THE IMPORTANCE OF LONG WAVE REFLECTIONS IN TIDAL MODELLING ON A CONTINENTAL SHELF

Fay Luxford, Peter K Stansby, Benedict D Rogers

Abstract


This paper investigates the tidal phase error found in a 2-D hydrodynamic model of the Southern Bight of the European continental shelf; an error also found in other models of the region. After identifying the predominant mechanisms controlling the tidal flow in the Southern Bight: bathymetry, bottom friction and coastline reflections, analysis of each mechanism is made. Sensitivity to bathymetry is tested, to bed friction using values based on physical bed properties and to coastline reflection of tidal waves by comparing standing/propagating wave analysis from model results with observations. It was found that using more physically realistic friction values improved the prediction of tidal amplitudes but had minimal effect on tidal phase and an unrealistic reduction in the bathymetry level would be required to correct the phase error. However analysis of tidal reflections revealed that the model under-predicts the amplitude of the reflected wave which may cause the erroneous phase pattern. It is proposed that the reflectiveness of the coastline has increased over time due to the cumulative effect of coastal engineering such as sea walls and barrages reducing energy dissipation. It is concluded that more attention needs to be given to the representation of coastlines in models; something which is currently neglected in model calibrations which focus on changing the bathymetry, bottom friction and boundary conditions to achieve the best model fit. It is suggested that the modelling of this process needs to be improved, especially when calculating long-term sediment transport from the hydrodynamic predictions where residual velocities are important and of small magnitude relative to velocity amplitudes.

Keywords


tidal modelling; reflections; phase error; Southern Bight

Full Text:

PDF

References


Bourban, S., Durand, N., Wilson, S., Cheeseman, S. 2012. Coastal shelf model of northern European waters to inform tidal power industry decisions, Proceedings of the XIXth TELEMAC-MASCARET User Conference, 143-150.

Brown, T. 1987. Kelvin wave reflection at an oscillating boundary with applications to the North Sea, Continental Shelf Research, 7, 351–365.

Cazenave, P.W. 2012. Past and present sediment transport of the north-west European continental shelf, Ph.D. University of Southampton, England.

Cea, L. and French, J.R. 2012. Bathymetric error estimation for the calibration and validation of estuarine hydrodynamic models, Estuarine, Coastal and Shelf Science, 100, 124-132.

Heemink, A.W., Mouthaan, E.E.A., Roest, M.R.T., Vollebregt, E.A.H., Robaczewska, K.B., Verlaan, M. 2002. Inverse 3D shallow water flow modelling of the continental shelf, Continental Shelf Research, 22, 465-484.

Hendershott, M., Speranza, A., 1971. Co-oscillating tides in long, narrow bays: the Taylor problem revisited, Deep-Sea Research, 18, 959–980.

Hollebrandse, F.A.P. 2005. Temporal development of the tidal range in the southern North Sea, M.Sc. Delft University of Technology, The Netherlands.

HR Wallingford 2002. Southern North Sea Sediment Transport Study Phase 2, Report number: EX 4526.

Jung, T.S. 2014. Effects of coastal development on sea level change in the western coast of Korea, Proceedings of the 34th International Conference on Coastal Engineering.

Lees, B.J. 1983. Observations of tidal and residual currents, Deutsche Hydeografishe Zeitschrift, 36, issue 1, 1-24.

Nicholls, R.J., Bradbury, A., Burningham, H., Dix, J., Ellis, M., French, J., Hall, J.W., Karunarathna, H.U., Lawn, J., Pan, S., Reeve, D.E., Rogers, B.D., Souza, A., Stansby, P.K., Sutherland, J., Tarrant, O., Walkden, M., Whitehouse, R. 2012. iCOASST – Integrating coastal sediment systems, Proceedings of the 33rd International Conference on Coastal Engineering, 1(33), sediment. 100.

Pelling, H.E., Green, J.A.M., Ward, S.L. 2013. Modelling tides and sea-level rise: To flood or not to flood, Ocean Modelling, 63, 21 -29.

Pingree, R.D., Griffiths, D.K. 1979. Sand transport paths around the British Isles resulting from M2 and M4 tidal interactions. Journal of the Marine Biological Association of the UK, 59, 497-513.

Pugh, D.T. and Vassie, J.M. 1976. Tide and surge propagation offshore in the Dowsing region of the North Sea, Deutsche Hydeografishe Zeitschrift, 29, 163-213.

Rienecker, M., Teubner, M. 1980. A note on frictional effects in Taylor’s problems, Journal of Marine Research, 38, 183–191.

Taylor, G. 1921. Tidal oscillations in gulfs and rectangular basins, Proceedings of the London Mathematical Society, 20, 148–181.

Thompson K.W. 1987. Time dependent boundary conditions for hyperbolic systems, Journal of Computational Physics, 68, 1-24.

Verboom, G.K., Ronde, J.G., Van Dijk, R.P. 1992. A fine grid tidal flow and storm surge model of the North Sea, Continental Shelf Research, 12, 2/3, 213-233.

Woodworth, P.L., Shaw, S.M., Blackman, D.L. 1991. Secular trends in mean tidal range around the British Isles and along the adjacent European coastline, Geophysical Journal International, 104, 593-609.




DOI: https://doi.org/10.9753/icce.v34.currents.27