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Huan-wen Liu - One of the best experts on this subject based on the ideXlab platform.

  • Analytical study of Bragg resonance by singly periodic sinusoidal ripples based on the modified mild-Slope Equation
    Coastal Engineering, 2019
    Co-Authors: Huan-wen Liu, Pengzhi Lin
    Abstract:

    Abstract The wave propagation over singly periodic sinusoidal ripples is studied analytically based on the modified mild-Slope Equation (MMSE). Firstly, each ripple region is divided into four monotonic subintervals such that there is only one regular singular point of the MMSE within each subinterval which is located at one of the two endpoints. Secondly, in each subinterval, due to the monotonicity, the implicit MMSE can be transformed into an explicit MMSE (EMMSE). Thirdly, in each subinterval, due to the unique regular singularity, a general solution in terms of Frobenius series to the EMMSE can be constructed and the convergence condition of the series solution is analyzed and graphically demonstrated. Finally, by using the mass-conserving matching conditions at each common boundary between any two adjacent subintervals, an analytical formula of the reflection coefficient is established. The present solution is validated against various existing solutions, especially, it is identical to a numerical solution to the MMSE. It is shown that, as the number of ripples increases, the peak amplitudes of both the primary and subharmonic Bragg resonances increase while the resonance bandwidths decrease, and the zero reflection occurs more frequently. When the number becomes very large, the peak amplitudes of the primary and subharmonic Bragg resonances achieve unity and the resonance bandwidths approach to their limit resonance bands. As the height of ripples increases, the peak amplitudes of both the primary and subharmonic Bragg resonances and the bandwidth of the primary resonance increase accordingly, and the positions of both the primary and subharmonic Bragg resonances downward shift to low frequency more significantly, but the number of the zero reflection keeps the same.

  • explicit modified mild Slope Equation for wave scattering by piecewise monotonic and piecewise smooth bathymetries
    Journal of Engineering Mathematics, 2014
    Co-Authors: Huan-wen Liu, Xiaomei Zhou
    Abstract:

    The mild-Slope Equation and modified mild-Slope Equation (MMSE) have played an important role in modeling the interaction between waves and bathymetries or structures. However, they are implicit Equations whose coefficients are defined by an implicit dispersion relation. In this paper, for both two-dimensional bathymetries and three-dimensional axisymmetric bathymetries with piecewise monotonicity and piecewise second-order smoothness, we are able to transform the implicit MMSE into an explicit Equation by introducing a new independent variable. Besides, an alternative form of the implicit MMSE is also transformed into an explicit Equation under the same assumptions. These explicit Equations make it much easier to obtain analytic solutions to the MMSE. As practical examples, two analytic solutions to the present explicit MMSE for wave reflection by a single linear Slope and for wave scattering by a submerged circular truncated shoal are constructed.

  • analytic study to wave scattering by a general homma island using the explicit modified mild Slope Equation
    Applied Ocean Research, 2013
    Co-Authors: Xiyuan Zhai, Huan-wen Liu, Jianjian Xie
    Abstract:

    Abstract In this paper, an exact analytic solution in terms of Taylor series to the explicit modified mild-Slope Equation (EMMSE) for wave scattering by a general Homma island is constructed and the convergence of the series solution is analyzed. To validate the new analytic solution, comparisons are made against the existing solutions including analytic solutions to both the long-wave Equation and Helmholtz Equation, approximate analytic solutions to the modified mild-Slope Equation, numerical solutions to the mild-Slope Equation and experimental solutions. Because of the use of the governing Equation EMMSE together with mass-conserving matching conditions along the toe of the shoal, the present model is valid for not only waves in the whole spectrum from long waves to short waves but also bathymetries with the maximal seabed Slope being as high as 4.27:1. Since the general Homma island is an extension of the original Homma island, the present solution can be very conveniently used to study the effects of bottom topography on combined refraction and diffraction. It is found that the larger the shoal size is, the more significant the wave amplification against the cylinder is.

  • exact solution to the modified mild Slope Equation for wave scattering by a cylinder with an idealized scour pit
    Journal of Waterway Port Coastal and Ocean Engineering-asce, 2013
    Co-Authors: Huan-wen Liu, Qiuyue Wang, Guoji Tang
    Abstract:

    AbstractIn this paper, wave scattering by a vertical cylinder with a scour pit governed by the modified mild-Slope Equation (MMSE) is studied analytically. The scour pit around the cylinder is assumed to be axi-symmetric and idealized with its radial profile being a power function. This assumption permits transformation of the two-dimensional MMSE into an ordinary differential Equation (ODE) in the radial direction through the technique of variable separation. By employing a newly derived explicit form of the resultant ODE of the MMSE in the scour pit region, an exact solution to the MMSE is constructed in terms of a Fourier-cosine series and Taylor series. To validate this new analytic solution to the MMSE, a comparison among the present solution, analytic solution to the long wave Equation, and analytic solution to the Helmholtz Equation is made and a good agreement is obtained. It is found that the present MMSE model is valid for a maximum bottom Slope of approximately 0.927. Based on the present solut...

  • the series solution to the modified mild Slope Equation for wave scattering by homma islands
    Wave Motion, 2013
    Co-Authors: Huan-wen Liu, Jianjian Xie
    Abstract:

    Abstract Based on a newly derived explicit form of the modified mild-Slope Equation (MMSE), a series solution is constructed for wave scattering by Homma island and the convergence of the solution is analyzed. It is found that an intuitive and commonly adopted depth-averaged zero-flux condition on the cylinder surface is wrong and an alternative Robin-type condition is derived. To validate the present solution, comparisons are conducted against various known solutions to the long-wave Equation, Helmholtz Equation, the mild-Slope Equation (MSE) and time-dependent MSE. It is shown that the present approach can model wave scattering from very long waves to very short waves. Comparison between the present MMSE solution and its degenerated MSE version is also conducted. Significant contribution of the mass-conserving matching conditions in improving solution accuracy revealed by Porter and Staziker is confirmed for this particular island, which mainly occurs for intermediate waves. By using the present solution, wave amplification is investigated for original Homma island and a modified Homma island. Finally, contour lines of wave amplification in the vicinity around a modified Homma island are presented.

Peter Troch - One of the best experts on this subject based on the ideXlab platform.

  • accurate and fast generation of irregular short crested waves by using periodic boundaries in a mild Slope wave model
    Energies, 2019
    Co-Authors: Panagiotis Vasarmidis, Vasiliki Stratigaki, Peter Troch
    Abstract:

    In this work, periodic lateral boundaries are developed in a time dependent mild-Slope Equation model, MILDwave, for the accurate generation of regular waves and irregular long and short crested waves in any direction. A single wave generation line inside the computational domain is combined with periodic lateral boundaries. This generation layout yields a homogeneous and thus accurate wave field in the whole domain in contrast to an L-shaped and an arc-shaped wave generation layout where wave diffraction patterns appear inside the computational domain as a result of the intersection of the two wave generation lines and the interaction with the lateral sponge layers. In addition, the performance of the periodic boundaries was evaluated for two different wave synthesis methods for short crested waves generation, a method proposed by Miles and a method proposed by Sand and Mynett. The results show that the MILDwave model with the addition of periodic boundaries and the Sand and Mynett method is capable of reproducing a homogeneous wave field as well as the target frequency spectrum and the target directional spectrum with a low computational cost. The overall performance of the developed model is validated with experimental results for the case of wave transformation over an elliptic shoal (Vincent and Briggs shoal experiment). The numerical results show very good agreement with the experimental data. The proposed generation layout using periodic lateral boundaries makes the mild-Slope wave model, MILDwave, an essential tool to study coastal areas and wave energy converter (WEC) farms under realistic 3D wave conditions, due to its significantly small computational cost and its high numerical stability and robustness.

  • modelling of a flap type wave energy converter farm in a mild Slope Equation model for a wake effect assessment
    Iet Renewable Power Generation, 2017
    Co-Authors: Nicolas Tomeybozo, Jimmy Murphy, Tony Lewis, Peter Troch, G P Thomas
    Abstract:

    It is expected that large farms of wave energy converters (WECs) will be installed and as part of the consenting process it will be necessary to quantify their impact on the local environment. The objective of this study is to assess the impact a WEC farm has on the incoming wave field through the use of a novel methodology. This methodology assesses the changes of the significant wave height surrounding a flap-type WEC farm with a special focus on the lee of the farm. A time-dependent mild-Slope Equation model is employed to solve the propagation of surface waves and their interaction with the devices. The model represents the devices as obstacle cells with attributed absorption coefficients tuned against near-fields obtained from a boundary element method (BEM) solver. The wake effect of the farm is determined by using a step-by-step approach starting first with an assessment of one device and progressively incrementing to a larger number of flaps. The effect of incident sea states, device separations and water depth changes on the wake effect of the farm is also investigated. This work shows the potential of a WEC farm to reduce significant wave heights on the leeside.

  • The modelling of a flap type wave energy converter in a time-dependent mild-Slope Equation model
    2016
    Co-Authors: Nicolas Tomey-bozo, Jimmy Murphy, Tony Lewis, Peter Troch, Gareth Thomas, Aurélien Babarit
    Abstract:

    The accurate modelling of the wave field distribution around Wave Energy Convertors (WECs) has been a relevant subject of research in the recent years. Interaction effects in the wave field surrounding the devices are important to know either for power production optimisation of an array or for the quantification of its wake effect due to the absorption of the incoming wave energy. A considerable amount of works have studied arrays of WECs employing methodologies such as BEM based on potential flow theory, wave propagation models, or even CFD in some cases. This study presents an investigation on the modelling of the perturbed wave field by a flap type WEC in a time-dependent mild-Slope Equation model. The aim of this work is to verify the implementation of a flap in a mild-Slope Equation model against the wave field obtained from a BEM. Several regular wave cases show the results for different modelling techniques. The capability of modelling the diffracted wave intrinsically in the mild-Slope Equation model and the implementation of a coupling technique with a BEM are shown. In the last section a representation of the flap by applying the sponge layer technique is done. The understanding of all these techniques with their advantages and disadvantages is relevant for a further development of the wave field modelling. The improvement of the state of the art would allow to quantify more accurately the wake effect of a WEC farm and thus evaluate their capability of acting as a shield with respect to the incoming wave field.

  • a methodology for production and cost assessment of a farm of wave energy converters
    Renewable Energy, 2011
    Co-Authors: Charlotte Beels, Peter Troch, Julien De Rouck, Jens Peter Kofoed, Peter Frigaard, Jon Vindahl Kringelum, Peter Carsten Kromann, M H Donovan, Griet De Backer
    Abstract:

    To generate a substantial amount of power, Wave Energy Converters (WECs) are arranged in several rows or in a ‘farm’. Both the power production and cost of a farm are lay-out dependent. In this paper, the wave power redistribution in and around three farm lay-outs in a near shore North Sea wave climate, is assessed numerically using a time-dependent mild-Slope Equation model. The modelling of the wave power redistribution is an efficient tool to assess the power production of a farm. Further, for each lay-out an optimal (low cost) submarine cable network is designed. The methodology to assess the power production and cost of a farm of WECs is applied to the Wave Dragon Wave Energy Converter (WDeWEC). The WDeWEC is a floating offshore converter of the overtopping type, which captures the water volume of overtopped waves in a basin above mean sea level and produces power when the water drains back to the sea through hydro turbines. It is observed that the cable cost is relatively small compared to the cost of the WDeWECs. As a result, WDeWECs should be installed in a lay-out to increase power production rather than decrease cable cost, taking spatial and safety considerations into account. WDeWECs arranged in a single line produce the highest amount of power, but require an available sea area with a large width (51 km). Installing a single line of WDeWECs in front of a farm of wind turbines increases the time window for accessing the wind farm (applied to Horns Rev II e significant wave height smaller than 1e2 m during 8 h at minimum) by 9e14%. 2011 Published by Elsevier Ltd.

  • wake effects behind a farm of wave energy converters for irregular long crested and short crested waves
    32nd international conference on coastal engineering Book of Abstracts, 2011
    Co-Authors: Peter Troch, Charlotte Beels, Julien De Rouck, Griet De Backer
    Abstract:

    The contribution of wave energy to the renewable energy supply is rising. To extract a considerable amount of wave power, Wave Energy Converters (WECs) are arranged in several rows or in a ’farm’. WECs in a farm are interacting (e.g. the presence of other WECs influence the operational behaviour of a single WEC) and the overall power absorption is affected. In this paper wake effects in the lee of a single WEC and multiple WECs of the overtopping type, where the water volume of overtopped waves is first captured in a basin above mean sea level and then drains back to the sea through hydro turbines, are studied using the time-dependent mild-Slope Equation model MILDwave. The wake behind a single WEC is investigated for long-crested and short-crested incident waves. The wake becomes wider for larger wave peak periods. An increasing directional spreading results in a faster wave regeneration and a shorter wake behind the WEC. The wake in the lee of multiple WECs is calculated for two different farm lay-outs, i.e. an aligned grid and a staggered grid, with varying lateral and longitudinal spacing. The wave power redistribution in and behind each farm lay-out is studied in detail using MILDwave. In general, the staggered grid results in the highest overall wave power absorption.

Jing Han - One of the best experts on this subject based on the ideXlab platform.

  • understanding the temporal Slope of the temperature water isotope relation during the deglaciation using isocam3 the Slope Equation
    Journal of Geophysical Research, 2016
    Co-Authors: Jian Guan, Zhengyu Liu, Xinyu Wen, Esther C Brady, David Noone, Jiang Zhu, Jing Han
    Abstract:

    The temporal and spatial Slopes of water isotope-temperature relations are studied for the last 21,000 years over the middle and high latitudes using a series of snapshot simulations of global climate and water isotopes in the isotope-enabled atmospheric model isoCAM3. Our model simulation suggests that both the temporal Slope and spatial Slope remain largely stable throughout the last deglaciation. Furthermore, the temporal Slope can vary substantially across regions. Nevertheless, on average, and most likely, the temporal Slope is about 0.3‰ °C−1 and is about half of the spatial Slope. Finally, the relation between temporal and spatial Slopes is understood using a semiempirical Equation that is derived based on both the Rayleigh distillation and a fixed spatial Slope. The Slope Equation quantifies the Boyle's mechanism and suggests that the temporal Slope is usually smaller than the spatial Slope in the extratropics mainly because of the polar amplification feature in global climate change, such that the response in local temperature at middle and high latitudes is usually greater than that in the total equivalent source temperature.

Han Jing - One of the best experts on this subject based on the ideXlab platform.

  • Understanding the temporal Slope of the temperature-water isotope relation during the deglaciation using isoCAM3: The Slope Equation
    JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES, 2016
    Co-Authors: Guan Jian, Liu Zhengyu, Wen Xinyu, Brady Esther, Noone David, Zhu Jiang, Han Jing
    Abstract:

    The temporal and spatial Slopes of water isotope-temperature relations are studied for the last 21,000years over the middle and high latitudes using a series of snapshot simulations of global climate and water isotopes in the isotope-enabled atmospheric model isoCAM3. Our model simulation suggests that both the temporal Slope and spatial Slope remain largely stable throughout the last deglaciation. Furthermore, the temporal Slope can vary substantially across regions. Nevertheless, on average, and most likely, the temporal Slope is about 0.3 degrees C-1 and is about half of the spatial Slope. Finally, the relation between temporal and spatial Slopes is understood using a semiempirical Equation that is derived based on both the Rayleigh distillation and a fixed spatial Slope. The Slope Equation quantifies the Boyle's mechanism and suggests that the temporal Slope is usually smaller than the spatial Slope in the extratropics mainly because of the polar amplification feature in global climate change, such that the response in local temperature at middle and high latitudes is usually greater than that in the total equivalent source temperature.National Science Foundation of China [41130105, 41130962, 41005035]; China Scholarship Council; NSF C2P2; DOE SciDacSCI(E)ARTICLElotusescy@pku.edu.cn; zliu3@wisc.edu1710342-1035412

Jun Tang - One of the best experts on this subject based on the ideXlab platform.

  • Numerical study on influences of breakwater layout on coastal waves, wave-induced currents, sediment transport and beach morphological evolution
    Ocean Engineering, 2017
    Co-Authors: Jun Tang, Yongming Shen, Yigang Lyu, Mingliang Zhang
    Abstract:

    Abstract This study provides a numerical model to investigate the influences of breakwater layout on coastal waves, wave-induced currents, sediment transport and beach morphological evolution in the vicinity of breakwater. The numerical model is developed based on the sub-models for nearshore wave, wave-induced current, sediment transport and beach morphological evolution. Nearshore wave is simulated based on the parabolic mild-Slope Equation considering wave refraction, diffraction and breaking effects. Wave-induced nearshore current is modeled using the nonlinear shallow water Equations in which wave radiation stresses are provided by wave model for driving current. Then, the two-dimensional suspended sediment transport Equation, bed-load Equation and coast beach morphological evolution are coupled with the wave and current models for simulating sediment transport and morphological evolution in coastal waves and wave-induced currents. The numerical model is firstly tested by the experiment results for coastal waves, near-shore currents, sediment transport and beach morphological evolution around breakwater from the Large-scale Sediment Transport Facility at the US Army Corps of Engineer Research and Development Center ( Gravens and Wang, 2007 ). Then the model is used to study the influences of breakwater layout on coastal waves, wave-induced currents, sediment transport and beach morphological evolution by set several breakwater layouts in the LSTF basin.

  • numerical model for coastal wave propagation through mild Slope zone in the presence of rigid vegetation
    Coastal Engineering, 2015
    Co-Authors: Jun Tang, Shaodong Shen, Hui Wang
    Abstract:

    Abstract The study of wave propagation on coastal vegetation field is fundamental to assessing the effectiveness and limitations of vegetation in coastal protection. This paper presents a refraction–diffraction wave model for the investigation of wave propagation through a coastal mild Slope zone in the presence of rigid vegetation via numerical simulation. The model is based on the implementation of a module for vegetation-induced wave energy dissipation in the parabolic mild Slope Equation. The model is capable of simulating both wave refraction and diffraction and economical in computation and may bridge the gap between the wave energy spectrum and the phase-resolved models for wave propagation through coastal vegetation fields. The model is validated through by comparison with experimental results. The model is subsequently applied to a simulation of a wave propagating on a plane in the presence of different patterns of rigid vegetation. The sensitivity of the wave height to the plant height, the diameter and the stem density is investigated by comparison of the numerical results for wave height attenuation that results from different patterns of rigid vegetation. The numerical results show that wave height attenuation due to rigid vegetation has a higher variability for the different rigid plant conditions and that the attenuation of the wave height due to the rigid vegetation increases alongside the plant height under water as well as the diameter and plant stem density. The results further indicate that for wave propagates through coastal rigid vegetation zones with a high plant height under water, large diameter and high stem density, the wave height along the propagating direction is decreased nonlinearly with the increase of the wave propagating distance, and nonlinearity is more obvious for the plant with a higher height under water as well as a larger diameter and higher stem density.

  • water wave simulation in curvilinear coordinates using a time dependent mild Slope Equation
    Journal of Hydrodynamics, 2010
    Co-Authors: Jun Tang, Yongming Shen, Feifei Tong, Lei Cui
    Abstract:

    The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild Slope Equation. This was achieved in the following approach, firstly deriving the numerical model of the Equation, i.e., Copeland's hyperbolic mild-Slope Equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit (ADI) method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries.

  • numerical simulation of long shore currents induced by regular breaking wave
    Journal of Coastal Research, 2008
    Co-Authors: Yongming Shen, Jun Tang, Wenrui Huang
    Abstract:

    Abstract The hydrodynamics of coastal zones are extremely complicated, being influenced greatly by shallow water waves and currents induced by wave breaking. This paper presents numerical simulations of long-shore currents induced by the breaking of oblique incident waves in shallow coastal zones. The wave numerical model is based on parabolic mild Slope Equation, and so the wave radiation stress required for the generation of wave-induced currents are calculated based on the variables in the parabolic mild Slope Equation, and the long-shore currents have been numerically simulated based on these. The numerical models are validated against experimental data, and the results suggest that the long-shore current velocity and wave set-up increase with the increasing incident wave amplitude and offshore Slope steepness, as well as the wave set-up increase with the increasing incident wave period.

  • an efficient and flexible computational model for solving the mild Slope Equation
    Coastal Engineering, 2004
    Co-Authors: Jun Tang, Yongming Shen, Yonghong Zheng, Dahong Qiu
    Abstract:

    ThemildSlopeEquationisusedtodescribewavepropagatinginthenearshoreregion.Inthispaper,thefinitedifferencemethod isusedtodiscretizethegoverningellipticEquationandthediscretizedlinearEquationissolvedusingGPBiCG(m,n)method.Two cases of wave propagating are used to test the model, and reasonable agreements have been achieved. It is shown that the present algorithm: GPBiCG(m,n)withaflexibleanddiverseform,hasafastandrelativelyrobust convergencerate,andcanbeefficiently and economically run in either the linear or nonlinear wave model and easily used to a complicated region. D 2004 Elsevier B.V. All rights reserved.