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In spectral wave models, the nonlinear triad source term accounts for the transfer of energy to the bound higher harmonics. This paper presents an extension to commonly used spectral models that resolves the evolution of the bound wave energy by keeping track of the energy that has been bound by the triad interactions. This extension is referred to as the bound wave evolution (BWE) model. From this, the spatial evolution of the bound wave height is obtained, which serves as a proxy for the nonlinear wave shape. The accuracy of these bound wave heights, and thus wave shape predictions, is highly dependent on the accuracy of the triad source term. Therefore, in this study, the capability of the LTA and SPB triad formulations to capture the growth of the bound wave height is evaluated. For both of these formulations, it is found that slope dependent calibration parameters are required. Overall, despite being computationally more expensive, the SPB method proves to be significantly more accurate in predicting the bound wave evolution. In the shoaling zone, where the bound wave energy is dominated by triads, the BWE model is well capable of predicting the nonlinear wave's shape. In the surf zone, however, where a combination of triads and wave breaking control the spectral evolution, the BWE model over-predicts the bound wave height. Nevertheless, this paper shows the promising capabilities of spectral models to predict the nonlinear wave shape. [ABSTRACT FROM AUTHOR]

Internal solitary waves in polar regions have attracted much interest recently. It is important to understand how sea ice affects them as this may have a profound influence on human activities and the environment. In this study, experiments on internal solitary waves with and without two types of sea ice (ice sheet and ice keel) are presented, as well as corresponding simulations using the Korteweg-de Vries (KdV) equation, the Benjamin-Ono (BO) equation, and the variable-coefficient Korteweg-de Vries (vKdV) equation, which is a derivation of the KdV equation. Comparison between experiments without sea ice and simulations using the KdV and BO equations proves the suitability of the former over the latter for this study. The experiments with sea ice and theoretical simulations using the vKdV equation provide evidence for wave deformation, oscillation occurring in the rear of the wave, and a decrease in amplitude. The latter suggests possibilities of energy dissipation or the emission of small amplitude linear waves. The sharp vertices of the ice result in occasional inconsistency with the vKdV predictions. Nonetheless, the vKdV equation is still suitable for modeling internal solitary waves under sea ice, giving generally accurate results that can assist further studies. This is the first time the vKdV equation has been applied to investigate the impacts of sea ice on internal solitary waves.

In spectral wave models, the nonlinear triad source term accounts for the transfer of energy to the bound higher harmonics. This paper presents an extension to commonly used spectral models that resolves the evolution of the bound wave energy by keeping track of the energy that has been bound by the triad interactions. This extension is referred to as the bound wave evolution (BWE) model. From this, the spatial evolution of the bound wave height is obtained, which serves as a proxy for the nonlinear wave shape. The accuracy of these bound wave heights, and thus wave shape predictions, is highly dependent on the accuracy of the triad source term. Therefore, in this study, the capability of the LTA and SPB triad formulations to capture the growth of the bound wave height is evaluated. For both of these formulations, it is found that slope dependent calibration parameters are required. Overall, despite being computationally more expensive, the SPB method proves to be significantly more accurate in predicting the bound wave evolution. In the shoaling zone, where the bound wave energy is dominated by triads, the BWE model is well capable of predicting the nonlinear wave’s shape. In the surf zone, however, where a combination of triads and wave breaking control the spectral evolution, the BWE model over-predicts the bound wave height. Nevertheless, this paper shows the promising capabilities of spectral models to predict the nonlinear wave shape.

Sandy slope erosion leads to coast degradation and exacerbates coastal zone instability and failure. As an eco-friendly engineering technology, microbial-induced calcium carbonate precipitation (MICP) can provide a protection method against sandy slope erosion. In this study, a series of flume tests were conducted to investigate the wave erosion resistance of the MICP-treated sandy slope. The penetration tests were conducted to measure the slope surface strength, and the calcium carbonate content was evaluated by the acid washing method. The scanning electron microscope (SEM) was employed to study the microstructures of MICP-treated sand particles. In addition, the influence of MICP treatment on the wave shape and the excess pore water pressure was also analyzed. Results show that after four MICP treatments, the erosion resistance of the slope is significantly promoted, and no apparent erosion occurs after wave actions. The penetration resistance is also improved after MICP treatments, and the maximum penetration resistance of untreated and four-time MICP-treated slopes are about 0.14 MPa and 2.04 MPa, respectively. The calcium carbonate content on the slope surface can reach 7%. SEM analyses indicate that the intergranular bridging calcium carbonate crystals promote the wave erosion resistance of the sandy slope. [ABSTRACT FROM AUTHOR]

Wave nonlinearity plays an important role in cross-shore beach morphodynamics and is often parameterized in engineering-type morphodynamic models through a nonlinear relationship with the Ursell number. It is not evident that the relationship established in previous studies also holds for sheltered sites with fetch-limited seas as they are more prone to effects of local winds and currents, the waves are generally steeper, and the beaches are typically reflective. This study investigates near-bed orbital velocity nonlinearity from wave records collected at two sheltered beaches in The Netherlands and contrasts them to earlier observations made along the exposed, wave-dominated North Sea coast. Our observations at sheltered beaches show that the Ursell number has comparable skill in predicting wave nonlinearity as it has on previously studied exposed coasts. However, the orbital velocities at sheltered coasts are more asymmetric for the same Ursell number than on exposed coasts. When exposed coast data were examined for moments with comparable high-steepness waves, a similar effect on asymmetry was observed. In addition, following and opposing winds were found to have a clear relationship with total nonlinearity, while they did not affect the phase between skewness and asymmetry at the sheltered beaches. Refitting the free parameters of an Ursell-based predictor improved the bias for the asymmetry parameterization. Whether this has implications for modeling of the magnitude of wave-nonlinearity-driven sediment transport using engineering type models is strongly dependent on the sediment transport formulation used, as these formulations depend on additional calibration coefficients too. • The Ursell number has skill in predicting wave nonlinearity at low-energy beaches. • Waves at sheltered coasts are more asymmetric for same Ursell than at exposed coasts. • Wind speed holds a clear relationship with total velocity nonlinearity. [ABSTRACT FROM AUTHOR]

Physical experiments were conducted to examine the influence of adverse currents on the propagation of shallower water waves and their impact on the evolution of nonlinear wave shapes. Irregular waves, characterized by varying initial peak periods and amplitudes, were generated in a physical wave flume equipped with a bottom slope of 1/20. Three groups of spatially varying opposing currents were generated in the flume and interacted with the aforementioned wave trains. Experimental results confirm that strong opposing currents can significantly intensify local wave nonlinearity, thereby further influencing the deformation characteristics of waves. In contrast, a weak opposing current (without wave-blocking) has a negligible effect. Bicoherence analysis revealed that the degree of phase coupling among triads of waves increased with an elevated current velocity before wave-blocking. Nevertheless, during partial wave-blocking, the degree of phase coupling was seemingly weakened by an increase in opposing current. Moreover, the influence of a co-existing current in the formation of extreme waves was recognized. The study confirms that adverse currents notably affect extreme wave steepness and extreme wave skewness, with a negligible impact on extreme wave asymmetry. As a result, empirical formulas modified by current effects are presented, describing certain key nonlinear wave shapes as functions of the local Ursell number. • Strong opposing current can significantly intensify local wave nonlinearity, whereas a weak opposing current has a limited effect. • The influence of a co-existing current in the formation of extreme waves in shallow water was recognized. • Empirical formulas modified by current effects are presented. [ABSTRACT FROM AUTHOR]

ABSTRACT The initial stages of instantaneous dam-break waves are here evaluated spatially and temporally through 36 physical experiments. Different conditions were tested for downstream (J) and upstream (M) water depths and their ratios (r) to approach realistic conditions for prototype dams. Two non-dimensional parameters are proposed – effective height (HEF) and effective velocity (VEF) – to evaluate water depths and velocity peaks along the dam-break wave evolution. The maximum wave height is estimated as a function of r, whereas the HEF is inversely related to r. The maximum VEF peak is registered for r between 0.1 and 0.2, considered a critical description for real dams. The presence of downstream water depth also modifies the dam-break wave frontal shape and types of wave break features. Previously published classifications of the moving wave based on those features are now expanded with a first tested r = 0.8 in which no jet was identified (undulated movement).

A parametric analysis is performed on Al2O3–water nanofluid flow through the heated corrugated channels. The mixture approach is adopted to model the Al2O3–water nanofluid flow, and the finite volume method is applied for the discretization of governing equations. The numerical procedure is validated for the straight channel by using the available correlations. The studied parameters are the wave shape (triangular, trapezoidal, and sinusoidal), phase shift (0, π/2, and π), nanoparticle concentration (0–4%), and Reynolds number (6000–22,000). It is found that the trapezoidal configuration proposes the highest values of Nusselt number, while the sinusoidal one offers the best overall hydrothermal performance. Also, the results show that the channel with lower phase shift presents a better hydrothermal performance. The heat transfer rate and performance index enhance with the increase in Al2O3 nanoparticle volume fraction. Further, new correlations are presented for the subsided cases. [ABSTRACT FROM AUTHOR]

The effect of anaesthetic drugs on the cortex are commonly estimated from the electroencephalogram (EEG) by quantitative EEG monitors such as the Bispectral Index (BIS). These monitors use ratios of high to low frequency power which assumes that each neurological process contributes a unique frequency pattern. However, recent research of the effect of deep brain stimulation on EEG beta oscillations suggests that wave shape, a non-sinusoidal feature that is only measurable in the time-domain, can change the frequency 'signature' of a neurological rhythmical process by the inclusion or removal of harmonic frequencies. If wave shape variations are present in the EEG of anaesthetised patients, then quantitative EEG monitors likely overestimate the anaesthetic drug effect. The purpose of this paper is to investigate alpha-wave shape in the EEG of anaesthetised patients and demonstrate the effect of wave shape on the frequency ratios that are commonly utilised in the BIS quantitative EEG monitor. EEG data, demographic information, and surgery details were collected prospectively from 305 patients undergoing a general anaesthetic for elective surgery. Alpha-wave shape was categorised by triangularity of the EEG extrema, a measure of how peaked (towards a sawtooth wave) or flat (towards a square wave) the extremum was. The alpha-wave was then artificially modified to either a sawtooth wave or square wave, and BetaRatio and PowerFastSlow metrics calculated. Age was found to be the only significant predictor of alpha wave triangularity. The artificially modified square-alpha waves increased the power in the frequency spectrum at 26 Hz by 1-5 dB, and increased the BetaRatio by 0.7. The alpha-wave of anaesthetised patients contains non-sinusoidal components which likely impact depth of anaesthesia calculations. [ABSTRACT FROM AUTHOR]

Highlights • Mixing augmentation mechanism of the pulsed gaseous jet was studied numerically. • Three kinds of pulsed wave shapes were considered, namely sine, square and triangle waves. • Flow field properties between steady jet and pulsed jet were analyzed and compared. • Pulsed jet has advantages on reducing total pressure loss and mixing length. Abstract The mixing process plays an important role in the combustion realization of the scramjet engine. In the current study, the steady jet, as well as pulsed jets with different wave shapes namely sine, square and triangle waves, is investigated in order to achieve adequate fuel/air mixing. Flow field properties are studied numerically based on grid independency analysis and code validation. The vortex structures, as well as the flow field parameters such as mixing efficiency, total pressure recovery coefficient, fuel penetration depth and mixing length, are deeply analyzed for different jet-to-crossflow pressure ratios. The obtained results predicted by the three-dimensional Reynolds-average Navier-Stokes (RANS) equations coupled with the two equation SST κ - ω turbulence model show that the grid scale makes only a slight difference to wall pressure profiles for all cases studied in this article. Compared with the steady jet, the pulsed jets with different wave shapes are beneficial for the mixing efficiency improving of the transverse jet, and the pulsed jets have special advantages on reducing the total pressure loss and mixing length but not for improving the fuel penetration depth. When the jet-to-crossflow pressure ratio is high, the performance of pulsed jets is better, and different wave shapes in the pulsed jet result in different vortex structures. This should be studied and discussed deeply in the near future. [ABSTRACT FROM AUTHOR]

The paper deals with the influence of the wave shape, represented by water surface elevations and wave-induced nearbed velocities, on sediment transport under joint wave-current impact. The focus is on the theoretical description of vertically asymmetric wave motion and the effects of wave asymmetry on net sediment transport rates during interaction of coastal steady currents, namely wave-driven currents, with wave-induced unsteady free stream velocities. The cross-shore sediment transport is shown to depend on wave asymmetry not only quantitatively (in terms of rate), but also qualitatively (in terms of direction).Within longshore lithodynamics, wave asymmetry appears to have a significant effect on the net sediment transport rate. [ABSTRACT FROM AUTHOR]

The nonlinear wave shape, expressed by skewness and asymmetry, can be calculated from surface elevation or pressure time series using bispectral analysis. Here, it is shown that the same analysis technique can be used to calculate the bound superharmonic wave height. Using measured near-bed pressures from three different field experiments, it is demonstrated that there is a clear relationship between this bound wave height and the nonlinear wave shape, independent of the measurement time and location. This implies that knowledge on the spatially varying bound wave height can be used to improve wave shape-induced sediment transport predictions. Given the frequency-directional sea-swell wave spectrum, the bound wave height can be predicted using second order wave theory. This paper shows that in relatively deep water, where conditions are not too nonlinear, this theory can accurately predict the bispectrally estimated bound superharmonic wave height. However, in relatively shallow water, the mismatch between observed and predicted bound wave height increases significantly due to wave breaking, strong currents, and increased wave nonlinearity. These processes are often included in phase-averaged wind-wave models that predict the evolution of the frequency-directional spectrum over variable bathymetry through source terms in a wave action balance, including the transfer of energy to bound super harmonics. The possibility to calculate and compare with the observed bound super harmonic wave height opens the door to improved model predictions of the bound wave height, nonlinear wave shape and associated sediment transport in large-scale morphodynamic models at low additional computational cost.

Results of hydroacoustic observations of signals from weak earthquakes in natural conditions in the region of the Southern Kuril Islands are presented. Some earthquakes were registered by the the Yuzhno-Kurilsk Seismic Station, other were only recorded by hydrophone stations. The observations were specific as seismic signals were recorded in shallow waters, i.e. in high noise level conditions. Hydrophones were installed in Lake Lagunnoe (Kunashir) and Khromovaya Bay (Shikotan). Our analysis of hydroacoustic records received from the hydrophone stations revealed no evident precursory response of the geological medium to weak distant events. This means that neither before the period of earthquake preparation nor during the earthquake preparation period, any geoacoustic emission was not detected. It is shown that despite the unfavourable noise level conditions, even distant weak earthquakes can be confidently registered by hydrophone stations, and pending application of proper signal processing techniques, it can be possible to determine arrival times of seismic waves and to measure parameters of seismic waves. It is also established that the frequency spectrum of acoustic signals from the weak earthquakes recordable by the hydrophone stations is continuous and of noise type in the frequency range up to 90–100 Hz. It is revealed that in some cases, weak earthquakes and microearthquakes may be forerun by low frequency signals.

This paper focuses on the analysis of the flow field and pressures generated by flip-through impacts on a vertical breakwater. A multiphase Navier–Stokes model is used as a numerical wave tank to analyse the influence of interface steepness on pressures and forces generated in the real configuration of a breakwater caisson. The numerical simulations consist in a solitary wave propagating over a reef and impacting a caisson breakwater placed over a porous rubble mound. After careful validation, the model allows us to make an in-depth investigation of three flip-through impacts with different incidence angles at impact (least steep, medium steep and steepest flip-through impact). The main characteristics of flip-through impacts are identified for the three cases: no air entrapped, presence of an ascending jet with large accelerations and large pressures. The focusing phase before impact introduced by Lugni et al. [ 30 ] is only observed for the steepest case. The understanding of the process of this extreme impact is improved by analysing velocities and accelerations for the three cases. Pressures and forces are shown to be directly linked to the flip-through impact inclination at impact. The flow field and pressure variations inside the porous rubble mound are also analysed in this study. [ABSTRACT FROM AUTHOR]

The statistical properties of obliquely incident irregular waves over a planar sloping bottom were investigated numerically by the well-known numerical wave model FUNWAVE 2.0. Irregular waves based on the averaged JONSWAP spectra with various wave heights and peak periods were simulated to propagate over planar bottoms. A wide range of incident angles from 0° though 75° were considered to study the influence of incident angles. It was found that incident angles have a significant influence on the wave nonlinearity. The wavelet-based bicoherence revealed that the degree of triad wave interactions of primary waves and the higher harmonics was apparently weakened by increasing wave incident angles. Importantly, using the simulated data, the Klopman wave height distribution was improved by incorporating the influence of obliquely incident angles. It was found that the improved Klopman distribution shows better performance for describing wave height distributions in shallow water depth. Moreover, two empirical formulae are recommended to reflect the relationship between the skewness and the asymmetry of waves and the Ursell number for obliquely incident waves on plane sloping bottoms. [ABSTRACT FROM AUTHOR]

Field measurements of waves and currents were obtained at ten locations on an ebb-tidal shoal seaward of Ameland Inlet for a six-week period. These measurements were used to investigate the evolution of the near-bed velocity skewness and asymmetry, as these are important drivers for wave-induced sediment tranport. Wave shape parameters were compared to traditionally used parameterizations to quantify their performance in a dynamic area with waves and tidal currents coming in from different directions over a highly variable bathymetry. Spatially and temporally averaged, these parameterizations compared very well to observed wave shape. However, significant scatter was observed. The largest deviations from the parameterization were observed at the shallowest locations, where the contribution of wave-induced sediment transport was expected to be the largest. This paper shows that this scatter was caused by differences in wave-breaking, nonlinear energy transfer rate, and spatial gradients in tidal currents. Therefore, it is proposed to include the prior evolution of the wave before reaching a location in future parameterizations in numerical modeling instead of only using local parameters to predict wave shape.

Nearshore morphological modelling is challenging due to complex feedback between hydrodynamics, sediment transport and morphology bridging scales from seconds to years. Such modelling is, however, needed to assess long-term effects of changing climates on coastal environments, for example. Due to computational efficiency, the sediment transport driven by currents and waves often requires a parameterization of wave orbital velocities. A frequently used parameterization of skewness-only was found to overfeed the coast unrealistically on a timescale of years—decades. To improve this, we implemented a recently developed parameterization accounting for skewness and asymmetry in a morphodynamic model (Delft3D). The objective was to compare the effects of parameterizations on long-term coastal morphodynamics. We performed simulations with default and calibrated sediment transport settings, for idealized coastlines, and compared the results with measured data from analogue natural systems. The skewness-asymmetry parameterization was found to predict overall stable coastlines within the measured envelope with wave-related calibration factors within a factor of 2. In contrast, the original parameterization required stronger calibration, which further affected the alongshore transport rates, and yet predicted erosion in deeper areas and unrealistic accretion near the shoreline. The skewness-asymmetry parameterization opens up the possibility of more realistic long-term morphological modelling of complex coastal systems.

A mechanism for the growth of waves by wind is included in a time-domain Boussinesq-type model. To facilitate direct analysis of the effect of wind on nonlinear wave-wave interactions over a flat bottom, a set of three harmonic evolution equations is derived from the time-domain model. These equations simulate the evolution of the principal components of three-wave (triad) nonlinear interactions, now including the effect of wind. A case of wave recurrence, in which energy is cycled between three harmonics, shows that a following wind can increase energy exchange to higher harmonics owing to nonlinearity, whereas an opposing wind suppresses this interaction. The time-domain model is then used to simulate wave propagation over a planar slope in the presence of wind. It is shown that wave growth is assisted by onshore winds and hindered by offshore winds. In addition, wave skewness and asymmetry, which quantify wave shape, are also similarly affected by wind direction. The results also show that the skewness and asymmetry undergo cyclic oscillation during the shoaling process; the degree to which these statistics exhibit the effect of wind is thus spatially dependent and can likely explain earlier laboratory studies regarding the increased dependence of wave-shape statistics on wind speed in shallow water relative to that seen in deeper water. [ABSTRACT FROM AUTHOR]

The problem of finding the optimal incident wave of given duration that maximizes the efficiency of conversion of wave energy into work in percussive drilling with detachable drill bit is considered. The drill rod is modelled as 1D linearly elastic and the drill bit as a rigid mass. The bit/rock interaction is described by a history-dependent force versus penetration relation with different constant slopes for primary loading and unloading/reloading. A functional expressing the dependence of the efficiency on the shape of an arbitrary incident wave of given duration is derived and maximized. For short incident waves, there is a weak influence of the bit mass on the optimal wave shape which is nearly rectangular. For longer incident waves, there is a strong influence of the bit mass on the optimal wave shape which significantly differs from rectangular. The efficiencies for optimal waves approach those for rectangular waves for short waves. For long waves they approach or assume values which are independent of wave duration but decrease with increasing bit mass. Relative to commonly-used rectangular waves significant increase in efficiency can be achieved through optimization of the wave shape if the wave is not too short. Optimal incident waves can be realized accurately, e.g., by piezoelectric means. [ABSTRACT FROM AUTHOR]

This article compares the characteristics of wave run up on a shore in sloped bays of arbitrary section as calculated in terms of strict solutions of nonlinear shallow water theory. The solitary waves of the same amplitude, 'significant' duration, and different shapes are considered. For each geometry of a bay, parameterization of formulas is performed in order to eliminate the influence of the shape of waves approaching the shore on these formulas describing extreme wave run-up characteristics. The results obtained earlier for a plane beach and a parabolic beach are reproduced, and the new bay shapes (with a triangular cross section and with a cross-section profile varying proportionately to the coordinate in fourth and tenth degree) are considered. It is shown that in narrower bays the maximal run-up and run-down heights and the respective run-up and run-down velocities are higher than those in wider bays. At a run up of a solitary wave in a parabolic bay, run-up and run-down heights coincide, whereas in wider bays the run-up height exceeds the run-down height and in narrower bays, for example, in triangular ones, the opposite pattern (run-down height exceeds run-up height) is observed. [ABSTRACT FROM AUTHOR]

Fatigue life of asphalt mixes in laboratory tests is commonly determined by applying a haversine or sinusoidal load with a specific frequency. However, the frequency (time duration) and shape of horizontal tensile stress and strain pulses at the bottom the asphalt layer depend on pavement design (thickness and stiffness of layers) and loading specifications (speed and contact radius). The first objective of this paper is to introduce a novel function for a more realistic representation of 3D response (stress and strain pulses in longitudinal, transverse and vertical directions) at the bottom of the asphalt layer. The second objective is to establish a framework for determination of magnitude and shape of 3D response pulse at the bottom of the asphalt layer using artificial neural network. This framework enables designers to predict the shape and magnitude of stress and strain pulses in three directions based on some parameters related to pavement structure and loading specifications. [ABSTRACT FROM PUBLISHER]