Editorial

4 pages, 203 KiB

Open AccessEditorial

Selected Papers from the Future Paths and Needs in Wave Modelling Workshop

by Carl Trygve Stansberg and José Miguel Rodrigues

J. Mar. Sci. Eng. 2021, 9(4), 368; https://doi.org/10.3390/jmse9040368 - 30 Mar 2021

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As an outcome of the International Workshop “Future needs and challenges in wave modelling”, held by SINTEF in Trondheim, Norway, 21–22 October 2019, this Special Issue includes 10 full Journal scientific papers [...] Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

Research

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73 pages, 23934 KiB

Open AccessArticle

Nonlinear Fourier Analysis: Rogue Waves in Numerical Modeling and Data Analysis

by Alfred R. Osborne

J. Mar. Sci. Eng. 2020, 8(12), 1005; https://doi.org/10.3390/jmse8121005 - 09 Dec 2020

Cited by 6 | Viewed by 2935

Abstract

Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this [...] Read more.

Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this analysis. We demonstrate that small-time asymptotic spectral solutions of the 2+1 NLS equation can be constructed as the nonlinear superposition of many 1+1 NLS equations, each corresponding to a particular radial direction in the directional spectrum of the waves. The radial 1+1 NLS equations interact nonlinearly with one another. We determine practical asymptotic spectral solutions of the 2+1 NLS equation that are formed from the ratio of two phase-lagged Riemann theta functions: Surprisingly this construction can be written in terms of generalizations of periodic Fourier series called (1) quasiperiodic Fourier (QPF) series and (2) almost periodic Fourier (APF) series (with appropriate limits in space and time). To simplify the discourse with regard to QPF and APF Fourier series, we call them NLF series herein. The NLF series are the solutions or approximate solutions of the nonlinear dynamics of water waves. These series are indistinguishable in many ways from the linear superposition of sine waves introduced theoretically by Paley and Weiner, and exploited experimentally and theoretically by Barber and Longuet-Higgins assuming random phases. Generally speaking NLF series do not have random phases, but instead employ phase locking. We construct the asymptotic NLF series spectral solutions of 2+1 NLS as a linear superposition of sine waves, with particular amplitudes, frequencies and phases. Because of the phase locking the NLF basis functions consist not only of sine waves, but also of Stokes waves, breather trains, and superbreathers, all of which undergo complex pair-wise nonlinear interactions. Breather trains are known to be associated with rogue waves in solutions of nonlinear wave equations. It is remarkable that complex nonlinear dynamics can be represented as a generalized, linear superposition of sine waves. NLF series that solve nonlinear wave equations offer a significant advantage over traditional periodic Fourier series. We show how NLFA can be applied to numerically model nonlinear wave motions and to analyze experimentally measured wave data. Applications to the analysis of SINTEF wave tank data, measurements from Currituck Sound, North Carolina and to shipboard radar data taken by the U. S. Navy are discussed. The ubiquitous presence of coherent breather packets in many data sets, as analyzed by NLFA methods, has recently led to the discovery of breather turbulence in the ocean: In this case, nonlinear Fourier components occur as strongly interacting, phase locked, densely packed breather modes, in contrast to the previously held incorrect belief that ocean waves are weakly interacting sine waves. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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19 pages, 10471 KiB

Open AccessArticle

Numerical Study on Regular Wave Shoaling, De-Shoaling and Decomposition of Free/Bound Waves on Gentle and Steep Foreshores

by Mads Røge Eldrup and Thomas Lykke Andersen

J. Mar. Sci. Eng. 2020, 8(5), 334; https://doi.org/10.3390/jmse8050334 - 09 May 2020

Cited by 10 | Viewed by 2803

Abstract

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 [...] Read more.

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. Full article

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24 pages, 6186 KiB

Open AccessFeature PaperArticle

Wave Front Steepness and Influence on Horizontal Deck Impact Loads

by Carl Trygve Stansberg

J. Mar. Sci. Eng. 2020, 8(5), 314; https://doi.org/10.3390/jmse8050314 - 29 Apr 2020

Cited by 11 | Viewed by 2888

Abstract

In design storm sea states, wave-in-deck forces need to be analysed for fixed and floating offshore platforms. Due to the complex physics of wave impact phenomena, numerical analyses should be complemented by model test data. With a large statistical variability, such experiments usually [...] Read more.

In design storm sea states, wave-in-deck forces need to be analysed for fixed and floating offshore platforms. Due to the complex physics of wave impact phenomena, numerical analyses should be complemented by model test data. With a large statistical variability, such experiments usually involve running many 3-h storm realisations. Efforts are being done to establish efficient procedures and still obtain improved statistical accuracy, by means of an initial simplified screening based on parameters derived from the incident wave record only. Here, we investigate the vertical rise velocity of the incident wave elevation at a fixed point in space, which indirectly measures both the local slope and the near-surface orbital velocity. A derived simple deck slamming model is also suggested, to support the check of the physical basis of the approach. Correlation against data from a GBS wave-in-deck model test is used for checking this model. The results show that, although there is a significant random scatter in the measured impact forces, especially in the local slamming forces but also in the global forces, there is a correlation to the rise velocity. Comparisons to the simple load model also show promising results when seen on background of the complex physics and random scatter of the impact problem. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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15 pages, 6288 KiB

Open AccessArticle

Challenges in Description of Nonlinear Waves Due to Sampling Variability

by Elzbieta M. Bitner-Gregersen, Odin Gramstad, Anne Karin Magnusson and Mika Malila

J. Mar. Sci. Eng. 2020, 8(4), 279; https://doi.org/10.3390/jmse8040279 - 13 Apr 2020

Cited by 11 | Viewed by 2476

Abstract

Wave description is affected by several uncertainties, with sampling variability due to limited number of observations being one of them. Ideally, temporal/spatial wave registrations should be as large as possible to eliminate this uncertainty. This is difficult to reach in nature, where stationarity [...] Read more.

Wave description is affected by several uncertainties, with sampling variability due to limited number of observations being one of them. Ideally, temporal/spatial wave registrations should be as large as possible to eliminate this uncertainty. This is difficult to reach in nature, where stationarity of sea states is an issue, but it can in principle be obtained in laboratory tests and numerical simulations, where initial wave conditions can be kept constant and intrinsic variability can be accounted for by changing random seeds for each run. Using linear, second-order, and third-order unidirectional numerical simulations, we compare temporal and spatial statistics of selected wave parameters and show how sampling variability affects their estimators. The JONSWAP spectrum with gamma peakedness parameters γ = 1, 3.3, and 6 is used in the analysis. The third-order wave data are simulated by a numerical solver based on the higher-order spectral method which includes the leading-order nonlinear dynamical effects. Field data support the analysis. We demonstrate that the nonlinear wave field including dynamical effects is more sensitive to sampling variability than the second-order and linear ones. Furthermore, we show that the mean values of temporal and spatial wave parameters can be equal if the number of simulations is sufficiently large. Consequences for design work are discussed. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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15 pages, 2888 KiB

Open AccessArticle

Wind–Wave Modeling: Where We Are, Where to Go

by Luigi Cavaleri, Francesco Barbariol and Alvise Benetazzo

J. Mar. Sci. Eng. 2020, 8(4), 260; https://doi.org/10.3390/jmse8040260 - 07 Apr 2020

Cited by 35 | Viewed by 4281

Abstract

We perform a critical analysis of the present approach in wave modeling and of the related results. While acknowledging the good quality of the best present forecasts, we point out the limitations that appear when we focus on the corresponding spectra. Apart from [...] Read more.

We perform a critical analysis of the present approach in wave modeling and of the related results. While acknowledging the good quality of the best present forecasts, we point out the limitations that appear when we focus on the corresponding spectra. Apart from the meteorological input, these are traced back to the spectral approach at the base of the present operational models, and the consequent approximations involved in properly modeling the various physical processes at work. Future alternatives are discussed. We then focus our attention on how, given the situation, to deal today with the estimate of the maximum wave heights, both in the long term and for a specific situation. For this, and within the above limits, a more precise evaluation of the wave spectrum is shown to be a mandatory condition. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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16 pages, 6721 KiB

Open AccessArticle

Role of Nonlinear Four-Wave Interactions Source Term on the Spectral Shape

by Sonia Ponce de León and Alfred R. Osborne

J. Mar. Sci. Eng. 2020, 8(4), 251; https://doi.org/10.3390/jmse8040251 - 03 Apr 2020

Cited by 13 | Viewed by 2305

Abstract

The goal of this paper is to investigate the importance of the four-wave nonlinear interactions (SNL4) on the shape of the power spectrum of ocean waves. To this end, the following results are discussed: a number of authors have conducted modern experimental measurements [...] Read more.

The goal of this paper is to investigate the importance of the four-wave nonlinear interactions (SNL4) on the shape of the power spectrum of ocean waves. To this end, the following results are discussed: a number of authors have conducted modern experimental measurements of ocean waves over the past decades and found that the measured power spectrum has (a) a very high central peak (characterized by the parameter γ, developed in the 1970s in the JONSWAP program) and (b) enhanced high-frequency channels which lead to the phenomenon of “bimodality”, also a well-known phenomenon. We discuss how a numerical hindcast of the Draupner storm (1995) with the standard code WAVEWATCH-III with full Boltzmann interactions also reflects these previously experimentally determined spectral shapes. Our results suggest that the use of the full Boltzmann interactions (as opposed to the discrete interaction approximation often employed for forecasting/hindcasting) is important for obtaining this characteristic physical spectral shape of the power spectrum. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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20 pages, 1539 KiB

Open AccessArticle

Assessing an Improved Bayesian Model for Directional Motion Based Wave Inference

by Jordi Mas-Soler, Antonio Souto-Iglesias and Alexandre N. Simos

J. Mar. Sci. Eng. 2020, 8(4), 231; https://doi.org/10.3390/jmse8040231 - 26 Mar 2020

Cited by 4 | Viewed by 1869

Abstract

An innovative Bayesian motion-based wave inference method is derived and assessed in this work. The evaluation of the accuracy of the proposed prior distribution has been carried out using the results obtained during a dedicated experimental campaign with a scale model an Oil [...] Read more.

An innovative Bayesian motion-based wave inference method is derived and assessed in this work. The evaluation of the accuracy of the proposed prior distribution has been carried out using the results obtained during a dedicated experimental campaign with a scale model an Oil and Gas (O&G) semisubmersible platform. As for the Bayesian statistical inference approaches, the features of the proposed novel prior distribution, as well as the hypotheses adopted, are discussed. It has been found that significant improvements can be obtained if the new approach is adopted to estimate the sea conditions from measured vessel motions. Finally, it is possible to highlight a substantial reduction of the computing time when the sea conditions are estimated by means of the improved Bayesian method, if compared with the conventional approaches for motion-based wave inference. Full article

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26 pages, 15324 KiB

Open AccessArticle

Linking Experimental and Numerical Wave Modelling

by Sanne van Essen, Jule Scharnke, Tim Bunnik, Bülent Düz, Henry Bandringa, Rink Hallmann and Joop Helder

J. Mar. Sci. Eng. 2020, 8(3), 198; https://doi.org/10.3390/jmse8030198 - 13 Mar 2020

Cited by 9 | Viewed by 2817

Abstract

Experimental or numerical analysis of the response of ships and other floating structures starts with correct environmental modelling. The capabilities of numerical tools are rapidly expanding, but presently the evaluation of extreme events in waves (such as slamming, green water, air-gap exceedance) still [...] Read more.

Experimental or numerical analysis of the response of ships and other floating structures starts with correct environmental modelling. The capabilities of numerical tools are rapidly expanding, but presently the evaluation of extreme events in waves (such as slamming, green water, air-gap exceedance) still requires a combination of experiments and different levels of numerical tools. The present paper describes recent efforts within the Maritime Research Institute Netherlands (MARIN) to improve experimental and numerical wave modelling and especially their combination. The ultimate objective is to be able to reproduce any wave condition from a basin or from sea in numerical tools and vice versa, including a sound treatment of basin effects, numerical effects and statistical variability. The aspects that are of importance in both types of wave modelling are first introduced, after which a number of examples of recent projects is discussed. It can be concluded that important steps were made towards linking experimental and numerical wave modelling, but there are some challenges common to all wave reproductions. Some future planned studies focussing on how to deal with them are discussed as well. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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16 pages, 2820 KiB

Open AccessFeature PaperArticle

Influence of Spurious Waves on the Performance of Active Absorption Systems in Oblique Waves

by Thomas Lykke Andersen, Mads Røge Eldrup and Peter Frigaard

J. Mar. Sci. Eng. 2020, 8(3), 185; https://doi.org/10.3390/jmse8030185 - 09 Mar 2020

Cited by 1 | Viewed by 1965

Abstract

Existing active absorption systems do not take into account the spurious waves caused by the segmentation of the wavemaker. Thus, the theoretical estimated performance curves for oblique waves are only valid for infinitely narrow segments. In the present paper, it is demonstrated that [...] Read more.

Existing active absorption systems do not take into account the spurious waves caused by the segmentation of the wavemaker. Thus, the theoretical estimated performance curves for oblique waves are only valid for infinitely narrow segments. In the present paper, it is demonstrated that by ignoring the spurious waves, an unstable system might be designed for box-mode paddles (piecewise constant segmentation). For vertical hinged pistons (piecewise linear segmentation), the results are the opposite, as the stability of the system is improved at high frequencies when a finite paddle width is considered. It is also shown that finite discretization leads to a directional influence in the system, even for a pseudo-3D active absorption system. This effect is more pronounced for vertical hinged systems compared to box-mode paddles. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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17 pages, 7433 KiB

Open AccessArticle

Effect of Variations in Water Level and Wave Steepness on the Robustness of Wave Overtopping Estimation

by Nils B. Kerpen, Karl-Friedrich Daemrich, Oliver Lojek and Torsten Schlurmann

J. Mar. Sci. Eng. 2020, 8(2), 63; https://doi.org/10.3390/jmse8020063 - 21 Jan 2020

Cited by 6 | Viewed by 1836

Abstract

The wave overtopping discharge at coastal defense structures is directly linked to the freeboard height. By means of physical modelling, experiments on wave overtopping volumes at sloped coastal structures are customarily determined for constant water levels and static wave steepness conditions (e.g., specific [...] Read more.

The wave overtopping discharge at coastal defense structures is directly linked to the freeboard height. By means of physical modelling, experiments on wave overtopping volumes at sloped coastal structures are customarily determined for constant water levels and static wave steepness conditions (e.g., specific wave spectrum). These experiments are the basis for the formulation of empirically derived and widely acknowledged wave overtopping estimations for practical design purposes. By analysis and laboratory reproduction of typical features from exemplarily regarded real storm surge time series in German coastal waters, the role of non-stationary water level and wave steepness were analyzed and adjusted in experiments. The robustness of wave overtopping estimation formulae (i.e., the capabilities and limitations of such a static projection of dynamic boundary conditions) are outlined. Therefore, the classic static approach is contrasted with data stemming from tests in which both water level and wave steepness were dynamically altered in representative arrangements. The analysis reveals that mean overtopping discharges for simple sloping structures in an almost deep water environment could be robustly estimated for dynamic water level changes by means of the present design formulae. In contrast, the role of dynamic changes of the wave steepness led to a substantial discrepancy of overtopping volumes by a factor of two. This finding opens new discussion on methodology and criteria design of coastal protection infrastructure under dynamic exposure to storm surges and in lieu of alterations stemming from projected sea level rise. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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6 pages, 1595 KiB

Open AccessTechnical Note

Wave-Generated Current: A Second-Order Formulation

by Anne Katrine Bratland

J. Mar. Sci. Eng. 2020, 8(6), 418; https://doi.org/10.3390/jmse8060418 - 09 Jun 2020

Cited by 1 | Viewed by 2053

Abstract

In Stokes’ wave theory, wave numbers are corrected in the third order solution. A change in wave number is also associated with a change in current velocity. Here, it will be argued that the current is the reason for the wave number correction, [...] Read more.

In Stokes’ wave theory, wave numbers are corrected in the third order solution. A change in wave number is also associated with a change in current velocity. Here, it will be argued that the current is the reason for the wave number correction, and that wave-generated current at the mean free surface in infinite depth equals half the Stokes drift. To demonstrate the validity of this second-order formulation, comparisons to computational fluid dynamics (CFD) results are shown; to indicate its effect on wave loads on structures, model tests and analyses are compared. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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8 pages, 807 KiB

Open AccessTechnical Note

Modelling of Waves for the Design of Offshore Structures

by Ove Tobias Gudmestad

J. Mar. Sci. Eng. 2020, 8(4), 293; https://doi.org/10.3390/jmse8040293 - 19 Apr 2020

Cited by 7 | Viewed by 3391

Abstract

For the design of structures we need to select design safety levels to ensure structures shall safely operate and not collapse. These levels are given in relevant safety standards. For these levels we need to identify the actions and ensure that we design [...] Read more.

For the design of structures we need to select design safety levels to ensure structures shall safely operate and not collapse. These levels are given in relevant safety standards. For these levels we need to identify the actions and ensure that we design according to recognized codes. The objective of this technical note is to shed light on the identification of the design action due to waves to ensure that the design action events be incorporated in the design phase of the structures. The approach used in this technical note is to give a description of an actual extreme event, discuss the efforts and research that was undertaken to explain the event, investigate wave conditions which possibly could have been present at the day of the event, and present a challenge and suggestion for wave tanks to ensure that design action events really are identified during wave tank experiments. We will, in particular, discuss the need for modelling of nonlinear waves to ensure that the action effects from waves are properly identified. Full article

(This article belongs to the Special Issue Selected Papers from the Future Paths and Needs in Wave Modelling Workshop)

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