The stability formula for rock slopes under wave attack was revised in Van der Meer (2021), replacing the mean period Tm with the spectral period Tm-1.0. This rewritten formula closely resembles the Modified Van der Meer formula as in the Rock Manual (2007), with differences primarily in coefficients and the use of H2% in the Rock Manual and H1/3 in Van der Meer (2021).
The wave characteristics change significantly in shallow water due to nonlinearities and wave breaking. The result is a significant change in the wave height and period, especially when severe breaking occurs and infragravity waves become significant or even dominate the spectrum. This may lead to very large breaker parameters. At a certain point, existing stability formulas may thus become inaccurate, both the original and the Modified formula for shallow water. The primary objective of this paper is to identify when and where shallow water stability results deviate from established formulas and how these deviations can be described.
The analysis involves an in-depth examination of datasets from Van Gent et al. (2003), Eldrup (2019), and other relevant data to increase the understanding of waves in shallow water and how they affect rock slope stability.
The use of H2% in the Modified Van der Meer formula gives some difficulties as no reliable prediction method is available for that parameter when the relative depth is small, h/Hm0 depth < 1.5. The Van der Meer (2021) formula applies the significant wave height, and it may be chosen as either Hm0 or H1/3. These two parameters are almost identical in deep water for which the formula was derived, but significant differences may occur in shallow water. The application of the Van der Meer formula in shallow water indicates a preference for the use of Hm0 as it describes nonlinear waves better. The main conclusion is that the Van der Meer (2021) formula seems valid much further into the shallow water region than what the Rock Manual (2007) recommends and at least to relative water depths of h/Hm0 deep > 1.5. For shallow water with h/Hm0 depth < 1.5 no systematic trend with the energy period is observed anymore and constant combined stability numbers are given for guidance in preliminary design.
The influence of directional spreading of waves is significant for wave-induced loads, wave breaking and nonlinearity of the waves. For physical model testing performed at test facilities such as the Ocean and Coastal Engineering Laboratory at Aalborg University, it is crucial to validate if the test conditions match the target sea states by measurement and analysis of the generated directional wave field. Most of the existing methods assume a double summation sea state to be present which is valid in the prototype. However, waves in the laboratory are usually generated by single summation. The current paper presents a method to analyze short-crested waves generated by the single summation method. Compared to similar methods oblique reflections are considered instead of only in-line reflections. The results show that the method successfully decomposes the incident and reflected wave fields in the time domain. Thus, for example the incident wave height distribution may be obtained. The sensitivity of the new method to additional reflective directions, noise, calibration errors and positional errors of the wave gauges was found small.
For design validation of offshore structures and conceptualisation of wave energy converters, physical model testing performed in wave basin laboratories is often applied. In such cases, knowledge about the wave conditions is of great significance. For validation of the wave condition in such tests, different methods for estimation of the directional wave spectra may be applied. However, different assumptions are imposed in the methods and deviations here from providing uncertainties in the results. The following paper quantifies the influence of nonlinear effects on the accuracy of the estimated directional wave spectra. This is done by analysis of idealised, synthetically generated waves based on second order wave theory and secondly with simplified amplitude dispersion included. The present analyzes show that the uncertainties of the directional wave spectra are proportional to the level of nonlinearity present in the wave field.
A generic point-absorbing wave energy converter is modeled in CFD as a vertical cylinder, moored with a single catenary chain that is fully coupled through a dynamic mooring code. The method of choice is very complete and takes much of the non-linearities in the highly coupled system of the moored body into account. The paper presents numerical results compared with experimental data for surge, heave and pitch motion in both decay tests and regular waves. Further, the wave motion response of the cylinder is computed using both a viscous and a non-viscous formulation as a first attempt to quantify viscous effects. Results show a good match between numerical and experimental results in heave, while the surge and pitch motion are more difficult to reproduce. The mooring load cycle appearance compares well with the experiments in shape but gives higher peak values. Although made at low Keulegan-Carpenter numbers, the simulations show vortical structures due to the heave motion, and the resulting motions are clearly affected by the inclusion or exclusion of viscosity. More test-cases and detailed experimental results are needed for further quantification of the viscous impact on floating point absorbers.