Nonlinear Wave Effects Research Articles

An Empirical Model for Skillful Rogue Wave Forecasts

Abstract One of the leading goals of rogue wave research is to develop a robust rogue wave warning system to mitigate the danger they pose. One such system has been developed by the European Centre for Medium-Range Weather Forecasts (ECMWF), called the freak wave warning system (FWWS), based on nonlinear wave effects. The FWWS predicts maximum expected wave envelope height as a risk parameter for forecasts. Recently, a data-driven alternative has been proposed by Häfner et al., which was distilled from a neural network using wave buoy observations. However, it has yet to be evaluated by a spectral wave model for application to operational wave forecasting. The data-driven, learned model emphasizes bandwidth-controlled linear superposition as the predominant mechanism in crest-to-trough rogue wave generation, while nonlinear effects are a secondary term. The present work evaluates the performance of the empirical model using output from an ECMWF global wave hindcast. We find that the prediction models based on bandwidth effects have the highest log likelihood scores, with the empirical model outperforming all other tested models. In contrast, the expected maximum envelope wave height from the FWWS does not predict the occurrence of rogue waves. These results indicate that the empirical model with wave model input is a skillful predictor and should be considered for operational implementation to improve rogue wave forecasting. Significance Statement Rogue waves are unexpectedly large and unpredictable waves. Encounters with rogue waves can result in damage to marine vessels and offshore infrastructures. Research is devoted to developing systems to predict the risk of rogue wave events. A novel predictive model has been shown to perform well in predicting rogue wave occurrences based on wave buoy observations. This model is a symbolic expression distilled from an artificial neural network that incorporates known rogue wave dynamics and that can be evaluated alongside traditional risk estimates with minor adjustments to operational forecasting systems. This study evaluates the newly proposed empirical model in a forecasting setting. Our work demonstrates the efficacy of the empirical model for operational forecasting purposes.

Analysis of the overall structural strength and optimization recommendations for ultra-large container ships based on the improved equivalent design wave method

Ultra-large container ships face challenges in structural strength under complex sea conditions. The traditional equivalent design wave method inadequately considers nonlinear wave effects, leading to inaccuracies in strength assessments. This article improves the method by incorporating nonlinear wave effects and optimizing wave spectrum parameters to better simulate structural responses. A study on a container ship, using refined wave load calculations and finite element analysis, focusing on stress distribution in critical hull areas. The findings show that the enhanced method more accurately reflects real loading conditions, confirming the ship’s structural soundness and offering optimization suggestions for improved safety and longevity.

Enhancing the efficiency of gas sensing on perovskite BaTiO3 nanoparticles using dynamic shock wave flow environment

The effect of nonlinear dynamic shock waves on perovskite BaTiO3 nanoparticles (NPs) is investigated using a table top pressure-driven shock tube (Reddy Tube) for ammonia gas sensing applications with the Mach number of 2.2. In general, shock waves are a nonlinear high-pressure phenomenon characterized by high dynamic pressure and temperature. Raman and powder X-ray diffraction (XRD) methods were utilized to evaluate the molecular and structural characteristics of the BaTiO3 (BTO) NPs under the influence of dynamic shock waves. The surface absorption was assessed using UV- diffuse reflectance spectroscopy (UV-DRS). XRD data shows that BaTiO3 NPs crystallized in tetragonal crystal structure with P4mm space group and stable throughout the shocks, without undergoing any phase change. The average particle size of the control BaTiO3 was 31 nm, while those of shocked BaTiO3 were 62 nm (100 shocks) and 55 nm (200 shocks), demonstrating the significant change in morphology and showing that particles have irregular spherical morphology and are agglomerated by shock wave loaded conditions. Moreover, BaTiO3 nanoparticles were shocked after being tested with various concentrations of different gases at a temperature of 200°C. Under shock loaded conditions, the heightened sensing response for ammonia gases was between 5 and 20 ppm; also, sensing properties such as sensitivity, response, and recovery time indicated that BaTiO3 nanoparticles are a good potential ammonia gas sensing material for real-time sensor applications with enhanced characteristics.

Experimental investigation on wave-induced bending moments of a 6,750-TEU containership in oblique waves

This study aims at the experimental investigation of wave-induced motions and loads of a containership model without forward speed in -120 degree oblique regular waves to study the influence of the wave steepness and provide reference data for future benchmark studies. A mooring system with 4 horizontally arranged spring lines was used to maintain the heading angle of a 1/65 scaled 9-segmented model designed to be as rigid as possible.Focuses were on studying the nonlinear effects due to the wave steepness on the vertical bending moment (VBM) and horizontal bending moment (HBM) near amidships, and 6-DOF motions at the center of gravity (COG) of the model. Several wave series that are distinguished by wave steepness were considered in the experiment accordingly. Each series consists of waves with various periods that were intended to cover the peak of the wave bending moment transfer functions. Through this, the nonlinear wave effects on the responses of the rigid body at various periods were determined. It was confirmed that the steeper wave contributes to the increase in the higher-order harmonic components including slamming events in the bending moments measured. The change in the characteristics of the wave bending moments according to the change in wave steepness was found to be very different from the linear response.A detailed discussion was made on the influence of the mooring system on the asymmetric horizontal bending moment (HBM) and the change in the average yaw motion. Experiments with and without a mooring system under the same wave condition were conducted, and the effect of the mooring system was identified. It was qualitatively confirmed that the mooring system’s restoring moment correlates with the asymmetric HBM and average yaw movement change.

NONLINEAR EFFECTS IN CRYSTALLINE SOLIDS WITH SATURATION OF AMPLITUDE-DEPENDENT INTERNAL FRICTION, DECREASING WITH IN-CREASING FREQUENCY

As a result of modification of quasi-static elastic and inelastic hysteresis, dynamic hysteresis equations of state of crystalline solids with frequency-dependent saturation of amplitude-dependent internal friction decreasing with increasing frequency are proposed. The nonlinear propagation of initially harmonic longitudinal elastic waves in rods made of such materials is investigated by the perturbation method. Numerical, graphical and comparative analysis of the obtained solutions is carried out and characteristic amplitude-frequency dependenc-es of nonlinear wave effects are revealed. A method for determining the type of dynamic hysteresis for crystal-line solids with frequency-dependent saturation of amplitude-dependent internal friction is proposed.

Characterization of interfacial waves in stratified turbulent gas-liquid pipe flow using Particle Image Velocimetry and controlled disturbances

The work reports an experimental investigation on stratified gas-liquid pipe flow characteristics in the presence of controlled interfacial waves. Studies of this flow regime with controlled interfacial waves are scarce in the literature. Here, the disturbances are excited at the liquid interface by an oscillating paddle. The waves are synchronized with image acquisitions, enabling the utilization of phase-locked measurements and ensemble averaging techniques. Off-axis Particle Image Velocimetry (PIV) and Shadowgraph techniques were applied to provide information about mean and wave-induced modifications on the velocity fields. Results show that mean flow velocities in the liquid and gas phases close to the pipe walls adhere well to the single-phase flow log-law profile. In the liquid layer, this agreement was observed up to half of the water depth. Controlled disturbances enabled the estimation of the wave amplitude thresholds for the appearance of relevant nonlinear wave effects on the flow field. Results suggest that such a threshold can be fairly represented by a constant value of the non-dimensional parameter proposed in the work of Kirby (2008). Within the non-linear wave regimes investigated, noticeable changes in the flow field were observed close to the interface. However, near the wall the flow was weakly affected by the presence of waves, suggesting that interfacial wave effects are weakly coupled with near-wall disturbances and might be modelled independently. Moreover, contributions to interfacial shear stress due to the presence of waves were obtained experimentally. The results presented here are useful for validation and improvement of models used to predict flow characteristics in stratified flows. In addition, they contribute to shed further light on the physical mechanisms involved in the phenomenon.

Effects of nonlinear internal gravity waves on normal-incident reflection measurements of seafloor sediments.

Sonar data acquired by sub-bottom profilers and echosounder systems are widely used to estimate geoacoustic properties of marine sediments. However, the uncertainty of the seabed property estimates caused by water-column variability may limit the application. In this paper, the acoustic focusing and defocusing effects of nonlinear internal gravity waves on normal-incident acoustic reflection measurements are studied. The experiment data were collected in the South China Sea from two transceiver moorings located at two different sites, one of which contained strong nonlinear internal waves (NIWs), while another site did not. The observed reflection intensity variation at the internal wave site varied up to 10 dB. On the other hand, the bottom reflections at the other site without internal waves were stable, and a seafloor sediment sample collected there was analyzed to validate the sediment type inferred from bottom loss. Numerical simulations using ray-tracing and parabolic equation models confirmed the cause of this intensity fluctuation by the acoustic focusing and defocusing of NIWs. This study eventually showed that NIWs may induce a significant bias for geoacoustic property estimates from seabed reflection coefficients.

An alternative methodology for the simplified operational guidance in the framework of second generation intact stability criteria

Within the framework of the second-generation intact stability criteria (SGISc), a procedure to provide simplified operational guidance (OG) has been proposed. In particular, the phenomenon of parametric rolling has been investigated. The proposed methodology is meant to be an intermediate level between the suggested simplified OG and the deterministic OG, as defined in the MSC.1/Circ.1627. The proposed guidance relies on a simplified numerical tool able to assess ship roll motion due to non-linear irregular wave effects in the time domain. Outcomes are elaborated in the post-process phase, taking the maximum roll angle as leading criterion. Once defined the structure of this tool, an application has been carried out to a representative model of post-panamax container vessel. As benchmark study, the results have been compared to those obtained by the application of MSC.1/Circ.1228 and MSC.1/Circ.1627 (simplified OG) by means of polar diagram representation. Outcomes have been discussed and a general agreement can be found between the simplified OG and the proposed one. Although, it appears that the latter can detect dangerous roll motion for a more comprehensive set of sailing condition.

Coupled effects of nonlinear internal gravity waves and seabed properties on underwater sound propagation

Underwater sound propagation can be affected by strong sound speed gradients induced by nonlinear internal waves in the ocean. Meanwhile, geoacoustic properties of the seabed control acoustic reflections. Experimental data collected at the shelfbreak on the northeast of the South China Sea were analyzed to investigate the joint effects. Both two-dimensional (2D) and three-dimensional (3D) numerical sound propagation models with realistic seafloor and oceanographic inputs have been established to study the nonlinear internal wave effects observed on hydrophone vertical line array moorings. Compared to the 3D model, the prediction errors and uncertainties of the 2D scheme neglecting the transversal/azimuth energy propagation are discussed. In addition, the impact of sediment properties on 3D propagation effects affecting underwater soundscapes in the area is investigated. [Work supported by the Office of Naval Research.]

The role of idealized storms on the initial stages in sand wave formation: A numerical modeling study

Sand waves are rhythmic bedforms observed in many shallow shelf seas. By adopting a process-based numerical morphodynamic model, Delft3D, the effect of the storm-related processes on the growth and migration of sand waves was studied systematically in this paper. In our model, the storm effect was included by adopting the shear stresses due to the nonlinear wave effect, wave-current interaction, and wind-driven current. A series of numerical experiments were performed, and it was found that accounting for the wave nonlinearity is important in predicting the growth rate. Moreover, the effect of wave-current interaction on sand wave growth and migration is significant. The asymmetric velocity of water particles induced by wave-current interaction leads to net sediment transport rates which resulted in the migration of sand waves. The wind-driven current effect can breach the symmetry of the tidal current and cause the migration of sand waves. In our specified cases, the effect of wind-driven current or wave action on the LFGM was not significant, while the combination of these two effects causes a larger wavelength of sand waves. The model results show that the storms influence sand wave dynamics in the formation stage significantly and are therefore important to account for in designing offshore engineering operations in sand wave fields.

The Effect of Non-Linear Wave on Oil Spill Dispersion

On 31 March 2018, an oil spill accident polluted Balikpapan Bay. A failure occurred in a pipeline running from Penajam to Balikpapan Oil Refinery, East Kalimantan, Indonesia. Leaking pipeline caused the total estimated volume of leaked oil to approximate 44,000 Barrels of crude oil. MoTuM was used to simulate the dispersion of oil in the area. The modeling results indicate that a strong dynamic tidal current in the Bay controls the oil’s movement. The MoTuM software is suitable for spill combating, contingency plans, and backtracking. MoTuM is developed in Windows System, which integrates 3D Non-Orthogonal Boundary Fitted Ocean Hydrodynamics Model, Trajectory, Fates, Stochastic, Backtracking in Geographic Information System. This paper presents a further study of the effect of non-linear waves on the dispersion of oil in the Bay. The simulation results were validated by comparing the model with a satellite image. The agreement between the result of simulation and satellite image is excellent and shows that the non-linear wave is an essential factor for oil spill dispersion.

The nonlinear wave and current effects on fixed and floating bodies by a three-dimensional fully-nonlinear numerical wave tank

A three-dimensional, fully-nonlinear numerical wave tank (NWT) is developed and utilized to analyze the interaction between nonlinear waves and fixed or floating bodies with uniform current. The NWT is based on the potential flow theory and the boundary element method and simulates nonlinear wave-current-body interactions using MEL (Mixed Eulerian and Lagrangian) method. Moreover, the robust acceleration-potential approach is applied to evaluate the instantaneous wave-induced pressure acting on the body without using numerical time differentiation of velocity potential. In addition, artificial damping zone with gradually varying artificial damping coefficient is applied to prevent reflected waves from side walls and input and downstream boundaries. Using the developed NWT, current-affected incident waves are simulated and compared with measured wave elevations in both coplanar and adverse currents. Then, fixed bottom-mounted and truncated vertical cylinders are simulated in waves and currents and the wave run-up, wave-frequency, double-frequency and mean-drift forces are calculated and compared with published results from the second-order perturbation approach. The NWT is then further applied to freely-floating (with soft horizontal spring) truncated vertical cylinders and the wave-frequency and double-frequency motions for various current conditions and wave drift damping are analyzed. Based on the developed NWT, the validity of Aranha's semi-analytic solution for wave drift damping is assessed.

On the behavior of nonlinear hydrodynamic coefficients of a submerged cylinder beneath the water surface

This study aims at numerically exploring the behavior of flow fields and nonlinear hydrodynamic coefficients of a horizontal cylinder beneath the free surface flow considering the effects of nonlinear surface waves and various cylinder shapes. The computational model is based on two-dimensional incompressible Navier-Stokes solvers along with the treatment of the free surface flow using the volume of fluid method. The effect of the turbulent flow is also considered by using the shear stress transport turbulence model. The simulation result of a benchmark case study of the submerged cylinder is first validated with available experiment data, where a mesh convergence analysis is also performed. Afterward, the flow fields and hydrodynamic force coefficients around the cylinder surface are analyzed, and the influences of various cylinder shapes and Reynolds numbers on the hydrodynamic coefficients are investigated. A state diagram representing the hydrodynamic behavior including stable and unstable stages is finally proposed; this is an important criterion for the practice design of submerged civil structures under the free surface flow.

Biogeochemical responses to internal-wave impacts in the continental margin off Dongsha Atoll in the Northern South China Sea

This study aimed to understand the effects of nonlinear internal waves (NLIWs) on nutrient-involved biogeochemical processes and the consequences in the continental margin off Dongsha Atoll (DA) in the northern South China Sea (NSCS). Shipboard and mooring observations were conducted to determine hydrological and biogeochemical conditions mainly from two transects covering the DA-associated upper slope, shelf break, and shelf zones. A dense array of thermistor moorings and a temperature-fluorescence-sediment trap array were deployed on the same transect to determine the short-period variability of transport and shoaling of NLIWs across the shelf and to link physical variability to biogeochemical consequences induced by NLIW events. The shoaling of NLIWs appeared to uplift cooler and nutrient-rich subsurface water into the nutrient-deplete surface in shelf and nearshore environments as well as increase nutrient concentrations and biological production. We observed shoaling events that induced a notable range of upward fluxes in nitrate and nitrite (0.42–2.92 mmol N m−2 d−1) onto the euphotic zone to enhance and sustain new production, depending on the strength of shoaling activity in various observations. The shoaling-derived new production may fully elucidate the amount of sinking fluxes of particulate organic carbon measured from the shoaling field. According to short-time sequential observations during the passage of a single NLIW, the depressed waves may play a crucial role in enhancing the vertical transfers of surface-replete dissolved gases, carbon, or suspended constituents through the surface layers of stratified waters. This NLIW forcing appears to be effective in supplying cooler and nutrient-rich water to the DA-associated coral community, and this may be vital for improving the future development and conservation of the coral ecosystem.

Effects of nonlinear internal gravity waves on normal-incident reflection measurements of marine sediments

Sonar data acquired by sub-bottom profilers and multi-beam echosounder systems are widely used to estimate geoacoustic properties of marine sediments. However, the uncertainty of the seabed property estimates caused by water column variability may limit the application. In this study, we focus on the acoustic focusing and defocusing effects of nonlinear internal waves on normal-incident reflection measurements in the South China Sea. The field experiment was conducted using a transceiver mooring consisted of a sound source and a four channel vertical hydrophone array. The variation of acoustic signal reflections from sub-bottom layers during three days at the same site is observed. The effects of the nonlinear internal waves passing through the transceiver mooring are identified. The impact on the sub-bottom property estimates is investigated. [Work supported by the Office of Naval Research.]

Nonlinear wave effects on the oscillatory pore pressure induced forces on buried pipelines

ABSTRACT The present study investigates the influence of nonlinear waves on the oscillatory pore pressure-induced response around buried pipes. The study is carried out considering the applicable wave theories namely: linear, Stokes, cnoidal and solitary wave theories. The soil modelling is based on Biot’s consolidation equations which are solved using Finite Element tool COMSOL Multiphysics. Two case studies are considered for the investigation where the parameters of wave height and water depth are varied respectively for each case study to increase the wave nonlinearity. The hydrodynamic pressure on the seabed is based on the applicable wave theory which is chosen from Le-Mehaute’s diagram. The pore pressures, stresses and forces developed on the buried pipe are evaluated considering different wave theories. As the wave transforms from linear to cnoidal through stokes waves a gradual variation in the wave-induced soil response is observed, whereas the soil response from cnoidal to solitary waves is found to be considerably abrupt. It is observed that the magnitude of these wave-induced forces and stresses due to a solitary wave can be about twice that of a linear wave under a wave crest. Similarly, for the case of pipe under wave trough, linear wave theory gives a very high estimate of uplift force as compared to highly nonlinear solitary waves.

"HIFU Beam:" A Simulator for Predicting Axially Symmetric Nonlinear Acoustic Fields Generated by Focused Transducers in a Layered Medium.

"HIFU beam" is a freely available software tool that comprises a MATLAB toolbox combined with a user-friendly interface and binary executable compiled from FORTRAN source code (HIFU beam. (2021). Available: http://limu.msu.ru/node/3555?language=en). It is designed for simulating high-intensity focused ultrasound (HIFU) fields generated by single-element transducers and annular arrays with propagation in flat-layered media that mimic biological tissues. Numerical models incorporated in the simulator include evolution-type equations, either the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation or one-way Westervelt equation, for radially symmetric ultrasound beams in homogeneous and layered media with thermoviscous or power-law acoustic absorption. The software uses shock-capturing methods that allow for simulating strongly nonlinear acoustic fields with high-amplitude shocks. In this article, a general description of the software is given along with three representative simulation cases of ultrasound transducers and focusing conditions typical for therapeutic applications. The examples illustrate major nonlinear wave effects in HIFU fields including shock formation. Two examples simulate propagation in water, involving a single-element source (1-MHz frequency, 100-mm diameter, 90-mm radius of curvature) and a 16-element annular array (3-MHz frequency, 48-mm diameter, and 35-mm radius of curvature). The third example mimics the scenario of a HIFU treatment in a "water-muscle-kidney" layered medium using a source typical for abdominal HIFU applications (1.2-MHz frequency, 120-mm diameter, and radius of curvature). Linear, quasi-linear, and shock-wave exposure protocols are considered. It is intended that "HIFU beam" can be useful in teaching nonlinear acoustics; designing and characterizing high-power transducers; and developing exposure protocols for a wide range of therapeutic applications such as shock-based HIFU, boiling histotripsy, drug delivery, immunotherapy, and others.

Tsunami Squares modeling of landslide tsunami generation considering the ‘Push Ahead’ effects in slide/water interactions: Theory, experimental validation, and sensitivity analyses

Landslide tsunami generation is a complex physical process that involves solid materials interacting with water bodies and other 3D nonlinear wave effects. Modeling of this process ranks as an urgent task because wave source features are crucial clues for subsequent tsunami motions and hazards threatening coastlines. Herein, we introduce a concept of ‘Push Ahead’ (PA) in landslide/water interactions and propose a PA formulation integrated in a meshless numerical procedure named ‘Tsunami Squares’ (TS) for modeling of landslide tsunami generation. We draw comparisons on the physical significances of PA acceleration versus ‘Drag Along’ (DA) acceleration and conventional aerodynamic and hydrodynamic solutions. We carry out physical experiments of wave generation by block-dragging and gravel flows and corresponding TS simulations to study PA effects in landslide/water interactions. Wave features in TS simulations match the experimental observations in a reasonable range, providing a firm validation of the PA formulation in the TS approach. Sensitivity analysis that compares simulations with various ratios of PA acceleration is carried out both for the block-dragging and gravel flow experiments. The comparisons indicate that PA acceleration plays an important role in landslide wave generation and that larger PA accelerations make greater contributions to the initial wave source. We discuss intrinsic relations between PA formulation and the empirical equations derived from previous experiment studies that support the validity and applicability of the PA solution. We also insist that the complex 3D wave effects such as dispersion, shoaling, refraction, reflection and superposition, occurring in the experiments can be well reproduced in the TS simulations. The newly proposed PA acceleration that works together with our previously presented ‘Drag Along’ and ‘Lift Up’ effects can excellently illustrate the mechanical process of landslide water interactions. We conclude that TS simulations that do not include the ‘Push Ahead’ acceleration can seriously underestimate landslide tsunami size. • Development of a ‘Push Ahead’ acceleration in TS modeling of landslide/water interactions. • Model validation with well-designed experiments of waves generated by block slide and gravel flow. • Sensitivity analysis of the ‘Push Ahead’ acceleration that affects landslide tsunami generation. • Discussion on intrinsic relations between PA formulation and the empirical equations.

Hydrodynamic Properties of a Moored Floating Breakwater using CFD Approach

In presence of complex-hydrodynamic interaction between water wave and moving structure, a reliable method that can analyse nonlinear phenomena is necessarily required. This paper presents numerical investigation of a moored floating breakwater using computational fluid dynamic (CFD) approach. The mathematical model is based on the extended Reynolds Average Navier-Stokes (RANS) solver for solid-porous obstacle. A high amplitude wave with several wave periods were deliberately considered in the simulation to allow nonlinear wave effects on the floating structure such as wave breaking, overtopping, including viscous friction. Here, the two fluid calculation method for interface boundary between water and air is proposed to capture the complex free surface changes. In addition, the fractional average volume obstacle representation (FAVOR) using partial cell treatment method is employed to simulate the motion of breakwater boundary on the free surface. Approximations and validations on the hydrodynamic properties of the structure have been carried out which include wave transmission coefficient, sway, heave, pitch, and mooring forces. The results show that the CFD model can fairly simulate well on hydrodynamics of the floating breakwater. The discrepancies between numerical and experimental data can be partly attributed to the nonlinearity in the incident wave definition.

Classical nonlinear simulation of low-order modes of Lamb waves in plate

For the classical nonlinear research of low-order modes of Lamb waves, this paper firstly introduces the classical nonlinearity derived from the intrinsic nonlinear induced low-order Lamb waves (S0 and A0 modes). Theoretical and numerical calculations are studied in two aspects. The influence of nonlinear effects on the nonlinear effects of classical nonlinear low-order Lamb waves and the cumulative growth effect are analyzed by finite element simulation. The results show that the nonlinear effect produced by the superelastic material model is greater than the geometric nonlinearity, and the linear elastic material model does not produce nonlinear effects. In addition, as the third-order elasticity increases in the material, the amplitude of the second harmonic gradually increases. The second harmonic generated by the A0 mode with phase velocity mismatch is the S0 mode. It can be seen that the group velocity matching is not a necessary condition for generating the second harmonic. Since the phase velocity matching is not satisfied, there is no cumulative growth effect; The higher the S0 mode phase velocity matching degree, the more obvious the cumulative growth effect, and the second harmonic is the S0 mode.