Search Results (9)

It is well-known that the bound long waves play an important role on beach morphology. The existence of the current will modify the intensity of the waves. To examine the more realistic problem where the current is non-uniform, a third-order analytical solution for bichromatic waves on currents with constant vorticity is derived using a perturbation method. Earlier derivations of theories for interactions between waves and currents have been limited to cases of bichromatic waves on depth-uniform currents and cases of monochromatic waves on linear shear currents. Unlike the derivations of monochromatic waves, the moving-frame method cannot be used in the case of bichromatic waves because there are multiple waves with different celerities, and the flow can in no way be treated as steady-state. Moreover, for shear currents where the flows are rotational, the velocity potential cannot be simply defined. For these reasons, it is difficult to carry out mathematical operations when the dynamic free surface boundary condition is applied. However, with the consideration of the wave part of the fluid motion remaining irrotational, some of the terms in the expanded boundary conditions can be ignored; thus, the derivations can be further processed. As a result, the third-order explicit expressions for the stream function, the velocity potential, and the surface elevation can be solved. The nonlinear dispersion relation is also derived to account for interacting wave components with different frequencies and amplitudes which can be used to solved for wavenumbers of both wave trains. The obtained solutions are verified by reducing to those of previous results for monochromatic waves and uniform currents. Furthermore, the influence of constant vorticity on the wave kinematics is illustrated. A comparison between following/opposing currents is also carried out. Finally, the effects of the shear current on the strength of the bound long waves are also illustrated. Full article

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information. Full article

A new validation campaign was conducted at the W2 Harold Alfond Ocean Engineering Laboratory at the University of Maine to investigate the hydrodynamic loading on floating offshore wind substructures, with a focus on the low-frequency contributions that tend to drive extreme and fatigue loading in semisubmersible designs. A component-level approach was taken to examine the hydrodynamic loads on individual parts of the semisubmersible in isolation and then in the presence of other members to assess the change in hydrodynamic loading. A variety of wave conditions were investigated, including bichromatic waves, to provide a direct assessment of difference-frequency wave loading. An assessment of the impact of wave uncertainty on the loading was performed, with the goal of enabling validation with this dataset of numerical models with different levels of fidelity. The dataset is openly available for public use and can be downloaded from the U.S. Department of Energy Data Archive and Portal. Full article

Current mid-fidelity modeling approaches for floating offshore wind turbines (FOWTs) have been found to underpredict the nonlinear, low-frequency wave excitation and the response of semisubmersible FOWTs. To examine the cause of this underprediction, the OC6 project is using computational fluid dynamics (CFD) tools to investigate the wave loads on the OC5-DeepCwind semisubmersible, with a focus on the nonlinear difference-frequency excitation. This paper focuses on assessing the uncertainty of the CFD predictions from simulations of the semisubmersible in a fixed condition under bichromatic wave loading and on establishing confidence in the results for use in improving mid-fidelity models. The uncertainty for the nonlinear wave excitation is found to be acceptable but larger than that for the wave-frequency excitation, with the spatial discretization error being the dominant contributor. Further, unwanted free waves at the difference frequency have been identified in the CFD solution. A wave-splitting and wave load-correction procedure are presented to remove the contamination from the free waves in the results. A preliminary comparison to second-order potential-flow theory shows that the CFD model predicted significantly higher difference-frequency wave excitations, especially in surge, suggesting that the CFD results can be used to better calibrate the mid-fidelity tools. Full article

Surface water waves is an important research topic in coastal and ocean engineering due to its influences on various human activities. In this study, our purpose is to gain a deeper insight on the effects of non-hydrostatic (NHS) pressure on surface wave motions and its role in numerical modeling, based upon the high-order NHS model and optional vertical accelerations. The relative contribution of non-hydrostatic effects (P_nhs/P_hs) and its sensitivity on phase celerity and amplitude of dispersive waves are quantified. The vertical structure of P_nhs/P_hs clearly indicates stronger NHS effects in deeper waters and its significance near the surface. The NHS effects mainly slow down wave celerity and maintain incident amplitude for linear dispersive waves. The NHS effects are also responsible for increased amplitude and phase speed under strong non-linearity. The inter-relation between (un)realistic physical responses and model errors is discussed. Further, four experimental conditions for waves with complicated interactions are examined. Overall, the NHS effects play a critical role in side-band generation of bi-chromatic waves, and increased celerity and amplitude during nonlinear shoaling, as well as velocity moderation under co-existence of depth-varying currents. Possibly owing to weaker wave–wave interactions, however, wave directionality does not strongly interfere with FNHS/QNHS (Fully/Quasi Non-HydroStatic) effects on a fast-modulated nonlinear evolution of spatial focusing or diffraction waves. Full article

Three open source wave models are applied in 2DV to reproduce a large-scale wave flume experiment of bichromatic wave transformations over a steep-sloped dike with a mildly-sloped and very shallow foreshore: (i) the Reynolds-averaged Navier–Stokes equations solver interFoam of OpenFOAM^® (OF), (ii) the weakly compressible smoothed particle hydrodynamics model DualSPHysics (DSPH) and (iii) the non-hydrostatic nonlinear shallow water equations model SWASH. An inter-model comparison is performed to determine the (standalone) applicability of the three models for this specific case, which requires the simulation of many processes simultaneously, including wave transformations over the foreshore and wave-structure interactions with the dike, promenade and vertical wall. A qualitative comparison is done based on the time series of the measured quantities along the wave flume, and snapshots of bore interactions on the promenade and impacts on the vertical wall. In addition, model performance and pattern statistics are employed to quantify the model differences. The results show that overall, OF provides the highest model skill, but has the highest computational cost. DSPH is shown to have a reduced model performance, but still comparable to OF and for a lower computational cost. Even though SWASH is a much more simplified model than both OF and DSPH, it is shown to provide very similar results: SWASH exhibits an equal capability to estimate the maximum quasi-static horizontal impact force with the highest computational efficiency, but does have an important model performance decrease compared to OF and DSPH for the force impulse. Full article

More than three decades ago, it was noted that the ocean infragravity bound wave increasingly lags behind the forcing short-wave groups when propagating towards the shore. To date, the most recent theoretical prediction of this so-called phase lag remained a first-order approximation in terms of depth variations. Here, a new semi-analytical solution is proposed which does not rely on this approximation. Strong agreement is obtained when the new solution is compared with high-resolution laboratory data involving both bichromatic and random wave conditions. This newly proposed theoretical phase lag is then extensively compared with the former one, highlighting an increasing discrepancy between the two solutions as the relative bottom slope increases. The four influencing parameters, namely the bottom slope, the water depth, the incident short-wave peak period and the incident group period, are shown to impact, each in a specific way, the bound wave phase lag. While the latter is seen to increase with lower water depths and/or with higher short-wave peak periods, both the bottom slope and the group period can affect the phase lag in a different manner. Indeed, steeper bed slopes induce lower phase lags in shallow water but higher ones in deep water, while higher group periods induce higher phase lags for gentle slopes but lower ones for steep slopes. Full article

Methods for the separation of long-crested linear waves into incident and reflected waves have existed for more than 40 years. The present paper presents a new method for the separation of nonlinear bichromatic long-crested waves into incident and reflected components, as well as into free and bound components. The new method is an extension of a recently proposed method for the separation of nonlinear regular waves. The new methods include both bound and free higher harmonics, which is important for nonlinear waves. The applied separation method covers interactions to the third order, but can easily be extended to a higher orders. Synthetic tests, as well as physical model tests, showed that the method accurately predict the bound amplitudes and incident and reflected surface elevations of nonlinear bichromatic waves. The new method is important in order to be able to describe the detailed characteristics of nonlinear bichromatic waves and their reflection. Full article

This paper describes a set of spectral and eigen analysis in order to identify seiche generation from a large-scale laboratory dataset. The experiments were performed in the large-scale “Canal d’Investigació i Experimentació Marítima” wave flume at the Universitat Politècnica de Catalunya in Spain. Erosive and accretive wave regimes have been analyzed, including monochromatic waves and bichromatic wave groups with different bandwidths. Each test started with approximately the same underlying beach conditions. Video runup measurements are also used to better understand the role of the bandwidth in the generation of swash oscillation. Some evidence of the influence of low frequency waves on runup and sediment transport pattern is found. Good agreements between eigenmode families for volume flux and sediment volume variations are also shown. Full article