We show that significant water wave amplification is obtained in a water resonator consisting of two spatially separated patches of small-amplitude sinusoidal corrugations on an otherwise flat seabed. The corrugations reflect the incident waves according to the so-called Bragg reflection mechanism, and the distance between the two sets controls whether the trapped reflected waves experience constructive or destructive interference within the resonator. The resulting amplification or suppression is enhanced with increasing number of ripples and is most effective for specific resonator lengths and at the Bragg frequency, which is determined by the corrugation period. Our analysis draws on the analogous mechanism that occurs between two partially reflecting mirrors in optics, a phenomenon named after its discoverers Charles Fabry and Alfred Perot.
In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. For seakeeping and stationkeeping model tests, we normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. The purpose of the work presented in the paper is to provide a semi-empirical nonlinear wave crest distribution of three-hour duration for practical use, i.e. as an acceptance criterion for wave calibration tests. The semi-empirical formulas proposed in this paper were developed through regression analysis of a large number of fully nonlinear wave crest distributions. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distribution. The wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical formulas, comparisons among crest distributions from wave calibration tests, numerical simulations and the semi-empirical formulas are presented in this paper.
Rogue waves or freak waves are very large amplitude waves compare to the ambient waves in a given sea state. There are very few recording of such waves and therefore, despite years of research, very little is known about their properties. Here we invoke a statistical approach to find out about the typical shape of these giant waves. We consider different sea states and unidirectional vs crossing seas and study how each environment affects the morphology of oceanic rogue waves.
Oceanic rogue waves are short-lived very large amplitude waves (a giant crest typically followed or preceded by a deep trough) that appear and disappear suddenly in the ocean causing damage to ships and offshore structures. Assuming that the state of the ocean at the present time is perfectly known, then the upcoming rogue waves can be predicted via numerically solving the equations that govern the evolution of the waves. State of the art radar technology can now provide accurate wave height measurements over large spatial domains and when combined with advanced wave-field reconstruction techniques together render deterministic details of the current state of the ocean (i.e. surface elevation and velocity field) at any given moment of time with a very high accuracy. The ocean density is, however, stratified (mainly due to the salinity and temperature differences). This density stratification, with today’s technology, is very difficult to measure accurately. As a result, in most predictive schemes these density variations are neglected. While the overall effect of the stratification on the average state of the ocean may not be significant, here we show that these density variations can strongly affect the prediction of oceanic rogue wave. Specifically, we consider a broadband oceanic spectrum in a two-layer density stratified fluid and study, via extensive statistical analysis, the effects of the strength of the stratification (difference between densities) and the depth of the thermocline on the prediction of upcoming rogue waves.
Here, we show that location of an upcoming rogue wave can be inferred, well in advance, from spatial distribution of energy flux across the ocean surface. We use a statistical approach, and by investigating hundreds of numerical rogue wave realizations in weakly nonlinear wave fields establish a quantitative metric via which predictions can be made. Direct simulations are performed by a higher-order spectral method (HOS), and JONSWAP distribution is used to initialize the wave field. The presented metric may establish a readily achievable measure to identify turbulent locations within a sea, through which timely preventive measures can be taken to minimize damages to lives and properties.
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