Numerical tests are performed to investigate wave transformations of nonlinear nonbreaking regular waves with normal incidence to the shore in decreasing and increasing water depth. The wave height transformation (shoaling) of nonlinear waves can, just as for linear waves, be described by conservation of the mechanical energy flux. The numerical tests show that the mechanical energy flux for nonlinear waves on sloping foreshores is well described by stream function wave theory for horizontal foreshore. Thus, this theory can be used to estimate the shoaled wave height. Furthermore, the amplitude and the celerity of the wave components of nonlinear waves on mildly sloping foreshores can also be predicted with the stream function wave theory. The tests also show that waves propagating to deeper water (de-shoaling) on a very gentle foreshore with a slope of cot(β) = 1200 can be described in the same way as shoaling waves. For de-shoaling on steeper foreshores, free waves are released leading to waves that are not of constant form and thus cannot be modelled by the proposed approach.
Implementation of alternative energy supply solutions requires the broad involvement of local communities. Hence, smart energy solutions are primarily investigated on a local scale, resulting in integrated community energy systems (ICESs). Within this framework, the distributed generation can be optimally utilised, matching it with the local load via storage and demand response techniques. In this study, the boat demand flexibility in the Ballen marina on Samsø—a medium-sized Danish island—is analysed for improving the local grid operation. For this purpose, suitable electricity tariffs for the marina and sailors are developed based on the conducted demand analysis. The optimal scheduling of boats and battery energy storage system (BESS) is proposed, utilising mixed-integer linear programming. The marina’s grid-flexible operation is studied for three representative weeks—peak tourist season, late summer, and late autumn period—with the combinations of high/low load and photovoltaic (PV) generation. Several benefits of boat demand response have been identified, including cost savings for both the marina and sailors, along with a substantial increase in load factor. Furthermore, the proposed algorithm increases battery utilisation during summer, improving the marina’s cost efficiency. The cooperation of boat flexibility and BESS leads to improved grid operation of the marina, with profits for both involved parties. In the future, the marina’s demand flexibility could become an essential element of the local energy system, considering the possible increase in renewable generation capacity—in the form of PV units, wind turbines or wave energy
Driven by increased integration of renewable energy sources, the widespread decarbonization of power systems has led to energy price fluctuations that require greater adaptability and flexibility from grid users in order to maximize profits. Industrial loads equipped with flexible resources can optimize energy consumption rather than merely reacting to immediate events, thereby capitalizing on volatile energy prices. However, the absence of sufficient measured data in industrial processes limits the ability to fully harness this flexibility. To address this challenge, we present a black-box optimization model for optimizing the energy consumption of cooling systems in the aquaculture industry using Extreme Gradient Boosting (XGBoost) and Bayesian Optimization (BO). XGBoost is employed to establish a nonlinear relationship between cooling system power consumption and available measured data. Based on this model, Bayesian Optimization with the Lower Confidence Bound (LCB) acquisition function is used to determine the optimal discharge temperature of water into breeding pools, minimizing day-ahead electricity costs. The proposed approach is validated using real-world data from a case study at the Port of Hirtshals, Denmark based on measurements from 2023. Our findings illustrate that leveraging the inherent flexibility of industrial processes can yield financial benefits while providing valuable signals for grid operators to adjust consumption behaviors through appropriate price mechanisms. Furthermore, machine learning techniques prove effective in optimizing energy consumption for industries with limited measured data, delivering accurate and practical estimates.
In the present paper, the experimental data on wave run-up on slender monopiles from recently published small and large scale tests are reanalyzed using different methods for the wave analysis. The hypothesis is that the post processing has an impact on the results, due to limited depth and highly nonlinear waves in many of the tests. Thus, the identified maximum waves by a zero-down crossing analysis are highly influenced by the reflection analysis method as well as by bandpass filtering. The stagnation head theory with the run-up coefficient is adopted and new coefficients are presented. The hypothesis is verified, and the applied bandpass filter is identified as a large contributor to conservatism in previous studies, as the steep, nonlinear waves that produce the highest run-up can be heavily distorted by the bandpass filter.
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.
Integrated community energy systems are an emerging concept for increasing the self-sufficiency and efficiency of local multi-energy systems. This idea can be conceptualized for the smart island energy systems due to their geographical and socioeconomic context, providing several benefits through this transformation. In this study, the energy system of the Ballen marina—located on the medium-sized Danish island of Samsø— is investigated. Particular consideration is given to the integration of PV, BESS, and—in the future—flexible loads. For this purpose, the BESS is modelled, incorporating the battery degradation process. The possibilities to improve energy utilization and maximize self-consumption from the marina's PV units are identified and evaluated, demonstrating a substantial enhancement of the local system operation.
This paper investigates the influence of a crown wall on wave overtopping on rubble mound breakwaters. Existing data is used to modify the EurOtop overtopping formula updated by Eldrup et al. (2022) to cover the influence of the crown wall. The effect of raising the wall above the armor crest (elevated wall) or lowering the wall below the armor crest (lowered wall) is investigated. A crown wall at the armor crest level is considered as the reference case. By increasing the elevation of either the armor crest or the crown wall, overtopping is reduced and by lowering either of them, overtopping increases. The influence of the crown wall height, elevated or lowered compared to the armor crest, is not considered accurately in the present design guidelines and thus corrections are suggested. For an elevated wall, a modified crest width has been defined, to better describe the presence of the armor crest in front of the wall. For the lowered wall the effective freeboard might be taken as the average of the wall and armor freeboards. The improvement compared to existing methods is significant, especially for breakwaters with a large elevated wall. The proposed modifications to the EurOtop Manual increase the range of applicability with respect to the wall configuration.
The expansion of Carbon Capture, Utilization, and Storage (CCUS) highlights the growing need for carbon dioxide (CO2) pipeline transportation. While pure CO2 is non-corrosive, impurities such as H2O and NO2 create a corrosive environment that risks pipeline integrity. This study investigates how H2O and NO2 concentrations, along with temperature, influence corrosion under CO2 pipeline conditions. The investigation was performed in an autoclave setup emulating a linear velocity of 0.96 m/s at 100 bar and temperatures of 5 °C and 25 °C, testing X52 and GR70, and a more corrosion-resistant 9Cr alloy. The results indicated that the presence of NO2 elevated the corrosion rate compared to scenarios without. Low H2O concentration led to a corrosion rate of up to five times higher at 5 °C, compared to at 25 °C, in the presence of NO2. Low to moderate corrosion was observed for the carbon steels without NO2 and with 70 ppmv H2O at both temperatures. Reducing the H2O concentration below 70 ppmv and removing NO2, while SO2 and O2 are present, will only result in low to moderate corrosion in the carbon steel CO2 pipeline. The corrosion rate for X52 and GR70 was 0.065 mm/y and 0.016 mm/y higher or 5 and 3 times greater, respectively, at 5 °C compared to 25 °C. The study concludes that H2O should be maintained below 70 ppmv and NO2 should be eliminated to prevent severe corrosion. Emphasizing the importance of CO2 specification compliance and the need for further research into CO2 compositions that align with the specifications.
Physical model tests are often conducted during the design process of coastal structures. The wave climate in such tests often includes short-crested nonlinear waves. The structural response is related to the incident waves measured in front of the structure. Existing methods for separation of incident and reflected short-crested waves are based on linear wave theory. For analysis of nonlinear waves, the existing methods are limited to separation of nonlinear long-crested waves. For short-crested waves, the only options so far have been to use estimates without the structure in place. The present paper thus presents a novel method for directional analysis of nonlinear short-crested waves: Non-Linear Single-summation Oblique Reflection Separation (NL-SORS). The method is validated on numerical model data, as for such data, the target is well defined as simulations may be performed with fully absorbing boundaries. Second- and third-order wave theory is used to demonstrate that small errors on the celerity of nonlinear components in the mathematical model of the surface elevation can be obtained if a double narrow-banded directional spectrum is assumed, ie the primary frequency and the directional spreading function must be narrow banded. As the increasing nonlinearity of the waves often arise from waves shoaling on a sloping foreshore, the directional spreading of the waves will decrease due to refraction, and a broad directional spreading function will thus not be experienced in highly nonlinear conditions. The new NL-SORS method is shown to successfully decompose nonlinear short-crested wave fields and estimate the directional spectrum thereof.
When an offshore wind power plant is connected to the grid, there is a risk of amplification of certain harmonics and appearance resonances at the point of connection due to the interaction between the grid network and the wind power plant network. Hence, the plant developer is obliged to maintain the harmonic distortion at the point of common coupling within the planning level limits using harmonic compensation, which is usually done by passive filters. In this paper a novel active harmonic compensation technique using voltage feedback from a non-local bus has been proposed and analyzed. Its effectiveness has been demonstrated through real time simulations on a test system model.