scholarly journals On the Deterministic Prediction of Water Waves

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 9 ◽  
Author(s):  
Marco Klein ◽  
Matthias Dudek ◽  
Günther F. Clauss ◽  
Sören Ehlers ◽  
Jasper Behrendt ◽  
...  
Keyword(s):  
Water Waves ◽  
Linear Wave ◽  
Wave Steepness ◽  
Forecast Horizon ◽  
Linear Dispersion ◽  
Similarity Parameter ◽  
Linear Solution ◽  
Basic Module ◽  
Wave Prediction ◽  
Non Linear

This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM)—are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.

scholarly journals Relation between orbital velocities, pressure and surface elevation in non-linear nearshore water waves

2021 ◽  
Author(s):  
Kévin Martins ◽  
Philippe Bonneton ◽  
David Lannes ◽  
Hervé Michallet
Keyword(s):  
Free Surface ◽  
Surface Energy ◽  
Water Waves ◽  
Energy Levels ◽  
Sea Surface ◽  
Surface Elevation ◽  
Linear Wave ◽  
Free Surface Elevation ◽  
High Frequencies ◽  
Non Linear

AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.

scholarly journals SURF SIMILARITY

1974 ◽  
Vol 1 (14) ◽  
pp. 26 ◽  
Author(s):  
J.A. Battjes
Keyword(s):  
Phase Difference ◽  
Incident Wave ◽  
Water Waves ◽  
Slope Angle ◽  
Wave Steepness ◽  
Similarity Parameter ◽  
General Terms ◽  
Depth Ratio ◽  
Run Up ◽  
Set Up

This paper deals with the following aspects of periodic water waves breaking on a plane slope breaking criterion, breaker type, phase difference across the surfzone, breaker height-to-depth ratio, run-up and set-up, and reflection. It is shown that these are approximately governed by a single similarity parameter only, embodying both the effects of slope angle and incident wave steepness. Various physical interpretations of this similarity parameter are given, while its role is discussed m general terms from the viewpoint of model prototype similarity.

Systematic Experimental Validation of High-Order Spectral Method for Deterministic Wave Prediction

2019 ◽  
Author(s):  
Marco Klein ◽  
Matthias Dudek ◽  
Günther F. Clauss ◽  
Norbert Hoffmann ◽  
Jasper Behrendt ◽  
...  
Keyword(s):  
Spectral Method ◽  
Experimental Validation ◽  
Linear Method ◽  
Wave Spectrum ◽  
High Order ◽  
Linear Wave ◽  
Short Term ◽  
Wave Prediction ◽  
Non Linear ◽  
High Order Spectral Method

Abstract The applicability of the High-Order Spectral Method (HOSM) as a very fast non-linear method for deterministic short-term wave prediction is discussed within this paper. The focus lies on the systematic experimental validation of the HOSM in order to identify and evaluate possible areas of application as well as limitations of use. For this purpose, irregular sea states with varying parameters such as wave steepness and underlying wave spectrum are addressed by numerical simulations and model tests in the controlled environment of a seakeeping basin. In addition, the influence of the propagation distance is discussed. For the evaluation of the accuracy of the HOSM prediction, the surface similarity parameter (SSP) is utilized, allowing a quantitative validation of the results. The results obtained are compared to linear wave prediction to discuss the pros and cons of a non-linear deterministic short-term wave prediction. In conclusion, this paper shows that the non-linear deterministic wave prediction based on HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance.

Non-linear dispersion of water waves

1967 ◽  
Vol 27 (2) ◽  
pp. 399-412 ◽  
Author(s):  
G. B. Whitham
Keyword(s):  
Water Waves ◽  
Wave Train ◽  
Periodic Wave ◽  
Wave Number ◽  
Amplitude Wave ◽  
Linear Dispersion ◽  
Elliptic Case ◽  
Non Linear ◽  
Wave Trains ◽  
Linear Water Waves

The slow dispersion of non-linear water waves is studied by the general theory developed in an earlier paper (Whitham 1965b). The average Lagrangian is calculated from the Stokes expansion for periodic wave trains in water of arbitrary depth. This Lagrangian can be used for the various applications described in the above reference. In this paper, the crucial question of the ‘type’ of the differential equations for the wave-train parameters (local amplitude, wave-number, etc.) is established. The equations are hyperbolic or elliptic according to whetherkh0is less than or greater than 1.36, wherekis the wave-number per 2π andh0is the undisturbed depth. In the hyperbolic case, changes in the wave train propagate and the characteristic velocities give generalizations of the linear group velocity. In the elliptic case, modulations in the wave train grow exponentially and a periodic wave train will be unstable in this sense; thus, periodic wave trains on water will be unstable ifkh0> 1·36, The instability of deep-water waves,kh0> 1·36, was discovered in a different way by Benjamin (1966). The relation between the two approaches is explained.

An Approach to Calculate the Probability of Wave Impact on an FPSO Bow

2004 ◽  
Author(s):  
C. Guedes Soares ◽  
R. Pascoal ◽  
E. M. Anta˜o ◽  
A. J. Voogt ◽  
B. Buchner
Keyword(s):  
Impact Load ◽  
Second Order ◽  
Experimental Program ◽  
Ship Motions ◽  
Linear Wave ◽  
Wave Steepness ◽  
Wave Impact ◽  
Non Linear ◽  
Local Wave ◽  
The Impact

This work aims at characterizing the probability of wave impact and expected impact load on the bow geometry of an FPSO. In order to determine the instants when impact occurs, an experimental program was performed on a specific bow shape. The bow was instrumented with pressure transducers and the test program, also making use of video recordings, was designed such that it was possible to determine the correlation between undisturbed wave shape and the impact pressure time traces. It has been found that wave impact at the bow is highly correlated with the local wave steepness, which for very high waves has at least second order effects. A comparison between the probability distributions of local wave steepness of the experimental undisturbed wave time trace and numerical simulations of second order wave theory is provided and it confirmed that the latter is very adequate for calculations. The experimental results were further used to determine how the probability of impact varies with free surface vertical velocity. It was found that the significant wave height of the sea state itself does not have significant influence on the result and a regression model is derived for that type of bow. The proposed model for determining the probability of impact load is based on combining both models. The analytical nature makes it fast and easy to expand to other cases of interest and some example calculations are shown to demonstrate the relative ease of the procedure proposed. The position of the impact is determined by the non-linear wave crests and the ship motions. The ship motions can be determined based on a linear response to the non-linear waves considered.

Comparison of Two Versions of the MNLS With the Full Water Wave Equations

2020 ◽  
Author(s):  
Tianning Tang ◽  
Ye Li ◽  
Harry B. Bingham ◽  
Thomas A. A. Adcock
Keyword(s):  
Schrödinger Equation ◽  
Water Waves ◽  
Schrodinger Equation ◽  
Wave Equations ◽  
Wave Crest ◽  
Inherent Limitation ◽  
Linear Dispersion ◽  
Non Linear ◽  
Non Linear Propagation ◽  
Linear Propagation

Abstract Versions of the non-linear Schrödinger equation are frequently used for modelling the non-linear propagation of water waves. In this paper, we compare two models against the results of fully non-linear numerical simulations. We consider uni-directional versions of the non-linear Schrödinger equation of Dysthe et al. with the hybrid model of Trulsen et al. The model of Trulsen et al. is shown to have clear advantages in all situations considered including modelling wave crest statistics for highly non-linear cases. However, for very broad bandwidths this model does start to break down, presumably due to the inherent limitation of the envelope representation of water waves. This in turn leads to a small, non-physical, leakage of energy in nonlinear simulations, although, this leakage is much smaller than for the version with 5th order linear dispersion relationship.

The Average Shape of Large Waves in the Norwegian Sea: Is Non-Linear Physics Important?

2019 ◽  
Author(s):  
Tianning Tang ◽  
Margaret J. Yelland ◽  
Thomas A. A. Adcock
Keyword(s):  
Field Data ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Problem ◽  
Linear Dispersion ◽  
Norwegian Sea ◽  
Linear Wave Theory ◽  
Average Shape ◽  
Non Linear ◽  
Average Wave

Abstract Linear wave theory predicts that in a random sea, the shape of the average wave is given by the scaled autocorrelation function — the “NewWave”. However, the gravity wave problem is non-linear. Numerical simulations of waves on deep water have suggested that their average shape can become modified in a number of ways, including the largest wave in a group tending to move to the front of the group through non-linear dispersion. In this paper we examine whether this occurs for waves in the Norwegian Sea. Field data measured from the weather ship Polarfront is analysed for the period 2000 to 2009. We find that, at this location, the effect of non-linearity is small due to the moderate steepness of the sea-states.

Deterministic non-linear wave prediction using probe data

2010 ◽  
Vol 37 (10) ◽  
pp. 913-926 ◽  
Author(s):  
E. Blondel ◽  
F. Bonnefoy ◽  
P. Ferrant
Keyword(s):  
Linear Wave ◽  
Wave Prediction ◽  
Non Linear

Control Signal Optimization for Non-Linear Wave Generation

2018 ◽  
Author(s):  
J. B. H. Hicks ◽  
H. B. Bingham ◽  
R. Read
Keyword(s):  
Water Waves ◽  
Numerical Optimization ◽  
Wave Generation ◽  
Linear Wave ◽  
Linear Potential ◽  
Numerical Work ◽  
Flow Solver ◽  
Control Signals ◽  
Correction Scheme ◽  
Non Linear

This paper investigates the use of optimization for numerical-physical wave generation in wave tanks. Control signals for a wedge-shaped plunger-type wave generator are developed to produce stable non-linear, deep-water waves in both numerical and physical wave tanks. A fully non-linear potential flow solver developed at DTU is used for the numerical work. Numerical optimization proceeds by a defect correction scheme, resulting in optimized control signals for wavelengths of 0.7–2 m (corresponding to non-dimensional wave numbers kh = 2–5.5) and steepnesses of 3–11%.

scholarly journals 2- AND 3-DIMENSIONAL DETERMINISTIC FREAK WAVES

1982 ◽  
Vol 1 (18) ◽  
pp. 43
Author(s):  
Soren Peter Kjeldsen
Keyword(s):  
Dimensional Case ◽  
Linear Wave ◽  
Linear Dispersion ◽  
New Techniques ◽  
Freak Waves ◽  
3 Dimensional ◽  
Non Linear ◽  
Stokes Waves ◽  
First Results ◽  
Wave Trains

The present paper deals with a new non-linear technique for generation of violent breaking freak waves (plunging breakers) at specified positions and times in wave basins. First, results concerning generation of non-linear wave trains, Stokes-waves and wave solitons in deep water are given. Then the technique for generation of non-linear wave transients are given with specified non-linear dispersion properties. Finally, the new techniques are used to obtain collisions between non-linear solitons coming both from the same direction (2-dimensional case), and from different directions (3-dimensional case) leading to generation of steep and violent plunging breakers.

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