Nonlinear Wave Shape Research Articles

Universal Narrowband Wavefront Shaping with High Quality Factor Meta-Reflect-Arrays.

Optical metasurfaces offer unprecedented flexibility in light wave manipulation but suffer weak resonant enhancement. Tackling this problem, we experimentally unveil a new phase gradient metasurface platform made entirely from individually addressable high quality factor (high-Q) silicon meta-atoms. Composed of pairs of nearly identical nanoblocks, these meta-atoms support dipolar-guided-mode resonances that, due to the controlled suppression of radiation loss, serve as highly sensitive phase pixels when placed above a mirror. A key novelty of this platform lies in the vanishingly small structural perturbations needed to produce universal phase fronts. Having fabricated elements with Q-factor ∼380 and spaced by λ/1.2, we achieve strong beam steering, up to 59% efficient, to angles 32.3°, 25.3°, and 20.9°, with variations in nanoantenna volume fractions across the metasurfaces of ≤2.6%, instead of >50% required by traditional versions. Aside from extreme sensitivity, the metasurfaces exhibit near-field intensity enhancement over 1000×. Taken together, these properties represent an exciting prospect for dynamic and nonlinear wave shaping.

Net sheet-flow sediment transport rate: Additivity of wave propagation and nonlinear waveshape effects

Net wave-induced sheet-flow sediment transport rate, Qnet, can be produced by two co-existing effects: nonlinear waveshape and wave propagation, which alter the intra-wave boundary layer flow and sediment concentration. A intriguing question is whether the two effects can be simply added (the additivity hypothesis). This paper addresses this question based on simulations of a one-phase numerical model for sheet-flow sediment transport and examinations of the governing equations for boundary layer flow and sediment concentration. The additivity for the mean velocity (or streaming) is first demonstrated under typical field conditions. The main reason is that the two driving forces, i.e., momentum transfer produced by wave propagation and intra-wave asymmetry of flow turbulence produced by nonlinear waveshape, do not affect each other. The net sediment flux is separated into wave- and current-related components. Since the mean concentration profile is determined by the first-order process, the ‘current’-related flux produced by the two effects, following the mean velocity, can be superimposed. After examining the leading Fourier components, the wave-related flux is also found to follow the additivity hypothesis. The findings are confirmed by numerical experiments. The implication of this work is that a practical formula for Qnet can be designed with two separate components for nonlinear-waveshape and wave-propagation effects.

Smoothed Particle Hydrodynamics simulations of reef surf zone processes driven by plunging irregular waves

As waves interact with the slopes of coral reefs and other steep bathymetry profiles, plunging breaking usually occurs where the free surface overturns and violent water motion is triggered. Resolving these surf zone processes pose significant challenges for conventional mesh-based hydrodynamic models, due to the rapidly-deforming nature of the free surface and associated flows. Yet the accurate prediction of these surf zone hydrodynamics is critical for predicting a wide range of nearshore processes driven by wave breaking (e.g., wave dissipation and energy transfers; mean water levels and currents; and wave runup). In this study we assess the ability of the mesh-free, Lagrangian particle-based numerical modelling approach Smoothed Particle Hydrodynamics (SPH) based on DualSPHysics, to simulate the fine-scale hydrodynamic processes driven by irregular wave transformation over a fringing reef profile, by comparing results against detailed experimental observations from a physical modelling study. To greatly improve the computational efficiency, the SPH model was coupled to the mesh-based multi-layer nonhydrostatic wave-flow model SWASH. With this coupled approach, SWASH was used to efficiently simulate the evolution of non-breaking waves from the wavemaker up to the fore reef slope, with the SPH model then used to simulate the detailed hydrodynamic processes over the reef from just offshore of the breakpoint to the shoreline. The SPH model was able to accurately reproduce the complex free surface deformations during plunging breaking, the spectral evolution of waves across the reef flat (including nonlinear wave shape), the mean water levels and currents, and wave runup at the shoreline. Using the long duration simulations (>400 wave periods), the model was able to reproduce the full range of wave motions over the reef (from sea-swell to infragravity frequencies), including the increasing dominance of low frequency waves towards the shoreline and the large cross-reef standing wave motions excited by the reef geometry.

Nonlinear wavefront engineering with metasurface decorated quartz crystal

Abstract In linear optical processes, compact and effective wavefront shaping techniques have been developed with the artificially engineered materials and devices in the past decades. Recently, wavefront shaping of light at newly generated frequencies was also demonstrated using nonlinear photonic crystals and metasurfaces. However, the nonlinear wave-shaping devices with both high nonlinear optical efficiency and high wave shaping efficiency are difficult to realize. To circumvent this constraint, we propose the idea of metasurface decorated optical crystal to take the best aspects of both traditional nonlinear crystals and photonic metasurfaces. In the proof-of-concept experiment, we show that a silicon nitride metasurface decorated quartz crystal can be used for the wavefront shaping of the second harmonic waves generated in quartz. With this crystal-metasurface hybrid platform, the nonlinear vortex beam generation and nonlinear holography were successfully demonstrated. The proposed methodology may have important applications in nonlinear structured light generation, super-resolution imaging, and optical information processing, etc.

A Numerical Study of Wave‐Driven Mean Flows and Setup Dynamics at a Coral Reef‐Lagoon System

AbstractTwo‐dimensional mean wave‐driven flow and setup dynamics were investigated at a reef‐lagoon system at Ningaloo Reef, Western Australia, using the numerical wave‐flow model, SWASH. Phase‐resolved numerical simulations of the wave and flow fields, validated with highly detailed field observations (including >10 sensors through the energetic surf zone), were used to quantify the main mechanisms that govern the mean momentum balances and resulting mean current and setup patterns, with particular attention to the role of nonlinear wave shapes. Momentum balances from the phase‐resolved model indicated that onshore flows near the reef crest were primarily driven by the wave force (dominated by radiation stress gradients) due to intense breaking, whereas the flow over the reef flat and inside the lagoon and channels was primarily driven by a pressure gradient. Wave setup inside the lagoon was primarily controlled by the wave force and bottom stress. The bottom stress reduced the setup on the reef flat and inside the lagoon. Excluding the bottom stress contribution in the setup balance resulted in an over prediction of the wave‐setup inside the lagoon by up to 200–370%. The bottom stress was found to be caused by the combined presence of onshore directed wave‐driven currents and (nonlinear) waves. Exclusion of the bottom stress contribution from nonlinear wave shapes led to an over prediction of the setup inside the lagoon by approximately 20–40%. The inclusion of the nonlinear wave shape contribution to the bottom stress term was found to be particularly relevant in reef regions that experience a net onshore mass flux over the reef crest.

ECG Beat Representation and Delineation by Means of Variable Projection.

The electrocardiogram (ECG) follows a characteristic shape, which has led to the development of several mathematical models for extracting clinically important information. Our main objective is to resolve limitations of previous approaches, that means to simultaneously cope with various noise sources, perform exact beat segmentation, and to retain diagnostically important morphological information. We therefore propose a model that is based on Hermite and sigmoid functions combined with piecewise polynomial interpolation for exact segmentation and low-dimensional representation of individual ECG beat segments. Hermite and sigmoidal functions enable reliable extraction of important ECG waveform information while the piecewise polynomial interpolation captures noisy signal features like the baseline wander (BLW). For that we use variable projection, which allows the separation of linear and nonlinear morphological variations of the according ECG waveforms. The resulting ECG model simultaneously performs BLW cancellation, beat segmentation, and low-dimensional waveform representation. We demonstrate its BLW denoising and segmentation performance in two experiments, using synthetic and real data. Compared to state-of-the-art algorithms, the experiments showed less diagnostic distortion in case of denoising and a more robust delineation for the P and T wave. This work suggests a novel concept for ECG beat representation, easily adaptable to other biomedical signals with similar shape characteristics, such as blood pressure and evoked potentials. Our method is able to capture linear and nonlinear wave shape changes. Therefore, it provides a novel methodology to understand the origin of morphological variations caused, for instance, by respiration, medication, and abnormalities.

SIMULATION OF LONG-TERM SHORELINE CHANGE DRIVEN BY LONGSHORE AND CROSS-SHORE SEDIMENT TRANSPORT

Driven by wave and current, sediment transport alongshore and cross-shore induces shoreline changes in coasts. Estimated by breaking wave energy flux, longshore sediment transport in littoral zone has been studied for decades. Cross-shore sediment transport can be significant in a gentle-slope beach and a barred coast due to bar migration. Short-term beach profile evolution (typically for a few days or weeks) has been successfully simulated by reconstructing nonlinear wave shape in nearshore zone (e.g. Hsu et al 2006, Fernandez-Mora et al. 2015). However, it is still lack of knowledge on the relationship between cross-shore sediment transport and long-term shoreline evolution. Based on the methodology of beach profile evolution modeling, a semi-empirical closure model is developed for estimating phase-average net cross-shore sediment transport rate induced by waves, currents, and gravity. This model has been implemented into GenCade, the USACE shoreline evolution model.

The Relationship between Sea-Swell Bound Wave Height and Wave Shape

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.

Experimental and numerical assessment of deterministic nonlinear ocean waves prediction algorithms using non-uniformly sampled wave gauges

We assess the capability of fast wave models to deterministically predict nonlinear ocean surface waves from non-uniformly distributed data such as sampled from an optical ocean sensor. Linear and weakly nonlinear prediction algorithms are applied to long-crested irregular waves based on a set of laboratory experiments and corresponding numerical simulations. An array of wave gauges is used for data acquisition, representing the typical spatial sampling an optical sensor (e.g., LIDAR) would make at grazing incidence. Predictions of the weakly nonlinear Improved Choppy Wave Model are compared to those of the Linear Wave Theory with and without a nonlinear dispersion relationship correction. Wave models are first inverted based on gauge data which provides the initial model parameters, then propagated to issue a prediction. We find that the wave prediction accuracy converges with the amount of input data used in the inversion. When waves are propagated in the models, correctly modeling the nonlinear wave phase velocity provides the main improvement in accuracy, while including nonlinear wave shape effects only improves surface elevation representation in the spatio-temporal region where input data are acquired. Surface slope prediction accuracy, however, strongly depends on the appropriate nonlinear wave shape modeling.

An improved Lagrangian model for the time evolution of nonlinear surface waves

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al.’s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.

Experimental study of sheet-flow sediment transport under nonlinear oscillatory flow over a sloping bed

The seabed is sloped in shallow coastal regions, where strong nonlinear shoaling waves can generate sheet-flow sediment transport. Both wave nonlinearity and bottom slope can lead to a wave-averaged (net) sediment transport rate, but the bottom slope effect is often overlooked in existing sediment transport models. A full-scale experimental study of sheet-flow sediment transport under the oscillatory flows with nonlinear features (skewness or asymmetry) was conducted in an inclinable oscillatory water tunnel, so the bottom-slope-induced net transport rate in the context of nonlinear waves was experimentally investigated. The tests cover a variety of nonlinear wave shape, bottom slope (0 to 2.5∘) and two sediment diameters (0.24 and 0.51 mm). Since the downslope direction is the “offshore” direction in our tests, it is found that bottom slope reduces the net “onshore” transport rate due to wave nonlinearity. The slope contribution to the net transport rate is evaluated by taking the difference between the measured net transport rate from a sloping-bed experiment and the measured net transport rate from the corresponding horizontal-bed experiment. The results suggest that slope-induced net transport rate is insensitive to wave nonlinearity, and its variation with bottom slope can be considered linear in the context of predicting net transport rate. Comparisons between this study and a preceding sinusoidal-flow study of Yuan et al. (2017b) suggest that nonlinear waves can be approximated as sinusoidal flows for estimating the slope contribution to the net transport rate. Subsequently, an empirical model for predicting net sheet-flow transport rate due to bottom slope is established based on dimensional analysis. This model can be simply added to existing sheet-flow sediment transport models to improve their applicability in coastal regions.

FIELD STUDY ON INFLUENCE OF TIDAL CURRENTS ON INTRA-WAVE SEDIMENT TRANSPORT

Sediment transport by currents and waves determines the evolution of shoals and channels on the ebb-tidal delta. The channels are an important conduit for shipping and are often dredged to maintain access at considerable cost. A better understanding of the sediment transport processes within the channels is the basis for a more cost-effective maintenance strategy. In the vicinity of ebb-tidal inlets, waves from offshore encounter tidal currents. Depending on the tidal phase, incoming waves face strong positive or negative current gradients. Besides changes in wave height, period and direction, the current gradients also affect the nonlinear wave shape and corresponding velocity profile.

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.

Virtual Analog Models of the Lockhart and Serge Wavefolders

Wavefolders are a particular class of nonlinear waveshaping circuits, and a staple of the “West Coast” tradition of analog sound synthesis. In this paper, we present analyses of two popular wavefolding circuits—the Lockhart and Serge wavefolders—and show that they achieve a very similar audio effect. We digitally model the input–output relationship of both circuits using the Lambert-W function, and examine their time- and frequency-domain behavior. To ameliorate the issue of aliasing distortion introduced by the nonlinear nature of wavefolding, we propose the use of the first-order antiderivative method. This method allows us to implement the proposed digital models in real-time without having to resort to high oversampling factors. The practical synthesis usage of both circuits is discussed by considering the case of multiple wavefolder stages arranged in series.

Testing and Applications of Non-Linear Wave Shaping Circuits Based on Zener Diodes at Cryogenic Temperatures

Applications of wave-shaping clipping circuits based on Zener diodes are of great interest in a wide range of modern electronic systems. As well, given the strong interest in space research and trips to distant planets, where the journey takes long periods. Therefore, the matter requires reliance on electronic systems with special specifications commensurate with the nature of the extremely low-temperature environments, down to cryogenic level (around 90 K). So, the present paper was concerned with studying the stability of the performance of different non-linear wave-shaping systems, based on silicon Zener diodes, whenever operates at very low temperatures down to cryogenic levels. From which, it is clear that for BZX79-C4V7 and BZX79-C5V6 Zeners, such electronic systems were shown to be insensitive to temperature variations. On the other hand, low breakdown voltage Zeners (BZV86-1V4 and BZX83-C3V6), the clipping edges were shown to be increased with lowering temperatures from 300 K down to 93 K. Finally, for Zener diodes with VZ greater than 6.0 V (BZX83-C6V8 and BZX55C9V1), the temperature coefficient is positive, so the clipping edges decrease with lowering temperatures, for the same range of temperatures.

Nonlinear optical Fourier transform in an optical superlattice with "x+2" structure.

We proposed a simple method to realize optical Fourier transform during the nonlinear wave shaping processes. In this method, an integrated optical superlattice is designed to realize multiple optical functions, which plays important roles in both the nonlinear harmonic generation process and the optical Fourier Transform process. We demonstrated our method by the nonlinear generation of Airy beams as an example. It is a universal method for beam shaping and is of practical importance for designing compact nonlinear optical devices.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two‐phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross‐shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one‐dimensional vertical (1DV) model by simplifying the two‐dimensional vertical (2DV) ensemble‐averaged two‐phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near‐bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high‐velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low‐wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near‐bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape.

Synthesis of the Hilbert transform of a train of rectangular pulses

A novel method of synthetising the Hillbert transform of a pulse train by nonlinear waveshaping circuits which avoids the use of complicated linear circuits is described.