Tides in the NE Atlantic and consequences for tidal energy on the NW European
Shelf
Judith Wolf
Abstract
There is a resurgence of interest in tidal modelling for the identification of the tidal
energy resource, which is a significant and predictable source of marine renewable energy.
The UK has a significant part of the world tidal energy resource, and half of the estimated
European resource, with the second largest tidal range in the world occurring in the Severn
Estuary, due to a quarter-wave resonance of the main lunar semi-diurnal M2 tide across the
Celtic Sea to the shelf edge. We see a large flux of energy across the shelf edge in the SW
Approaches into the Celtic Sea. Thus it is of interest to understand the origin of these large
tidal energy resources. The barotropic ocean tide propagates around ocean basins as Kelvin
and Poincare wave: in the North Atlantic the M2 tide is near to the normal mode frequency of
12.8h (Platzman, 1975). The ocean tide induces a co-oscillating tidal response on the shallow
continental shelves as a response to the rise and fall of the water at the shelf edge - in order to
maintain the energy flux, the tidal wave is amplified as it moves into shallow water and slows
down (with phase speed = √𝑔ℎ, where g is the gravitational acceleration and h is water
depth), but the detail of the response at the shelf edge can be variable, depending on latitude
and frequency.
Due to density stratification there are also internal tides induced on the pycnocline which
can be important in internal mixing and dissipation (see Green, 2010; Nycander, 2005; Zaron
and Egbert, 2006). The internal tides are large and non-linear in the Celtic Sea which makes
this area rather unique and understanding the tidal energy budget more challenging. Flather
(1976) showed an M2 budget for the UK shelf based on a 2D model without considering
stratification. His solution led to the important development of the Flather radiation boundary
condition allowing iteration of the elevation and current comnponents of the tide at the shelf
edge boundary.
An accurate and well-used solution for global ocean tides is provided by the Oregon State
University (OSU) Tidal Inversion Software, derived from satellite altimetry, which in recent
years has revolutionised the knowledge of the global tides (Egbert and Erofeeva, 2002).
These can be used to extract boundary conditions to force regional tidal models, where the
boundary is taken into the NE Atlantic Ocean to avoid effects on the internal solution due to
the model boundary. Key results are tidal elevation and currents from a validated tidal model
from which energy flux and dissipation can be easily calculated. Which model should be used
for these calculations? In recent years the ADCIRC (2D, unstructured) and POLCOMS
AMM (3D, structured) models are available, as well as the Flather CS3X 2D structured grid
model. Some applications of these results to the calculation of tidal energy flux across the
NW European shelf edge and tidal energy dissipation are discussed, with reference to the
work of John Huthnance on coastal trapped waves (starting from Huthnance, 1975), internal
tides and shelf edge processes.