Wave Forces Research Articles

Optimal multiple tuned mass dampers for monopile supported offshore wind turbines using Genetic Algorithm

This study investigates the parametric optimization of multiple-tuned mass dampers (MTMDs) deployed along the length of a tower and monopile structure subjected to stochastic wind and wave forces. The structural components, comprising the tower and monopile, are conceptualized as Euler–Bernoulli beams. The interaction with the soil is modeled through viscoelastic springs distributed along the monopile. The rotor nacelle assembly (RNA) and blades are abstracted into a concentrated mass at the tower’s apex. The MTMDs are characterized as spring–mass–dashpot systems strategically positioned at intervals along the tower and monopile. The investigation involves a random vibration analysis under wind and wave loads, employing the Kaimal spectrum for wind and the JONSWAP spectrum for waves. The study focuses on optimizing the TMD parameters using H2 optimization techniques, with the optimization criteria being the minimization of the standard deviation of the tower’s top displacement response. Additionally, meta-heuristic algorithms like the genetic algorithm (GA) are utilized to refine the determination of these optimal parameters. A key aspect of the research includes a parametric study that reveals variations in optimal parameters as the number of TMDs is altered, maintaining a consistent total mass across the MTMDs.

Eddy–Internal Wave Interactions and Their Contribution to Cross-Scale Energy Fluxes: A Case Study in the California Current

Abstract Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes.

Resonant response of a flexible semi-submersible floating structure: experimental analysis and second-order modelling

The dynamics and nonlinear wave forcing of a flexible floating structure are investigated experimentally and numerically. The floater was designed to match sub-harmonic rigid-body natural frequencies of typical floating wind turbine substructures, with the addition of a flexible bending mode. Experiments were carried out for three sea states with phase-shifted input signals to allow harmonic separation of the measured response. We find for the weakest sea states that sub-harmonic rigid-body motion is driven by even-harmonic difference frequency forcing, and by linear forcing for the strongest sea state. The flexible mode was tested in a soft, linearly forced layout, and a stiff layout, forced by second-, third- and fourth-harmonic frequency content, for increasing severity of the sea state. Further insight is gained by analysis of the amplitude scaling of the resonant response. A new simplified approach is proposed and compared with the recent method of Orszaghova et al. (J. Fluid Mech., vol. 929, 2021, A32). We find that resonant surge and pitch motions are dominated by even-harmonic potential-flow forcing and that odd-harmonic response is mainly potential-flow driven in surge and mainly drag driven in pitch. The measured responses are reproduced numerically with second-order forcing and quadratic drag loads, using a recent and computationally efficient calculation method, extended here for the heave, pitch and flexible motions. We are able to reproduce the response statistics and power spectra for the measurements, including the subharmonic pitch and heave modes and the flexible mode. Deeper analysis reveals that inaccuracies in the even-harmonic forcing content can be compensated by the odd-harmonic loads.

Global asymptotic stability of endemic equilibria and stability of traveling waves for a diffusive SIR epidemic model with logistic growth

AbstractThis paper deals with the asymptotic behavior of solutions for the diffusive epidemic model with logistic growth. In the first part, we consider the initial boundary value problem on the bounded domain and derive the stabilization of the solutions of the reaction–diffusion system to a constant equilibrium. In the second part, we consider the initial value problem on $${\mathbb {R}},$$ R , and derive the stability of forced waves under certain perturbations of a class of initial data.

3D numerical modeling of wave–monopile–seabed interaction in the presence of a scour hole

Coastal engineers are deeply concerned about wave-induced seabed instability around monopile foundations. Most prior studies have primarily focused on the seabed response around monopiles on flat seabeds, often neglecting the presence of scour holes commonly found in engineering practice. This study thoroughly investigates seabed response and liquefaction around monopiles of scour holes. The examination involves analyzing 3D flow velocities, dynamic wave loads, pore pressures, soil effective stresses, and wave forces around a monopile with a scoured profile. The analysis uses a model that integrates the interactions between waves, seabed, and structures, and it is implemented within the OpenFOAM framework. The study meticulously assesses the impact of scour holes on seabed responses and liquefaction zones around monopile foundations. Numerical results reveal that: (1) The magnitude of the pore pressure within the scoured seabed is reduced relative to a flat seabed; (2) Considering the scour hole effect leads to a more uniform distribution of liquefaction depth around the monopile; (3) This effect intensifies with a higher saturation degree, while it exhibits a pattern of increase, followed by a decrease with an increase in permeability.

Repeatability of beach morphology change under identical wave forcing

Laboratory investigations of beach morphology change under wave action are undertaken to gain insight into coastal processes, design coastal structures and validate the predictions of numerical models. For the results of such experiments to be reliable, it is necessary that they are repeatable. The equilibrium beach concept, that beach morphology will evolve to a quasi-static equilibrium shape for a given forcing suggests that experiments should be repeatable to some degree. However, sediment transport in turbulent breaking and broken waves is complex and highly variable and the level of repeatability at different temporal and spatial scales is challenging to measure, as such, previous work has restricted comparisons to small numbers of waves. Here we use the results of two identical, 20-h large-scale wave flume experiments to investigate the repeatability of sediment transport and beach morphology change under waves at timescales down to individual swash events. It is shown that while flow characteristics from identical swash events are very repeatable, the sediment transported can be very different in both magnitude and direction due to differences in turbulence, sediment advection and morphological feedback. Over longer periods containing multiple matching swash events however, the beach responds in a very similar manner, with the level of morphological repeatability increasing with time. The results also demonstrate that gross swash zone sediment transport remains high even as a beach profile approaches quasi-equilibrium, but the proportion of individual swash events that cause large sediment fluxes (>±7.5 kg/event/m) reduces with time. The results of this laboratory study indicate that beach morphology change has a level of determinism over timescales of several minutes and longer, giving confidence in the results from physical modelling studies. However, the large differences in sediment transport from apparently identical swash events questions the value in pursuing numerical predictions of sediment transport at the wave-by-wave timescale unless the reversals in sediment transport between apparently near identical swash events can also be predicted.

Dust-storm forcing of Rossby waves on Mars

Off-nadir measurements by the Mars Climate Sounder are an underutilized source of information about planetary-scale waves and their role in the climate. More than 8 Mars years of data is currently available. The data set is used here to investigate a pair of waves whose vertical structure is well aligned with the off-nadir contribution function of the A3 channel. Both waves have a zonal wavenumber of 1 and a large amplitude in the high-latitude, winter-season, westerly jet. One is an eastward-traveling free wave with a period of 15–20 sols; it recurs annually in the north, appearing in most years in a roughly 50-sol span that ends near the winter solstice. The other is a forced Rossby wave that alternates between the north and the south, emerging at the autumnal equinox and subsiding at the vernal equinox. It is stationary with respect to the surface in the south and quasi-stationary in the north. A-type and C-type regional dust storms cause a conspicuous increase in the amplitude of the northern forced wave through their effect on the meridional overturning circulation. The dust-storm enhancement of the overturning circulation is initially confined in longitude, as determined by the spatial distribution of dust in the southern hemisphere at the start of the storm. The amplification of the forced wave is a consequence of this zonal asymmetry. The wave amplitude increases rapidly at the start of each dust storm and returns to its pre-storm level 10–15 sols later when the distribution of dust becomes zonally uniform. A detailed description of the forced wave is obtained from the OpenMARS reanalysis, whose reliability is confirmed by comparisons with the off-nadir measurements. During the early stage of the A and C storms, the wave amplitude exceeds 3 km in geopotential height and the center of the polar vortex is displaced from the pole. In addition, the northern forced wave exhibits a pre-winter-solstice phase reversal whose origin is not known.

Technical note: Multi-year changes in the Brewer–Dobson circulation from Halogen Occultation Experiment (HALOE) methane

Abstract. This study makes use of Halogen Occultation Experiment (HALOE) methane (CH4) in a search for multi-year changes in the Brewer–Dobson circulation (BDC). Changes in CH4 are determined for three successive 5-year time spans from 1992 to 2005, and there are significant differences between them. There is a clear separation between the changes in the Northern Hemisphere near 30 hPa and at the transition of the shallow and deep branches of the BDC. The CH4 changes are positive and large in the shallow branch following the eruption of Pinatubo, but they then decrease and agree with tropospheric trends in the late 1990s and early 2000s. CH4 decreases in the upper part of the deep branch from 1992 to 1997 or following the eruption of Pinatubo. CH4 continues to decrease in the deep branch in the late 1990s but then increases in the early 2000s, although those changes are small compared with the seasonal and interannual variations of CH4. Multi-year changes are due, in part, to wave forcings during the El Niño–Southern Oscillation (ENSO) of 1997–1998 and beyond and to episodic, sudden stratospheric warming (SSW) events during both time spans. It is concluded that time series of HALOE CH4 provide effective tracer diagnostics for studies of the nature of the BDC from 1992 to 2005.

Self-similarity of the dipole–multipole transition in rapidly rotating dynamos

The dipole–multipole transition in rapidly rotating dynamos is investigated through the analysis of forced magnetohydrodynamic waves in an unstably stratified fluid. The focus of this study is on the inertia-free limit applicable to planetary cores, where the Rossby number is small not only on the core depth but also on the length scale of columnar convection. By progressively increasing the buoyant forcing in a linear magnetoconvection model, the slow magnetic–Archimedean–Coriolis (MAC) waves are significantly attenuated so that their kinetic helicity decreases to zero; the fast MAC wave helicity, on the other hand, is practically unaffected. In turn, polarity reversals in low-inertia spherical dynamos are shown to occur when the slow MAC waves disappear under strong forcing. Two dynamically similar regimes are identified – the suppression of slow waves in a strongly forced dynamo and the excitation of slow waves in a moderately forced dynamo starting from a small seed field. While the former regime results in polarity reversals, the latter regime produces the axial dipole from a chaotic multipolar state. For either polarity transition, a local Rayleigh number based on the mean wavenumber of the energy-containing scales bears the same linear relationship with the square of the peak magnetic field measured at the transition. The self-similarity of the dipole–multipole transition can place a constraint on the Rayleigh number for polarity reversals in the Earth.

Visual identification of wave load on a four-cylinder array with incomplete waterline information

This study utilized computer vision technology to identify the wave force acting on a four-cylinder array arranged in a square configuration, particularly when confronted with a visual obstruction. In the absence of comprehensive waterline data, a theoretical derivation based on linear wave theory was formulated to ascertain the wave force. Experimental trials were executed in a wave flume to authenticate the identification of wave force under both regular and irregular wave conditions. The simultaneous capture of images from four cameras was employed, with the Canny operator utilized for extracting the dynamic waterline encompassing the array of four cylinders. This affirms the efficacy of the proposed method in identifying wave force within visual obstructions of waterlines. Utilizing a single-camera perspective that encompassed 35% of the waterline surrounding the cylindrical array, the identification errors of the standard value were found to be less than 10%. The reduction of identification error can be achieved by enhancing the completeness of waterline information.

An Eddy Pair in the Northwestern Bay of Bengal: Characteristics, Dynamics and Interannual Variability

AbstractMesoscale eddies are active in the Bay of Bengal and have profound effects on the dynamic conditions, the transport of heat and salt, and the primary productivity. We report a pair of periodic eddies in the Bay of Bengal and examine their characteristics, dynamic mechanisms and interannual variability based on satellite observations and a nonlinear 1.5‐layer reduced‐gravity model. The eddy pair mainly occupies the northwestern Bay of Bengal from March to May and consists of a cyclonic eddy in the north and an anticyclonic eddy in the south. The anticyclonic eddy is generated by local wind forcing, whereas the cyclonic eddy is significantly contributed by equatorial and coastal Kelvin waves. On an interannual scale, the eddy pair was exceptionally weak in 1999, 2000 and 2008 due to the extreme La Niña events in these years when the westerly wind anomaly over the equatorial Indian Ocean weakened the local wind forcing and coastal Kelvin waves. This study provides new knowledge on periodic eddies in the Bay of Bengal and advances our understanding of the dynamic connections between this marginal sea and the equator.

Effects of wave forces on sediment transport patterns in micro-tidal estuaries

Estuarine sediment transport is driven by the combined action of a multitude of influencing factors, including astronomical tides, waves dynamics, and river discharges. This study focuses on the effects of wave forces on sediment transport patterns in micro-tidal estuaries near Wanbao Beach, China. Numerical simulations are carried out using Delft3D. Modeling scenarios are configured using different wave characteristics, spanning from typical waves to those with a return period of 50 years. Results show that waves have a positive effect on landward sediment transport, resulting a larger active range of sediment. By comparing the spatial geomorphic variations under varying wave conditions, we find that modifications in significant wave height (Hs) primarily impact the position of erosion and deposition zones, whereas alterations in spectral peak period (Tp) predominantly influence the magnitude of these changes. The finding is further demonstrated by a comparison of residual currents under different wave intensities. Analysis of sediment transport rates in different transects indicates that the sediment transport rate is highest at the mouth transects and lowest at the alongshore transects. Moreover, variations in sediment transport rates exhibit distinctive patterns between the two outlet transects, even when subjected to identical wave conditions. The disparities are attributed to differences in runoff and the topographical features in proximity to the estuaries. Additionally, we find the sediment transport rate becomes insensitive to the variations in Hs when Hs is larger than a threshold value. The threshold decreases with increasing Tp.

Simulation of elastic guided waves in concrete structures: A parametric study for construction materials

Concrete buildings constructed globally are susceptible to diverse circumstances of use and exposure to environmental elements. Diverse varieties of construction materials are used in the building sector to fabricate edifices and constructions. Architects and construction project managers use these classifications of materials and products to precisely determine the materials and techniques employed in building projects. This study presents a simulation of elastic guided waves in concrete structures, which is motivated by the vast variety of uses of such structures. The elastic-guided wave technique is a technology used for nondestructive assessment. This approach utilizes acoustic waves that travel along an extended structure, directed by its limits. This enables the propagation of waves over a significant distance while minimizing energy dissipation. Currently, the Elastic guided wave method is extensively used for the examination and evaluation of various engineering structures, namely for inspecting metallic pipelines globally. From a single place, it is possible to investigate distances of several hundred meters in some instances. Additionally, there are apps available for the examination of rail tracks, rods, and metal plate constructions. In this research, a novel mathematical model is introduced for accurately replicating elastic guided waves in concrete structures in practical applications. To reinforce the current concrete structure using mathematics, graphene oxide powders with improved mechanical properties are obtained using the role of the mixture, and the Halpin-Tsai micromechanical model is used. After obtaining the mathematical modeling of the current concrete structure using the theory of shear deformation with four unknown high-order terms and Hamilton’s principle, the equations are solved using free and forced wave propagation approaches. Finally, some applicable suggestions for improving the efficiency and dynamic stability of the presented concrete structure reinforced by graphene oxide powders are presented in detail in the results section.

Small-scale field experiment on wave forces on a U-OWC breakwater

A small-scale field experiment is conducted on a U-Oscillating Water Column (U-OWC) incorporated into a model of caisson breakwater at the Natural Ocean Engineering Laboratory (NOEL) laboratory of Reggio Calabria (Italy). The U-OWC or REWEC (REsonant Wave Energy Converter) is a device belonging to the family of Oscillating Water Columns (OWCs), characterized by the introduction of a U-duct. Such a device is innovative, absorbing a high percentage of incoming sea energy and, then, to produce electricity via a Power-Take-Off (PTO). The aim of the present study is the investigation of the wave pressures and forces acting on the U-OWC monolithic coastal defense structure. Moreover, the structural response of the U-OWC structure is also investigated under the occurrence of wave crests, by calculating the hydrodynamic forces realized in the active parts of the U-OWC. It is shown as a global additional force is realized, which contributes to increase the overall stability of the structure. Considering the wave loads acting on the U-OWC caisson, the post-process of the overall dataset recorded during the real field experiment at NOEL laboratory reveals the occurrence of both quasi-static loading (non-breaking), and of impact loading (impulsive) due to wave breaking. Thus, a systematic analysis is pursued in order to identify the loading cases acting on the U-OWC breakwater. When high non-breaking sea waves interact with the breakwater, “Quasi-Standing (QS)” wave pressures and forces occur at modified structure with two peaks of equal intensity. Instead, the impact of extreme breaking waves against the U-OWC structure generates asymmetrical wave pressure records beneath the wave crests, with two peaks with different intensity: the first one greater than the second one. In these cases, “Slightly Breaking (SB)” wave forces and “Impact Loads (IL)” are identified. Wave pressure distributions and forces acting on the U-OWC model are, then, investigated for the three classes of wave loads. Moreover, the probability of occurrence of maximum positive peak forces is determined from the experimental dataset, given a number of parameters. In particular, when QSWs occur, the maxima peak forces are recorded for deeper water depths dn, d’ and a, at given significant wave height HSi. Instead, for SBWs and ILs, the extreme wave loads are realized, when the most severe sea states occur with higher HSi , and for decreasing water depth dn. d’ and a. Then, the influence both of the length of the berm and of the width of the U-duct in the front structure is considered. When the dimensions of both structural elements is reduced, the maxima wave forces occur in a fixed recorded sea state. Then, the Quasi-Determinism (QD) nonlinear model at the U-OWC breakwater is introduced for evaluation of Quasi-Standing wave loads, showing a good agreement among analytical and experimental results. Finally, the Goda's model is applied to calculate the wave pressure distributions acting on the external walls of the U-OWC model. The theoretical results given by the Goda's formulae are compared with experimental data, overestimating experimental results for both QSWs and SBWs and, significantly, underestimating IL conditions.

Power capture and power take-off load of a self-balanced dual-flap oscillating surge wave energy converter

Wave energy converters are an important part of future renewable energy infrastructure. Predicting their power matrix, capture width ratio, and power take-off loads at a targeted site is required for performance assessment before deployment. Because their testing is very expensive, numerical modeling and simulations play a significant role in those assessments. Linear potential flow theory has limited accuracy under large amplitude wave forcing. More accurate predictions can be obtained by using higher-fidelity models, which are computationally expensive. We present a framework for multi-fidelity numerical simulations to determine the hydrodynamic response, wave capture capability, and power take-off load of a full-scale dual-flap oscillating surge wave energy converter. This design exploits out-of-phase motion by setting the distance between the flaps to half the wavelength of the most occurring wave. The simulations are validated using a 1:10 model experiments in a wave tank. Based on these validations, it was determined that Euler simulations provide an acceptable prediction with 90% reduction in computational time with only 11% error. Utilizing Euler simulations at full-scale, the results demonstrate that the annual electrical energy output is 1.79 GWh under regular wave conditions. One significant improvement over single-flap designs is the capture width ratio which exceeds unity.

Wave Dynamics Around a Floating Circular Flexible Plate Over a Permeable Bed

Abstract In this paper, to determine the efficacy of the porous bed on damping far-field wave energy, the wave dynamics around a circular plate is studied. By combining the appropriate boundary conditions, the unknown potential is attained for the free surface and the plate-covered region. The Bessel series solution is attained further, by employing the matched eigenfunction expansion technique. Wave force excitation on the circular plate, deflection of the plate, and flow distribution is calculated and examined to comprehend the efficacy of the current investigation. Moreover, the motion of the plate is assessed in the time domain. The study reveals a substantial reduction in wave amplitude on the plate’s leeward side because of the energy dissipation by the porous bed. Also the study concludes that for intermediate values of porosity with larger wavenumbers, approximately 50% of wave power is dissipated with respect to incident wave power.

Analysis of Wave-Induced Forces on a Floating Rectangular Box with Analytical and Numerical Approaches

A three-dimensional mathematical hydrodynamic model associated with surface wave radiation by a floating rectangular box-type structure due to heave, sway, and roll motions in finite water depth is investigated based on small amplitude water wave theory and linear structural response. The analytical expressions for the radiation potentials, wave forces, and hydrodynamic coefficients are presented based on matched eigenfunction expansion method (MEFEM). The correctness of the analytical results of wave forces is compared with the construction of a numerical model using the open-source boundary element method code NEMOH. In addition, the present result is compared with the existing published experimental results available in the literature. The effects of the different design parameters on the floating box-type rectangular structure are studied by analyzing the vertical wave force, horizontal wave force, torque, added mass, and damping coefficients due to the heave, sway, and roll motions, and the comparison analysis between the forces is also analyzed in detail. Further, the effect of reflection and transmission coefficients by varying the structural width and drafts are analyzed.

Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine

Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine

Preconditioned Stratospheric Modulation on the Occurrence of Stratospheric Final Warmings

AbstractStratospheric Final Warmings (SFWs) are considered to have a distinct impact on the surface weather and stratospheric ozone. Most SFWs are predominantly wave‐driven, while previous studies generally focused on the effects of tropospheric anomalous wave forcing on stratospheric wave amplification. This study demonstrates the crucial role of preconditioned stratospheric modulation on the occurrence of wave‐driven SFWs in the Northern Hemisphere, using ERA5 reanalysis. In most cases, the preconditioned stratospheric state is the key factor in determining the occurrence of both early and late SFWs. The tropospheric anomalous wave forcing cannot independently trigger most SFWs without stratospheric modulation. The proportion of anomalous stratospheric signals followed by SFWs is much higher than that of anomalous tropospheric forcing, even if the proportions of SFWs preceded by anomalous stratospheric signals and tropospheric wave forcing are similar. Additionally, about 25% of SFWs are only preceded by stratospheric modulation without anomalously strong tropospheric wave amplification.

Characteristics and Mechanism of Interhemispheric Coupling in Austral Winter Revealed by Long‐Term Reanalysis Data for the Whole Middle Atmosphere

AbstractGlobal characteristics of dynamical fields for the interhemispheric coupling (IHC) initiated with a sudden stratospheric warming (SSW) in the southern hemisphere in the austral winter were examined using the global reanalysis for the whole neutral atmosphere from a data assimilation with satellite observations over 15 years of 2005–2019. Even in the austral winter, a strong cold equatorial stratosphere associated with the SSW, which is essential for the IHC, occurs about once every two years. The mechanism of the IHC in the austral winter is basically similar to that in the boreal winter. However, there are two significant differences in the IHC characteristics between the austral and boreal winters. One is that the SSW in the austral winter occurs mainly at midlatitudes, whereas the SSW in the boreal winter occurs mainly at high latitudes. As a result, a warm temperature anomaly simultaneously appears in the southern polar mesosphere in the austral winter, which is not observed for the boreal winter. The other is related to the seasonal variation of the quasi‐two‐day wave activity and induced forcing and gravity wave forcing in the summer mesosphere. For the IHC events occurring in July, when these wave activities and forcings are high, the response in the summer mesosphere is similar to that of the boreal winter. In contrast, for late August and September, when these wave forcings are weak, the response in the summer mesosphere is small. This result indicates that the IHC characteristics are largely influenced by the seasonal variation of these waves.