Effects Of Wave Nonlinearity Research Articles

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

Combination of HOSM and FORM for extreme wave-induced response prediction of a ship in nonlinear waves

This paper proposes a method for predicting the extreme values of linear and nonlinear wave-induced responses of a ship in nonlinear waves. The method is based on a combination of the Higher Order Spectrum Method (HOSM) and First Order Reliability Method (FORM), allowing the most-probable wave episodes for extreme values of interest to be efficiently calculated. The proposed HOSM + FORM approach is first applied to extreme wave crest prediction, and the results are validated through comparisons against Monte Carlo simulations. The HOSM + FORM approach is then used to predict the extreme wave-induced vertical bending moment (VBM) distribution in a container ship. The wave-induced VBM is assumed to be linear with respect to the incident wave profile by leveraging pre-computed VBM transfer functions. Finally, the extreme value distribution of nonlinear roll motion in beam seas is investigated. The proposed HOSM + FORM approach is shown to predict the extreme linear and nonlinear wave-induced responses efficiently and accurately. The effect of wave nonlinearity is found to be significant under circumstances where the VBM is sensitive to high-frequency waves or large roll angles are excited by the wave crests.

Near‐Bed Sediment Transport Processes During Onshore Bar Migration in Large‐Scale Experiments: Comparison With Offshore Bar Migration

AbstractDetailed information on nearshore sediment transport processes during onshore bar migration were obtained from large‐scale laboratory experiments with bichromatic wave groups on a relatively steep initial beach slope (1:15). Detailed measurements of velocity and sand concentration near the bed from shoaling up to the outer breaking zone including suspended sediment and sheet flow transport are presented. The analysis focuses on onshore migration under an accretive wave condition but comparison to an erosive condition highlights important differences. Decomposition shows that total transport mainly results from a balance of short wave‐related, bedload onshore transport and current‐related, suspended offshore transport. When comparing the accretive to the more energetic erosive condition, the balance shifts toward onshore transport, and onshore migration, because the short wave‐related transport does not decrease as much as the current‐related transport. This is related to the effects of skewness and asymmetry combined with less sediment suspension in the water column and undertow magnitude under the accretive condition. Transports from streaming in the wave boundary layer and from infragravity waves become visible but only play a subordinate role. Identified priorities for numerical model development include parametrization of wave nonlinearity effects and better description of wave breaking and its influences on sediment suspension.

Combined nonlinear wave and current induced instantaneously-liquefied soil depth in a non-cohesive seabed

Progressive waves usually coexist with a steady current in coastal environments. Superposing a following or opposite current onto the progressive waves could significantly alter the excess pore-water pressure distribution within the seabed. Unlike previous studies which were predominantly limited to the pure wave cases, the instantaneous liquefaction of a non-cohesive seabed is investigated analytically under the combined loading of 3rd order Stokes waves and a steady current. Explicit expressions are derived for the transient pore pressure distribution in a seabed with instantaneously-liquefied zone and the corresponding instantaneous liquefaction depth, which are verified by degradation analyses and comparisons with the existing offshore field observations. The phase lag of excess pore pressure is taken into account in the theoretical derivation. Parametric study is then performed to examine the effects of wave non-linearity and superimposing a current on the instantaneous liquefaction depth. It is indicated that wave-nonlinearity effects on the instantaneous liquefaction depth are not neglectable, especially when the wave height gets larger and the current velocity is reduced. The envelope for the variation of maximum instantaneous liquefaction depth with both wave period and current velocity is further constructed. To superimpose an opposing current onto the progressive waves with a relatively small wave period could be beneficial for the prevention of instantaneous liquefaction. Nevertheless, the variation trends of the maximum instantaneous liquefaction depth are attributed to the synthetical effect of the alternations of both wavelength and wave height during nonlinear wave-current interactions. • Analytical solutions for instantaneous liquefaction depth under combined Stokes 3rd order waves and a steady current. • To superimpose an opposing current onto waves could be beneficial for liquefaction prevention. • Variations of maximum liquefaction depth with wave number are attributed to the synthetical effect of wave-current interactions.

Investigation on mechanisms of fast opposing water waves influencing overlying wind using simulation and theoretical models

We use large-eddy simulation (LES) and theoretical analyses to study the turbulent flow over fast opposing water waves. A novel nonlinear viscous model for airflow perturbations induced by Stokes waves is developed, which can account for wave-perturbation viscous stress and the nonlinear forcing by multimode interactions of wave-correlated quantities in the wind field. Overall, the nonlinear viscous model can describe the wave-coherent airflow in the LES results for high-order Stokes waves, which demonstrates the negligible effects of wave-perturbation turbulent stress in the wind. According to the model, the dominant components of the fundamental mode of the airflow perturbation primarily result from the linear response of the wind to the wave and, thus, are not substantially affected by the nonlinear forcing. However, the weak components of the fundamental mode, which produce the form drag on the wave, are created by the combined effects of the nonlinear forcing and the wave-perturbation viscous stress. We found that the main mechanism for generating the nonlinear forcing is the interaction between the second harmonic and the fundamental mode of the wave-correlated quantities in the air. In this mechanism, wave nonlinearity exerts its effects mainly through the second harmonic of the wave surface, instead of the second harmonic of the wave kinematics. Therefore, it is further demonstrated that a second-order Stokes wave is sufficient to capture the wave nonlinearity effects on the form drag.

The Dynamic Sea Clutter Simulation of Shore-Based Radar Based on Stokes Waves

The sea clutter model based on the physical sea surface can simulate radar echo at different times and positions and is more suitable for describing dynamic sea clutter than the traditional models based on statistical significance. However, when applying the physical surface model to shore-based radar, the effects of wave nonlinearity, breaking wave, shadow, and radar footprint size must be considered. In this paper, a dynamic sea clutter simulation scheme based on a nonlinear wave is proposed that uses random Stokes waves instead of linear superposition waves to simulate the nonlinear dynamic sea surface and then calculates echo in the form of scattering cells. In this process, the relationship between wind speed and the nonlinear factor of the Stokes wave is derived, a simple model of shadow modulation is provided, and a method for appending the sea clutter spikes formed by breaking waves is developed. The experimental results show that the simulated sea clutter and the real measured clutter have good consistency in intensity, amplitude statistical distribution, Doppler spectrum, and spatiotemporal correlation. The proposed scheme is suitable for the sea clutter simulation of shore-based radar and can also adjust the relevant parameters to extend to other types of sea clutter simulation.

Resonant sloshing in a rectangular tank under coupled heave and surge excitations

This paper investigates the resonant sloshing excited by coupled surge and heave excitations. A rectangular tank with a width-to-length ratio of W/L = 1/2 and an intermediate liquid depth of h/L = 0.2 are considered. Through laboratory experiments and numerical simulations, the nonlinear characteristics of the sloshing wave and dynamic pressure are investigated, and their correlations with the external excitation frequency are explored. It is found that when the sum or difference of the surge and heave frequencies approach to the system's odd-number-order natural frequencies, the resonant sloshing occurs even though neither the surge nor the heave excitation triggers resonance by itself. Nevertheless, the most violent sloshing happens when both heave and surge excitations locate in their corresponding resonant regions. The excitation frequency that induces the maximal resonance is slightly larger than that of the analytical value due to the effect of wave nonlinearity. The rising time and impact pressure during slamming under different excitation conditions are also analysed and discussed.

Effects of wave nonlinearity on submerged flexible vegetation dynamics and wave attenuation

Dynamic characteristics and wave attenuation mechanism of flexible vegetation have propelled to the forefront in investigations of coastal engineering. Given that existing studies of wave nonlinearity are mainly restricted to rigid vegetation assumptions, this study was undertaken to quantitatively determine the effect of wave nonlinearity on submerged flexible vegetation dynamics as well as wave attenuation based on flexible vegetation dynamic model and experimental results. Meanwhile, the influence of different wave theories along with different determination methods of characteristic wave velocity was evaluated quantitatively. Results reveal that wave nonlinearity exerts substantial nonlinear and nonmonotonic effects upon flexible vegetation dynamics and wave attenuation rate. The maximum horizontal force, stem tip excursion, and wave height attenuation rate increase as the dimensionless Ursell number increases on the whole under the present investigation conditions. Moreover, it is suggested that different wave theories and determination methods of characteristic wave velocity can result in slight discrepancies of flexible vegetation dynamics, which may further affect wave attenuation by flexible vegetation. Determining the impacts of wave nonlinearity, wave theory, and characteristic wave velocity provides clearer insight into the wave attenuation mechanism of flexible vegetation, which is of great benefit to the flexible vegetation dynamics and related wave attenuation model improvement.

Parameterization of nearshore wave breaker index

The performances of phase-averaged parametric nearshore wave transformation models depend significantly on a reliable estimate of the wave breaker index γ (the breaker height-to-depth ratio), a free model parameter that essentially controls the amount of breaking energy dissipation. While the previous studies have suggested separate relationships between γ and the offshore wave steepness (s0) or the normalized local water depth (kh), the parameterization of γ still requires further investigation considering a wider variety of conditions and a sounder physical basis. In this study, we use the field datasets of wave height and the inverse modelling approach to reveal a composite dependence of γ on both s0 and kh. Specifically, the results show a positive dependence of γ on kh for larger s0, and a negative dependence of γ on kh for smaller s0. Based on such composite relationships, a new γ formula is proposed, and its performance is verified against the available datasets of wave height in three coasts and 14 laboratory tests. Implementation of this new formula in a parametric wave model leads to the error reduction of wave height prediction by 10–24% (mean = 19%) relative to seven widely used models in literatures. In particular, a remarkably higher model accuracy is obtained under wave conditions with small offshore wave steepness, which is important for studying onshore sediment transport and beach recovery. Two counteractive physical mechanisms for wave nonlinearity effects, namely the breaking intensification mechanism and the breaking resistance mechanism, are suggested to explain the opposite γ-kh relationships within different ranges of s0.

Numerical investigation of solitary wave attenuation and resistance induced by rigid vegetation based on a 3-D RANS model

Mangrove forests can significantly attenuate tsunami waves and thus play an important role in coastal protection. As a first approximation, the problem is modeled utilizing solitary waves impinging on emergent/submerged rigid cylinders. A three-dimensional (3-D) numerical model using cyclic boundary conditions was developed based on the IHFOAM solver to investigate the effects of wave nonlinearity and vegetation configuration on the solitary wave attenuation. The numerical model was established based on the Reynolds Averaged Navier-Stokes (RANS) equations combined with the standard k – ω shear stress transport (SST) turbulence model and the volume of fluid (VOF) surface capturing schemes. The results indicate that different patterns are found in terms of flow field characteristics (velocity and turbulent kinetic energy) and forces exerted on the cylinders for various wave nonlinearity and vegetation configuration, which helps to better understand wave dissipation mechanism induced by vegetation. Different from the bulk drag coefficient derived by the conventional wave dissipation models, the direct force method was applied to quantify the time-varying and period-averaged drag coefficients (CD) of individual cylinders. The time-varying CD associated with maximum force and local velocity is defined as the representative CD, for comparison with the period-averaged CD in detail. Besides, by considering the submergence ratio, new generic CD formulas are proposed as functions of the modified Reynolds number (Re) and Keulegan-Carpenter number (KC) for illustrating the CD dynamics under solitary wave conditions. Finally, a preliminary comparison between the proposed CD formulas and existing formulas are given to reveal the intrinsic CD law, which may lead to improved understanding and modeling concerning wave-vegetation interaction.

Importance of Wave Non-linearity for 3D Morphodynamic Modelling

Mengual, B.; Bertin, X., and Martins, K., 2020. Importance of wave non-linearity for 3D morphodynamic modelling. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1201-1205. Coconut Creek (Florida), ISSN 0749-0208.The effect of wave non-linearity on morphological changes of a sandbar is investigated through a realistic application at Duck Beach (North Carolina, USA) of a 3D state-of-the-art process-based morphodynamic model, which couples sediment transport, currents and waves (vortex force formalism). From simplified 1D/2DH models, previous studies highlighted that acceleration skewness of non-breaking waves over a sandbar could promote its progressive onshore migration. This process can counterbalance the offshore migration occurring under breaking waves through the development of strong offshore-directed “undertow” currents near the seabed. Based on the existing literature, an additional bedload flux associated to acceleration skewness of waves is implemented in the 3D model. Numerical experiments with and without this additional term clearly demonstrate the need to account for this supplementary wave-induced transport to reproduce onshore migration phases of the sandbar. Effectively, even a model integrating wave asymmetry effects on bedload flux estimates and 3D wave-current interactions fails to reproduce the observed onshore migration of the sandbar.

Modeling of net sediment transport rate due to wave-driven oscillatory flow over vortex ripples

A one-dimensional-vertical (1-DV) model is developed for predicting net ripple-averaged sediment transport rate over a rippled bed under wave-driven oscillatory boundary layer flows. This model is extended from a sheet-flow model developed by Yuan and Tan [52], which is able to account for the effect of wave nonlinearity (velocity skewness and asymmetry) together with a mild bottom slope. The rippled bed is conceptualized as a flat bed with a large bottom roughness accounting for the presence of ripples in modeling the boundary layer flow and sediment concentration. The vortex-shedding effect is incorporated into the model by adding a pick-up rate on top of the one induced by skin-friction turbulence. The model performance is good for 2-D ripples under periodic oscillatory flows, which are used for calibrating the model. We also showed that it is applicable for 3-D ripples and irregular oscillatory flows. In addition, this 1-DV model can capture some intermediate ripple- and period-averaged physical processes, e.g., cycle averages of velocity, sediment concentration and sediment flux, suggesting that the model correctly captures the underlying physics. The relative importance of vortex-shedding effect is shown to be controlled by ripple dimension, sediment grain size and the driving mechanisms for net sediment transport rates.

A coupled mathematical model for accumulation of wave-induced pore water pressure and its application

Prediction of the wave-induced instability of seabed due to the build-up of pore water pressure is essential for coastal engineers involved in the foundation design of marine infrastructure. Most Previous studies have been limited to decoupled residual mechanism for the rise in excess pore water pressures. In this study, the existing decoupled approach has been improved to consider the coupling effect between the development of pore water pressures and evolution of seabed stresses. Comparisons with the existing wave flume tests and geotechnical centrifuge wave tests have demonstrated that the developed coupling approach is capable of reproducing the accumulation of pore water pressure under cyclic wave loadings, and shows more promising predictions compared to the existing decoupled model, especially for the case of standing waves. The validated framework is further extended to a field scale numerical model to investigate the development of pore water pressures and the corresponding liquefaction susceptibility of seabed to water waves. The numerical results have revealed the different mechanism for wave-induced pore pressure build-up in marine soils between the developed model and the existing decoupled model. The coupling effect of residual pore pressure and seabed stress could accelerate pore pressure accumulation, which implies that the existing decoupled model may underestimate the liquefaction potential of seabed, particularly under standing wave loadings. Furthermore, results of the developed model have shown that the effect of wave nonlinearity on advancing seabed liquefaction is more noticeable for progressive waves than that for standing waves.

Weakly nonlinear propagation of pressure waves in liquids containing translational bubbles acting a drag force

Weakly nonlinear (i.e., finite but small amplitude) propagation of plane pressure waves in liquids uniformly containing many spherical microbubbles is theoretically investigated. Although the effects of a translation of bubbles and a drag force acting on bubbles are incorporated, the creation, extinction, coalescence, break up, and polydispersity of bubbles are not considered. From the second order of approximation based on the method of multiple scales, the KdV–Burgers equation for a low frequency long wave is derived from the basic equations for bubbly flows composed of the conservation equations in a two-fluid model installing a virtual mass force and the bubble-dynamics equation for spherical symmetric oscillating translational bubbles. As a result, the translation of bubbles increased an effect of wave nonlinearity in a far field.

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.

Phase‐Averaged Drag Force of Nonlinear Waves Over Submerged and Through Emergent Vegetation

AbstractAquatic vegetation protects the shoreline by dissipating the wave energy and reducing the mean water level. For the latter, the phase‐averaged depth‐integrated drag force induced by vegetation ( ) plays an essential role. For linear waves, the exerted by submerged vegetation ( ) and by the submerged part of emergent vegetation ( ) equal 0. As the wave nonlinearity increases, the profile of the horizontal velocity (u) becomes skewed and non–cosine shaped, and thus, both and are nonzero (phase average of u|u|≠0) and their significance increases. This study examines the effects of wave nonlinearity and vegetation submergence on based on stream function wave theory. In deep water, it is found that the wave nonlinearity slightly affects due to the negligible weight of in the overall . Both the wave nonlinearity and vegetation submergence have negligible effects on as well. In shallow water, takes up a large percentage in the overall for emergent vegetation, and a linear relationship between and vegetation submergence exists for waves with relatively small wave heights. The applicable range of the linear wave theory based is determined using from stream function wave theory as a reference solution. Moreover, a parametric model is developed for evaluating for random waves. The mean water level changes, or wave setup, on a vegetated sloping beach are validated and quantified using experimental data obtained from literature.

Numerical simulation of an oscillating water column device installed over a submerged breakwater

In this paper, an example of a symbiotic combination of marine structures is studied. The base hydrodynamic performance of a traditional offshore oscillating water column (OWC) device is compared against the case in which it is constructed over a submerged breakwater. Numerical simulations are performed with the open source package OpenFOAM and the toolbox waves2Foam. The classical free surface capturing method volume of fluid (VOF) is employed to model first-order Stokes waves. The effects of the dimensions (height and length) of the submerged breakwater on the hydrodynamic characteristics, such as wave energy conversion efficiency (ξ), reflection coefficient (Cr), transmission coefficient (Ct), and energy dissipation ratio (ED) are explored thoroughly. Moreover, the effect of wave nonlinearity induced by increasing incident wave heights on the OWC device is examined. The results show that a proper configuration of the submerged breakwater is significantly helpful to optimize the energy conversion curve. Varying breakwater length will lead to a periodic variation in energy absorption efficiency. In addition, a higher incident wave height will lead to a lower energy absorption efficiency but a stronger dissipation ratio.

The effects of wave non-linearity on wave attenuation by vegetation

Wave attenuation through mangrove forests has received more and more attention, especially in the context of increasing coastal erosion and sea-level-rise. Numerous studies have focused on studying the reduction of wave height in a mangrove forest. However, the understanding of this attenuation process is still in its infancy. In order to obtain more insight, a laboratory experiment, mimicking the processes of wave attenuation by coastal mangroves in the Mekong Delta, Vietnam was conducted. The reduction of wave height for different scenarios of mangrove densities and wave conditions was investigated. A new method to quantify vegetation attenuation induced by vegetation is presented. The wave height reduction is presented over a relative length scale (viz. the number of wavelengths), instead of an absolute length scale of the forest (e.g per meter or per 100 m). The effects of wave non-linearity on the wave height attenuation over the mangrove forest were investigated using the Ursell number. It is suggested that the non-linear character of waves has a strong influence on the attenuation of the waves inside the mangrove forest. A numerical model, mimicking the experiment was constructed in SWASH and validated using the experimental data. Finally, the data set was extended through numerical modelling so that a larger ranging relationship between wave attenuation per wave length and the Ursell number could be formulated.

Wave Nonlinearity Correction for Parametric Nearshore Wave Modelling

Zhang, C.; Zhang, Q.; Lei, G.; Cai, F.; Zheng, J., and Chen, K., 2018. Wave nonlinearity correction for parametric nearshore wave modelling. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 996–1000. Coconut Creek (Florida), ISSN 0749-0208.Many phase-averaged parametric nearshore wave models are based on the energy balance concept and use linear wave theory to calculate wave parameters (e.g., wave energy, wave height, wave setup). For a wave propagating into shallow water, however, its shape becomes skewed/asymmetric and the linear wave theory may not be appropriate. Seven cases of model-data comparison for regular wave transformation over sloping and barred beaches are carried out. It is shown that the model using linear wave theory underestimates the regular wave height near the breakpoint, and overestimates the breaking roller length in the surf zone. An empirical method is proposed to improve the performance of the parametric wave models in shallow waters by correcting the key model parameters to include wave nonlinearity effects. This includes (1) development of a new empirical formula for the nonlinear wave shape factor, (2) using a nonlinear wave celerity formula, and (3) implementing a new empirical formula for breaking roller slope. These formulas are functions of wave steepness and Ursell number. The proposed method systematically improves predictions of wave height, wave setup and roller evolution under regular wave transformation with different beach configurations. In particular, the peaks of wave height and mean water level near the breakpoint as well as the roller length variation in the surf zone are accurately captured by the wave nonlinearity-corrected model.

One-dimensional and two-dimensional Green–Naghdi equations for sloshing in shallow basins

This paper presents a verified model of weakly non-linear wave sloshing in shallow basins, based on level I Green–Naghdi (GN) mass and momentum equations derived for mild-sloped beds. The model is verified for sloshing of an initially sinusoidal free surface perturbation in a square tank with a horizontal bed. The model is also used to investigate free surface sloshing of an initial Gaussian hump in closed square basins, over horizontal and non-uniform bed topographies. Analysis of the free surface slosh motions demonstrates that the model gives predictions in satisfactory agreement with the analytical solution of linearised shallow water theory obtained by Lamb. Discrepancies between GN predictions and linear analytical solutions arise from the effect of wave non-linearities arising from the wave amplitude itself and wave–wave interactions.