Irregular Wave Transformation in a Boussinesq Wave Model

Author(s):  
H. -H. Prüser ◽  
H. Schaper ◽  
W. Zielke
1986 ◽  
Vol 1 (20) ◽  
pp. 205
Author(s):  
H.H. Pruser ◽  
H. Schaper ◽  
W. Zielke

Numerical wave models for shallow water waves are of particular importance for the calculation of the wave climate in harbours and coastal areas. Especially nonlinear time domain models, which are based on the Boussinesq-Wave- Equations, may be helpful in the future for simulating the interaction of currents with refraction, diffraction, reflection and for simulating shoaling..-of irregular waves in natural areas; a potential which has not yet been fully developed. During the last ten years numerical models, based on these equations, have been published; such as ABBOTT et. al. , HAUGUEL and SCHAPER / ZIELKE . Research on this topic is currently being carried on. Some efforts have been made to verify the capability of the models to describe the various physical phenomena. However, up to now, verification has been limited to regular waves. The aim of this paper therefore is, to consider questions concerning irregular, nonlinear waves.


Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1147 ◽  
Author(s):  
Shanju Zhang ◽  
Liangsheng Zhu ◽  
Jianhua Li

The prediction of wave transformation and associated hydrodynamics is essential in the design and construction of reef top structures on fringing reefs. To simulate the transformation process with better accuracy and time efficiency, a shock-capturing numerical model based on the extended Boussinesq equations suitable for rapidly varying topography with respect to wave transformation, breaking and runup, is established. A hybrid finite volume–finite difference scheme is used to discretize conservation form of the extended Boussinesq equations. The finite-volume method with a HLL Riemann solver is applied to the flux terms, while finite-difference discretization is applied to the remaining terms. The fourth-order MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) scheme is employed to create interface variables, with in which the van-Leer limiter is adopted to improve computational accuracy on complex topography. Taking advantage of van-Leer limiter, a nested model is used to take account of both computational run time and accuracy. A modified eddy viscosity model is applied to better accommodate wave breaking on steep reef slopes. The established model is validated with laboratory measurements of regular and irregular wave transformation and breaking on steep fringing reefs. Results show the model can provide satisfactory predictions of wave height, mean water level and the generation of higher harmonics.


Author(s):  
Shigeki Sakai ◽  
Kouetsu Hiyamizu ◽  
Hiroshi Saeki

2015 ◽  
Vol 6 (4) ◽  
pp. 1515-1523 ◽  
Author(s):  
Dionisio Ramirez ◽  
Juan Pablo Bartolome ◽  
Sergio Martinez ◽  
Luis Carlos Herrero ◽  
Marcos Blanco

Author(s):  
P. Agarwal ◽  
L. Manuel

In the design of wind turbines—onshore or offshore—the prediction of extreme loads associated with a target return period requires statistical extrapolation from available loads data. The data required for such extrapolation are obtained by stochastic time-domain simulation of the inflow turbulence, the incident waves, and the turbine response. Prediction of accurate loads depends on assumptions made in the simulation models employed. While for the wind, inflow turbulence models are relatively well established, for wave input, the current practice is to model irregular (random) waves using a linear wave theory. Such a wave model does not adequately represent waves in shallow waters where most offshore wind turbines are being sited. As an alternative to this less realistic wave model, the present study investigates the use of irregular nonlinear (second-order) waves for estimating loads on an offshore wind turbine, with a focus on the fore-aft tower bending moment at the mudline. We use a 5MW utility-scale wind turbine model for the simulations. Using, first, simpler linear irregular wave modeling assumptions, we establish long-term loads and identify governing environmental conditions (i.e., the wind speed and wave height) that are associated with the 20-year return period load derived using the inverse first-order reliability method. We present the nonlinear irregular wave model next and incorporate it into an integrated wind-wave-response simulation analysis program for offshore wind turbines. We compute turbine loads for the governing environmental conditions identified with the linear model and also for an extreme environmental state. We show that computed loads are generally larger with the nonlinear wave modeling assumptions; this establishes the importance of using such refined nonlinear wave models in stochastic simulation of the response of offshore wind turbines.


2005 ◽  
Vol 32 (8-9) ◽  
pp. 961-985 ◽  
Author(s):  
Hajime Mase ◽  
Kazuya Oki ◽  
Terry S. Hedges ◽  
Hua Jun Li

2014 ◽  
Vol 638-640 ◽  
pp. 1261-1265 ◽  
Author(s):  
Yun Peng Zhang ◽  
Ming Liang Zhang ◽  
Zi Ning Hao ◽  
Yuan Yuan Xu ◽  
Yang Qiao

This paper presents a spectral wave action model to simulate random wave deformation and transformation. The wave model is based on the wave action balance equation and can simulate wave fields by accounting for wave breaking, shoaling, refraction, diffraction and wind effect in coastal waters. It is a finite-difference, phase averaged model for the steady-state wave spectral transformation. The wave model is applied to verify different experimental cases and real life case of considering the several factor effects. The calculated results agree with the experimental and field data. The results show that the wave model presented herein should be useful in simulating the wave transformation processes in complicated coastal waters.


1986 ◽  
Vol 1 (20) ◽  
pp. 9 ◽  
Author(s):  
William R. Dally ◽  
Robert G. Dean

Based on a previous study by the authors of regular breaking waves in the surf zone, a model for random wave transformation across the nearshore region is developed. The results of a laboratory investigation of the effect of a steady opposing current on the wave decay process are presented and a proposed governing equation verified. Surf beat effects on wave transformation are then included in the model by representing the long wave as a temporally and spatiallyvarying current and mean water level. The concept of an equivalent water depth, which contains the effect of the current, is introduced and then included in a stochastic form in the random wave model. Surf beat is found to noticeably increase the decay of the root mean square wave height, especially in the inner surf where the beat is strongest. Comparison of the models to two field data sets show very good agreement for Hotta and Mizuguchi (1980), but rather poor for Thornton and Guza (1983). Possible explanations for the unexpected behavior of the second data set, pertaining to filtering, are discussed. Finally, a possible explanation for the dependence of random wave decay on deepwater steepness, noted by Battjes and Stive (1985), is presented.


2011 ◽  
Vol 1 (32) ◽  
pp. 20 ◽  
Author(s):  
Hee Min Teh ◽  
Vengatesan Venugopal ◽  
Tom Bruce

The increasing importance of the sustainability challenge in coastal engineering has led to the development of free surface breakwaters of various configurations. In this study, the hydrodynamic characteristics of a perforated semicircular free surface breakwater (SCB) are investigated for irregular wave conditions. The hydrodynamic performance of the breakwater is evaluated in the form of transmission, reflection and energy dissipation coefficients, which are then presented as a function of the relative submergence depth (D/d) and the relative breakwater width (B/Lp), where D = the depth of immersion, d = the water depth, B = the breakwater width and Lp = the wavelength corresponding to the peak wave period. It is found that the wave attenuation ability of the SCB model improves with the increase of D/d and B/Lp. The SCB performs better as an energy dissipater than as a wave reflector. Based on the analysis of measured data, some empirical equations are proposed to predict the performance of the breakwater under varying submergence depths. The behaviour of wave transformation around and within the breakwater’s chamber is discussed. Also, the measured horizontal wave forces acting on the SCB are reported.


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