University of Twente Student Theses


The Influence of Lateral Depth Variations on Tidal Dynamics in Semi-enclosed Basins

Boer, Wiebe P. (2009) The Influence of Lateral Depth Variations on Tidal Dynamics in Semi-enclosed Basins.

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Abstract:Understanding tidal dynamics is important for coastal safety, navigation and marine ecology. Many tidal basins around the world can be classified as semi-enclosed, i.e. bounded at three sides by coasts. Therefore, it is relevant to study tidal wave propagation in this type of basins. Taylor (1921) performed an idealized study on tidal wave propagation in a rectangular, rotating (due to the Earth’s rotation) semi-enclosed basin of uniform depth and derived fundamental wave solutions, i.e. Kelvin and Poincaré waves. His model has proven to be useful to obtain insight in the physical mechanisms underlying tidal wave propagation in semi-enclosed basins. In this study Taylor’s classical problem is extended to account for a basin geometry with basin-scale, lateral depth variations. In a straight infinite channel wave solutions (i.e. modified Kelvin and Poincaré modes) are found by means of a semi-analytical, hydrodynamic model allowing for depth variations in lateral direction. For small depth variations (compared to uniform depth) the properties of the modified wave modes remain close to those of the uniform depth solutions. However, for large depth variations the modified wave modes show considerably different behavior. It is found that the wave lengths of the modified Kelvin waves depend on the water depth near the coastal boundaries. The wave length increases with increasing depth near the coastal boundary along which the Kelvin wave propagates, whereas the wave length decreases with decreasing depth. Furthermore, it is found that the Kelvin waves obtain a cross-channel velocity component, which is radically different from the classical Kelvin wave solution. Depending on the type of lateral depth profile the (evanescent) Poincaré modes obtain a propagative and/or more evanescent character compared to the uniform depth solutions. Also the lateral amplitude structures of the free surface elevation (with respect to still water) and velocity components change considerably as a result of lateral depth variations, especially at locations where the water depth is relatively shallow. The solution to the Taylor problem allowing for lateral depth variations (i.e. a semi-enclosed basin of non-uniform depth) is written as a superposition of the modified wave modes in an infinite channel: an incoming Kelvin wave, a reflected Kelvin wave and a truncated sum of (reflected) Poincaré modes. A collocation technique is applied to satisfy the no-normal flow boundary condition at the basin’s closed end. In general, we find that for symmetrical depth profiles the elevation amphidromic points (EAPs) remain on the centre line of the basin (as for uniform depth), whereas for asymmetrical depth profiles they shift in lateral direction towards the deeper side of the basin on a straight line parallel to the longitudinal coast. In addition, the EAPs shift in longitudinal direction, due to altered Kelvin wave lengths. The displacements in longitudinal direction are generally much larger than the displacements in lateral direction. The current amphidromic points (CAPs) show similar shifts as the EAPs and remain located between two EAPs. As a result of the cross-channel velocity component of the modified Kelvin waves, the cross-channel velocity is not only present close to the basin’s closed end, but also farther away from this boundary. Finally, a practical case is studied by means of our hydrodynamic model: the Southern North Sea with and without large-scale sand extraction on the Netherlands Continental Shelf (NCS). Based on bathymetrical data a longitudinally averaged, lateral depth profile is determined for the Southern North Sea. It is found that adopting this realistic lateral depth profile for the Southern North Sea instead of assuming uniform depth leads to considerable changes in the tidal amplitudes and currents. Consequently, large-scale sand extraction is modeled by dividing the basin into two parts: one part with a sand extraction trench and one part without extraction trench The Influence of Lateral Depth Variations on Tidal Dynamics in Semi-enclosed Basins W.P. de Boer ii University of Twente in the lateral depth profile. It is concluded that large-scale sand extraction may considerably impact on the tidal system of the Southern North Sea. The tidal amplitudes and currents are not only locally affected, but also far away from the extraction area. These changes may have severe impacts on the morphodynamics and, consequently, coastal safety, ecology and cable and pipeline infrastructure. Based on the potential impacts of large-scale sand extraction on the tidal system of the Southern North Sea, it is recommended to account for tidal changes in present and future studies on this issue. For further research it is recommended to include bottom friction and (simple) longitudinal depth variations in our hydrodynamic model and study the consequent effects on the tidal system. Furthermore, it is recommended to compare these model results (i.e. with bottom friction included) with tide observations in actual (semi-enclosed) seas.
Item Type:Essay (Master)
Ministry of Transport, Public Works andWater Management Rijkswaterstaat Noordzee
Faculty:ET: Engineering Technology
Subject:56 civil engineering
Programme:Civil Engineering and Management MSc (60026)
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