Page 241 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

230 Fundamentals of Ocean Renewable Energy

forced with the two principal semidiurnal tidal constituents, M 2 and S 2 , these
represent peak spring tidal currents. The peak velocity vectors also provide a
qualitative overview of the tidal asymmetry [32], and the tidal flow appears to
be largely ebb-dominant (peak currents directed northwest) in Westray Firth,
7
and flood-dominant (peak currents directed southeast) in Stronsay Firth. Where
these two Firths join (i.e. in the vicinity of the Fall of Warness), the circulation is
further complicated by the presence of strong residual eddies with length scales
of around 4–5 km [33]. However, the tidal currents in this region appear to be
more symmetrical, and divergence of the peak velocity vectors indicates that
this is a bed-load parting zone [32]. The bathymetric/topographic restriction of
the Fall of Warness impedes the flow along the channel, which is driven by the
tidal pressure gradient. This impedance results in an acceleration of the flow
downstream of the restriction. This leads to a divergence of the residual flow
centred on the Fall of Warness, which is further complicated by variability in
bathymetry and geometry along and across the channel (Fig. 8.25).
The advantage of a 3D tidal model, compared with a depth-averaged 2D
model, is that the vertical distribution of variables in the water column is
calculated directly, rather than parameterized. Here, we show detailed results
for velocity and turbulence properties for all depths in the water column at three
locations which exhibit varying degrees of asymmetry: site 2 (ebb-dominant),
site 9 (symmetrical), and site 21 (flood-dominant) (Fig. 8.23).
Velocity time series for the three selected locations are plotted in Fig. 8.26.
Above the boundary layer, the asymmetry for sites 2 and 21 is evident at
all depths in the water column, and is more pronounced during spring tides.
Therefore, for all practical scenarios of energy extraction, that is device hub
placed at some height in the water column that is above the near-bed boundary
layer, strong velocity asymmetry will translate into an even stronger asymmetry
in power output (because power is related to velocity cubed). Such asymmetry in
the flow field is clearly undesirable from an electricity generation perspective,
and so symmetrical sites (such as site 9) are more attractive for commercial
development.
Turbulent kinetic energy (k) per unit mass is defined as
1
2
2
2
k = (u + v + w ) (8.46)
2
k is plotted at three contrasting locations (Fig. 8.27). The corresponding plot for
the rate of dissipation (
)of k is shown in Fig. 8.28, defined as
dk
∼ (8.47)
= P −
dt

7. Because the tidal wave propagates eastwards across the north of Scotland (Fig. 8.24), the tidal
currents are directed approximately southeastward along these Firths during the flood phase of
the tide.