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The results obtained give the time series of elevation of multiple-valued water surfaces, which can be obtained at any desired position over the horizontal domain of the images, at low cost and high computational efficiency.

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Measurements performed in two experimental study cases of shipping water on the deck of a fixed structure, due to single and multiple incident waves, were compared with measurements taken by conventional wave probe sensors and manual tracking to verify the performance of the methodology.

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This approach examines the stages of image processing and analysis through morphological operations, which have been implemented in plugins for free use in the open-source ImageJ software. This paper aims to propose a simplified and open-source image-based methodology to measure the spatio-temporal evolution of multiple-valued water surface elevations observed in two-dimensional hydrodynamic experiments, considering the problem of shipping water on a fixed structure as the topic of application.

However, conventional wave probe sensors do not provide measurements of these surfaces, which is required for appropriate model comparisons. Experimental research has shown that some phenomena can present multiple-valued water surfaces. Water elevation measurements in 2D hydrodynamic experiments are widely used for validating analytical and numerical models. The obtained results allowed to determine the minimum Kr values for each set of experiments and finding a useful non-dimensional relationship of Kr,(h-y1)/λ and Ir as a function of the dispersion parameter, kh. Both type of validations were successful so this model was used in order to determine Kr values at slopes that could not be physically reached by the extinction system. In parallel, an unsteady numerical model based on the Eulerian multiphase VOF was designed and validated according to the free surface displacement, ɳi, and the calculation of the Kr values. The variation of the reflection coefficient, Kr, was studied at several depths (h of 0.3, 0.4, and 0.5), periods (0.636 < T < 1.526), wave heights (0.010 < H < 0.064), slopes (3 < α < 17) and vertical end positions of the extinction system (y1 and y2 defined by y1 and α ), covering the linear and non-linear regions of the “Le Méhauté” chart. Twenty one type of waves were generated in the laboratory using a piston-type wave maker. In this work the phenomenon of the wave reflection has been studied using a self-developed passive extinction system. Finally, the model showed that a porosity of n=0.6 and the porous layer thickness η=36mm reduced the peak pressure the most. The evaluated model is then used to determine the hydrodynamic conditions on the landward slope, which showed that the pressure was the most influential hydrodynamic condition at the time of failure. The numerical model is evaluated by using these resistance coefficients in other time series of the physical tests. The numerical model is calibrated based on resistance coefficients as introduced earlier in the literature, which showed that the resistance coefficients of α=500 and β=2.0 performed best for the peak flow velocities and the peak pressures. Using the porousWaveFoam solver, a porous layer on the crest and landward slope is implemented, where the flow resistance of this porous layer largely depends on the resistance coefficients α and β. The geometry and wave conditions from the physical test at the Deltares Delta flume are implemented in an OpenFOAM® numerical model.

Therefore, the goal of this study is to determine the hydrodynamic conditions at the dike cover caused by the wave run-up on the seaward slope and by the overtopping flow over the crest and landward slope. However, such experiments are expensive and accurate measurements are difficult due to highly turbulent conditions. The performance of these blocks is assessed in physical tests, which provides insights into the stability of the blocks. The blocks are permeable, which reduces the flow velocity and the pressures along the landward slope. Innovative block revetments such as Grassblocks protect the subsoil of the dike against erosion. Wave overtopping can cause erosion on the landward slope due to high flow velocities and turbulence that cause high stresses on the cover.

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