Boundary Conditions for a Seiche model

Abstract

The Storm Surge Barrier in the New Waterway was built to protect the city and port of Rotterdam and the area of the lower Rhine against flooding during extreme conditions. This construction, consisting of two gigantic arc shaped barriers, is to be pivoted into the New Waterway and then lowered in case of an impeding emergency. The arc shape makes it a very efficient design against forces from the seaside, but if the level on the riverside surpasses the level on the seaside, a negative force will be exerted on the construction. Seiches contribute to this effect. The barrier only has a relatively small capacity to withstand a negative head difference. To accurately predict the maximum expected head difference a numerical model that handles seiches correctly is needed. In this thesis, the boundary conditions for such a numerical model are investigated. The program currently used to calculate the effects of seiches, RAS/FLOW predicts a head difference that exceeds the design specifications of the construction. However, the calculations done with Rasflow are not accurate with respect to the amplification of the seiches. The amplitude is overestimated significantly due to the use of an inaccurate boundary condition at the sea boundary of the model. The boundary condition at the channel entrance is very complex. Mendez Lorenzo (1997) studied a new boundary condition: the epsilon boundary. This boundary is a combination of a water level and a Riemann invariant with a factor epsilon. In the analytical case the results of this boundary condition match the analytical solution exactly. The step from the analytical boundary condition to a numerical boundary condition involves a set of derivations and simplifications that fixate the value for Epsilon. With a fixed value for epsilon, the amplification function obtained will only match one of the peaks in the spectrum: the peak for which the value of epsilon is set. In this thesis the addition of non-linear terms to the epsilon model can be found. The non-linear terms did not resolve the problem of the fixed epsilon. To reduce the complexity of the boundary condition a different approach to the problem is taken, namely a combination of a one and two-dimensional approach. In this model a two-dimensional sea area is attached to the onedimensional channel. Thus moving the complex boundary condition at the channel entrance to a simpler boundary condition on the open sea boundary. With this model it is possible to correctly model the amplification for more than one peak. The results obtained with this model are satisfactory and are recommended for a future implementation.