Abstract Abrupt changes in water depth are known to lead to abnormal free-surface wave statistics. The present study considers whether this translates into abnormal loads on offshore infrastructure. A fully non-linear numerical model is used which is carefully validated against experiments. The wave kinematics from the numerical model are used as input to a simple wave loading model. We find enhanced overturning moments, an increase of approximately 20%, occur over a distance of a few wavelengths after an abrupt depth transition. We observe similar results for 1:1 and 1:3 slopes. This increase does not occur in linear simulations.
Abstract Tides pose significant operational and engineering challenges and are critical drivers of many natural processes. Accurate tidal predictions are important for modeling these phenomena. Conventionally, tidal prediction is carried out using harmonic analysis, the accuracy of which degrades when non-stationary and nontidal forcing are present. While Munk and Cartwright’s response method avoids the assumptions that give rise to this degradation, the difficulty of defining realistic interactions between inputs has inhibited automated applications. Here, we develop a non-parametric framework for tidal analysis and prediction of sea levels under compound forcing. The approach embeds a class of neural networks capable of representing any arbitrary Volterra series—the mathematical basis of the response method—within the classic method. The new ML Response Framework overcomes the automation challenges imposed by the original method and can directly infer high-order nonlinear interactions. This makes the inclusion of meteorological and other non-tidal forcing straightforward. Furthermore, we show that by accounting for this nonstationarity explicitly, a better astronomical tidal estimate is obtained. A method is devised to obtain physical insights from the learned model, illustrating how it can be used to study the interaction and modulation of astronomical tides by external forcing. By taking a nonparametric approach, our framework makes the study of phenomena that heretofore could not be accounted for straightforward. We provide several case studies, including the analysis and prediction of tide-surge interaction, riverine tides, and nuisance flooding. These applications, and more, can be replicated using only three lines of code with the open-source Python package (RTide).
Due to the growing proportion of wind energy in Great Britain's energy mix, prolonged periods of low wind power generation have become a significant challenge for decarbonising the electricity system. As such, characterising drought severity and duration is important for ensuring the reliability of the electricity system. Employing concepts derived from hydrology, an extreme value analysis was carried out on wind drought events in Great Britain based on 72 years of ERA5 reanalysis data. The application of pooling procedures was found to be beneficial in robustly identifying wind droughts in cases where the capacity factor is not constantly below an arbitrary threshold. The sequent peak algorithm pooling was found to have particular relevance for electricity systems where energy storage technologies are used to compensate for low wind power generation. The Pearson-III distribution was identified as a suitable model to represent extreme wind droughts, while the Lognormal and Generalised Pareto distributions are also viable alternatives. Sustained periods of low wind power generation with a duration of 14 days were estimated to have a return period of five years and the longest event on record of approximately 26 days is expected to occur once every 100 years. The investigation of these wind droughts from a hydrological perspective has thus shown that they may not be particularly rare occurrences.
The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave's directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90 ° or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80 ° to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.
<p>This work focuses on two different aspects of the effect of an abrupt depth transition on weakly nonlinear surface gravity waves: deterministic and stochastic. It is known that the kurtosis of waves can reach a maximum near the top of such abrupt depth transitions. The analysis is based on three different approaches: (1) a novel theoretical framework that allows for narrow-banded surface waves experiencing a step-type seabed, correct to the second order in wave steepness; (2) experimental observations; and (3) a numerical model based on a fully nonlinear potential flow solver. To reveal the fundamental physics, the evolution of a wave envelope that experiences an abrupt depth transition is examined in detail; (a) we show the release of free waves at second order in wave steepness both for the super-harmonic and sub-harmonic or &#8216;mean&#8217; terms; (b) a local wave height peak that occurs near the top of a depth transition &#8211; whose exact position depends on several nondimensional parameters &#8211; is revealed; (c) furthermore, we examine which parameters affect this peak. The novel physics has implications for wave statistics for long-crested irregular waves experiencing an abrupt depth transition. We show the connection of the second-order physics at work in the deterministic and stochastic cases: the peak of wave kurtosis and skewness occurs in the neighborhood of the deterministic wave peak in (b) and for the same parameters set composed of a seabed topography, water depths, primary wave frequency and steepness, and bandwidth.</p>
<p>We have performed numerical simulations of steep three-dimensional wave groups, formed by dispersive focusing, using the fully-nonlinear potential flow solver <em>OceanWave3D</em>. We find that third-order resonant interactions result in directional energy transfers to higher-wavenumber components, forming steep wave groups with augmented kinematics and a prolonged lifespan. If the wave group is initially narrow banded, <em>quasi-degenerate interactions</em> resembling the instability band of a regular wave train arise, characterised by unidirectional energy transfers and energy transfers along the resonance angle, &#177;35.26&#176;, of the Phillips &#8216;figure-of-eight&#8217; loop. Spectral broadening due to the quasi-degenerate interactions eventually facilitates <em>non-degenerate interactions</em>, which dominate the spectral evolution of the wave group after focus. The non-degenerate interactions manifest primarily as a high-wavenumber sidelobe, which forms at an angle of &#177;55&#176; to the spectral peak. We consider finite-depth effects in the range of deep to intermediate waters (5.592 &#8805; <em>k<sub>p</sub>d</em> &#8805; 1.363), based on the characteristic wavenumber (<em>k<sub>p</sub></em>) and the domain depth (<em>d</em>), and find that all forms of spectral evolution are suppressed by depth. However, the quasi-degenerate interactions exhibit a greater sensitivity to depth, suggesting suppression of the modulation instability by the return current, consistent with previous studies. We also observe sensitivity to depth for <em>k<sub>p</sub>d</em> values commonly considered "deep", indicating that the length scales of the wave group and return current may be better indicators of dimensionless depth than the length scale of any individual wave component. The non-degenerate interactions appear to be depth resilient with persistent evidence of a &#177;55&#176; spectral sidelobe at a depth of <em>k<sub>p</sub>d</em> =1.363. Although the quasi-degenerate interactions are significantly suppressed by depth, the interactions do not entirely disappear for <em>k<sub>p</sub>d</em> =1.363 and show signs of biasing towards oblique, rather than unidirectional, wave components at intermediate depths. The contraction of the wavenumber spectrum in the <em>k<sub>y</sub></em>-direction has also proved to be resilient to depth, suggesting that lateral expansion of the wave group and the "wall of water" effect of Gibbs & Taylor (2005) may persist at intermediate depths.</p>
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