evolution can be simulated by application of the Exner
equation

∂z 1
∂q x ∂q y
=− + (10.14)
∂t 1 − p ∂x ∂y
where z is the change in bed level, p is the bed porosity, and q i is the transport
of sediment in the i direction. Therefore, in regions where there is a divergence
in sediment transport (i.e. a bed load parting), z will reduce. This will occur in a
region of tidal symmetry, since a maximum in bed-level change is associated
with zero residual sediment transport (Fig. 10.14). By contrast, in the case
of maximum residual sediment transport (either flood or ebb dominant), zero
bed-level change results. Neill et al. [35] examined the contrasting impact on
large-scale sediment transport and morphodynamics for a tidal stream array
located in regions of (a) tidal symmetry (either bed load parting or convergence),