scholarly journals A COMPUTER MODEL FOR THE REFRACTION OF NON-LINEAR WAVES

1982 ◽  
Vol 1 (18) ◽  
pp. 26
Author(s):  
J.B. Crowley ◽  
C.A. Fleming ◽  
C.K. Cooper
Keyword(s):  
Wave Spectrum ◽  
Future Research ◽  
Linear Wave ◽  
Wave Refraction ◽  
Linear Waves ◽  
Sea Bed ◽  
Water Region ◽  
Non Linear ◽  
Wave Heights ◽  
Bed Friction

A non-linear wave refraction model was developed which allows for the combined refraction and shoaling of Vocoidal waves over an arbitrary sea bed. The effects of bed friction and percolation are also catered for. The method is based on the cirular arc technique which is widely used for linear wave refraction. The method was extensively tested against Vocoidal wave refraction results obtained previously for a plane beach. A comparison of Vocoidal and linear wave refraction over an arbitrary sea bed indicated that Vocoidal waves refract less than linear theory, thereby yielding higher wave heights and angles of incidence at the breaker line. This result is in line with results of non-linear refraction over parallel bed contours quoted for other non-linear wave theories in literature. Further work is required before caustics can be adequately treated. Future research should include wave spectrum transfer and the re-evaluation of empirical relationships in use in the shallow water region and which will use this new higher-order refraction technique.

scholarly journals CURRENT DEPTH REFRACTION OF REGULAR WAVES

1984 ◽  
Vol 1 (19) ◽  
pp. 75 ◽  
Author(s):  
Ivar G. Jonsson ◽  
John B. Christoffersen
Keyword(s):  
Large Scale ◽  
Wave Motion ◽  
Regular Waves ◽  
Small Surface ◽  
First Order ◽  
Linear Waves ◽  
Sea Bed ◽  
Wave Heights ◽  
Complete Set ◽  
Bed Friction

The complete set of equations for the refraction of small surface gravity waves on large-scale currents over a gradually varying sea bed is derived and presented. Wave lengths, direction of propagation and wave heights are all determined along the so-called wave rays as solutions to ordinary, first-order differential equations. Dissipation due to bed friction in the combined current wave motion is included. The ray tracing method is used in an example. A method for the calculation of current depth refraction of weakly non-linear waves is proposed.

Flexible Riser Response Induced by Springing of an FPSO Hull

2007 ◽  
Author(s):  
Jelena Vidic-Perunovic ◽  
Niels J. Risho̸j Nielsen ◽  
Haiwen Zhang
Keyword(s):  
High Frequency ◽  
Wave Spectrum ◽  
Analytical Form ◽  
Second Order ◽  
Wave Frequency ◽  
Natural Vibration Frequency ◽  
Linear Wave ◽  
Flexible Riser ◽  
Excitation Wave ◽  
Non Linear

The hydrodynamic analysis of the flexible riser for offshore application is usually limited to the first order wave frequency motions of the floating vessel that holds the riser top end. In this paper effort is made to investigate the influence of non-linear second order springing deflection of the production vessel hull on flexible riser response. The system selected in this study consists of a free-hanging flexible riser configuration attached to an FPSO. Due to resonance between the excitation wave frequency and the natural vibration frequency of the hull, second order flexible vertical motions of the FPSO increase. This may influence the riser loads, presumably the tension force. Vertical motions including the second order high frequency contribution are assigned to the flexible riser at a point of attachment to the vessel. To account for the environmental loading, irregular sea is applied, characterized by modified linear wave spectrum. Second order excitation wave spectrum is truncated by use of WAFO routines for random second order wave simulation and an analytical form of the spectrum that accounts for the non-linear wave effects is proposed. Several environmental conditions are examined in order to consolidate the tendency in riser behaviour. The significance of the high-frequency quadratic terms in the loads along the flexible riser is discussed.

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.

Modelling the Heave Response of Tension Leg Platforms Using the Volterra Series

2003 ◽  
Author(s):  
Scott Taylor ◽  
Nicholas Haritos ◽  
Krish Thiagarajan
Keyword(s):  
Natural Frequency ◽  
Transfer Functions ◽  
Volterra Series ◽  
Wave Spectrum ◽  
Vertical Plane ◽  
Fatigue Cracking ◽  
Gas Production ◽  
Linear Wave ◽  
Non Linear ◽  
Volterra Method

Tension Leg Platforms (TLPs) are predominately used for deep water oil and gas production. The use of tendons creates a small amplitude, high cyclic response in the vertical plane (heave, roll and pitch). Under these conditions fatigue cracking becomes an important consideration. The amplitude of the vertical motion is minimised by ensuring the natural frequency of the TLP lies above the energetic part of the wave spectrum. However, due to non-linear wave loading effects, it is possible for waves to create an output at their sum-frequency, which may consequently equal the natural frequency of the platform. This phenomenon is more commonly known as ‘springing’. The Volterra method [1] is a technique used to model the behaviour of TLPs under these conditions. This approach quantifies the linear and non-linear (quadratic, cubic, etc) responses separately using transfer functions, which are determined from the input and output of the system. In this paper an orthogonalised Volterra series for use with both Gaussian and non-Gaussian input data is presented. The data used in the Volterra modelling was collected from tests conducted on a model TLP. The wave height and platform motion were measured at wave frequencies around one, a half and a third of the model’s heave natural frequencies. Both regular and irregular wave tests were performed to varying wave heights and frequencies. Using the Volterra method, the transfer functions were calculated up to the third order. Difficulties encountered due to the use of discrete data were identified and where possible their effects minimized. The results demonstrate clear evidence of springing, with dynamic amplification present at sum-frequencies close to the natural frequency of the platform for the non-linear responses.

Fatigue Loads on Offshore Wind Turbines Due to Weakly Non-Linear Waves

2005 ◽  
Author(s):  
Jenny M. V. Trumars ◽  
Niels Jacob Tarp-Johansen ◽  
Thomas Krogh
Keyword(s):  
Wind Turbine ◽  
Wave Model ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Linear Wave ◽  
Support Structure ◽  
Linear Waves ◽  
Non Linear ◽  
The Difference ◽  
Second Peak

Due to the pronounced dynamic behavior of wind turbines, fatigue load effects may be quite sensitive to the precise modeling of the frequency content of the wave loading. As the offshore wind turbine technology progresses, larger and larger turbines will be placed at still deeper waters, causing the resonant frequency of the first eigen mode of a traditional bottom-fixed support structure to be typically in the range from 0.25 Hz to 0.35 Hz. The deeper the water and the larger the turbine, the lower the frequency will be. As an example, wave measurements from the offshore wind farm Bockstigen show a second peak at approximately 0.3 Hz in the wave spectrum. Thus this peak, or similar peaks realized at shallow water sites, may very well be dynamically amplified in the response. This second peak cannot be modelled with a linear wave model, and a wave model taking non-linearities into account has to be used. In the presented work, both a linear and a non-linear wave model are used to study the fatigue in an offshore wind power plant and the difference is compared. Time series of irregular linear and non-linear waves are calculated, and structural calculations of an offshore wind turbine with a slender support structure are used in the analysis of the fatigue loads. The forces on the structure are calculated using Morison’s equation, integrating along the structure and lumping the loads in nodes for the structural calculations. The difference between the wave models is significant and the non-linear model yields higher fatigue damage than the linear one.

Action of Non-Linear Waves at a Solid Wall

1977 ◽  
Author(s):  
Mohamed S. Nasser ◽  
John A. McCorquodale
Keyword(s):  
Solid Wall ◽  
Linear Waves ◽  
Non Linear

scholarly journals Excitation Forces Estimation for Non-linear Wave Energy Converters: A Neural Network Approach

2020 ◽  
Vol 53 (2) ◽  
pp. 12334-12339
Author(s):  
M. Bonfanti ◽  
F. Carapellese ◽  
S.A. Sirigu ◽  
G. Bracco ◽  
G. Mattiazzo
Keyword(s):  
Neural Network ◽  
Wave Energy ◽  
Linear Wave ◽  
Network Approach ◽  
Neural Network Approach ◽  
Wave Energy Converters ◽  
Non Linear ◽  
Energy Converters

scholarly journals Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

2010 ◽  
Vol 34 (8) ◽  
pp. 1984-1999 ◽  
Author(s):  
Ahmadreza Zamani ◽  
Ahmadreza Azimian ◽  
Arnold Heemink ◽  
Dimitri Solomatine
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Wind Wave ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Data ◽  
Non Linear

scholarly journals A numerical study of glacier advance over deforming till

2010 ◽  
Vol 4 (3) ◽  
pp. 359-372 ◽  
Author(s):  
G. J.-M. C. Leysinger Vieli ◽  
G. H. Gudmundsson
Keyword(s):  
Effective Viscosity ◽  
Numerical Study ◽  
Thickness Distribution ◽  
Plug Flow ◽  
Linear Wave ◽  
Sediment Layer ◽  
Mixed Flow ◽  
Model Experiments ◽  
Non Linear ◽  
Glacier Advance

Abstract. The advance of a glacier over a deforming sediment layer is analysed numerically. We treat this problem as a contact problem involving two slowly-deforming viscous bodies. The surface evolution of the two bodies, and of the contact interface between them, is followed through time. Using various different non-linear till rheologies, we show how the mode of advance depends on the relative effective viscosities of ice and till. Three modes of advances are observed: (1) overriding, where the glacier advances through ice deformation only and without deforming the sediment; (2) plug-flow, where the sediment is strongly deformed, the ice moves forward as a block and a bulge is built in front of the glacier; and (3) mixed-flow, where the glacier advances through both ice and sediment deformation. For the cases of both overriding and mixed-flow, an inverse depth-age relationship within the ice is obtained. A series of model experiments show the contrast in effective viscosity between ice and till to be the single most important model parameter defining the mode of advance and the resulting thickness distribution of the till. Our model experiments indicate that the thickness of the deforming till layer is greatest close to the glacier front. Measurements of till thickness taken in such locations may not be representative of deforming till thickness elsewhere. Given sufficiently large contrast in effective viscosity between ice and till, a sediment bulge is formed in front of the glacier. During glacier advance, the bulge quickly reaches a steady state form strongly resembling single-crested push moraines. Inspection of particle paths within the sediment bulge, shows that particles within the till travel at a different speed from the bulge itself, and the push moraine to advance as a form-conserving non-linear wave.

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