Local Wave Research Articles

Modeling of Transformations during the Formation of Local Waves of SARS-CoV-2 Spreading at the Endemic Stage of the Pandemic

Modeling of Transformations during the Formation of Local Waves of SARS-CoV-2 Spreading at the Endemic Stage of the Pandemic

Wave overtopping of a vertical seawall in a surf zone: A joint analysis of numerical and laboratory data

This research uses physical and numerical experiments to investigate the wave overtopping of a vertical seawall in an uneven surf zone. The numerical experiments exploit two approaches, which differ in vertical resolution and computational time: CFD-RANS and SWASH. The tests were conducted with and without the wall, allowing the analysis of the spectral evolution in shallow water and its relationships with wave overtopping. The study assesses the performance of numerical models with different levels of complexity and uses laboratory and numerical data to understand the key variables that control the phenomena under study. The results indicate that while CFD-RANS is quantitatively in line with the laboratory measurements, SWASH overestimates the spectral moments and underpredicts the overtopping rate by a factor of 2. However, the numerical tools satisfactorily reproduce the physics of the processes, allowing us to focus on some aspects of engineering relevance. Laboratory and numerical data indicate that the overtopping rate depends not on the wave spectrum shape but on the high percentiles of the wave elevation distribution. This outcome clarifies that wave setup is a critical variable for prediction purposes.Finally, the article highlights that the surf zone’s spectral moments are correlated. The correlation structure is such that the mean spectral periods became proportional to the local wave energy despite these quantities being independent in deeper water. We warn that this phenomenon could result in spurious, unphysical relationships between mean spectral periods and overtopping rates. The analysis of further literature data corroborates this conclusion.

Transformation of a fully nonlinear breather-like package of internal waves over a bottom step in a layered fluid

In this paper, we study the process of transformation of a localized wave packet over a bottom step in a three-layer fluid, in which the height of the step is equal to or exceeds the thickness of the lower layer; therefore, density stratification becomes two-layer in the shallow water zone. In numerical experiments, both the height of the step and the width of the step were varied. The problem is solved in the framework of a fully nonlinear model of hydrodynamics of an inviscid incompressible stratified fluid. The primary analysis consisted in estimating the values of dimensionless parameters used, as a rule, in runup problems: the Froude and Iribarren numbers, the ratio of the characteristic wavelength to the characteristic slope width, the ratio of the topographic slope to the characteristic wave beam angle. Since the “cutoff” line for the lower pycnocline is partially or completely located on a step, one could expect the effects of run-up, breaking or reflection of waves propagating along the lower pycnocline, but this doesn’t happen. It is shown that the reflection of the wave packet from the step is minimal in all cases considered, a strong steepening of the wave is observed, but no breaking occurs in this case — the wave then just quickly decays on the lower pycnocline. An analysis of the spectral amplitudes and energy fields allows us to conclude that there is a transfer of energy from the lower pycnocline to the upper one. The breather in a two-layer fluid cannot exist, but the wave packet formed in the upper pycnocline after its destruction has much higher energy than it has before the step.

Novel Optical Solitary Wave Structure Solution of Lakshmanan-Porsezian-Daniel Model

The Lakshmanan-Porsezian-Daniel (LPD) model, an extended version of the nonlinear Schrödinger equation, plays a crucial role in comprehending optical solitons—self-reinforcing waves that maintain their form while traveling through a medium. This study employed the G′G2-expansion method to explore the model and present new exact solitary wave solutions with various nonlinearities, including the Kerr, anti-cubic, and parabolic laws. The findings provide solutions for different types of optical solitons, such as bright solitons, dark solitons, rational functions, and periodic solitons. The obtained results offer fresh insights into the complex LPD model, deepening our core understanding of optical soliton dynamics. Importantly, these findings have significant implications for soliton-based applications, specifically in modern communication networks and nonlinear optics, directly impacting optical fiber transmission. Furthermore, the research introduces singular solitons, a unique and highly localized wave phenomenon, through an influential and systematic approach to exact optical solutions for various models. As communication technology and nonlinear optics continue to advance, these findings hold substantial promise for practical applications in the development of cutting-edge optical devices and systems.

Conformally graded metamaterials for elastic wave guidance

Although metamaterials have been widely used for controlling elastic waves through bandgap engineering, the directed guidance of stress waves in non-periodic structures has remained a challenge. This work demonstrates that spatially graded metamaterials based on conformal mappings present a rich design space for controlling and attenuating wave motion — without the need for bandgaps. Conformal mappings transform an elementary unit cell by scaling and rotation into graded lattices with approximately geometrically similar unit cells. This self-similarity allows for control over the local wave dispersion throughout the metamaterial. As a key mechanism, it is shown that elastic waves cannot propagate through graded unit cells with significant size differences, except at low frequencies. This is exploited to create low-pass elastic wave guides, extending beyond classical bandgap engineering, since bandgaps are not required to achieve wave guiding and attenuation. Experiments confirm the low-pass elastic wave filtering capability of a planar truss metamaterial with conformal grading. Finally, a systematic design of curved metamaterial surfaces is presented, providing a flexible framework for programming low-pass attenuation and wave guiding in three dimensions.

Coupling dynamics of dissipative localized structures: From polarized vector solitons to soliton molecules

Dissipative solitons are well known as representative nonlinear localized wave packets resulting from the composite balance of dispersion, nonlinearity, gain and loss in optical cavities. Since the last three decades, dissipative solitons keep as one of the most active research topics in the framework of nonlinear physics, not only for fundamental researches but also for various industrial applications. From one hand, due to the rich nonlinear dynamics, dissipative solitons have been considered as an ideal testbed to study the pumping-dissipation-bifurcation complexities. On the other hand, the emergences of dissipative solitons are tightly linked with the emission of ultrashort laser pulses, as well as the formation of broadband optical frequency combs. Compared with single-soliton counterpart, the multi-component dissipative solitons have exhibited even more fascinating properties and much wider range of applications, therefore the coupling dynamics of dissipative solitons is the blooming and emergent research area in the last decade. From this point of view, this review article covers the latest developments of compound dissipative solitons, not only in passive Kerr resonators, but also in mode-locked laser cavities. Ranging from polarized vector solitons to soliton molecules, the rising degree of freedom of these multi-component localized structures is boosting the discovery of novel nonlinear dynamics and underpin the various photonic applications in light science.

Terahertz metamaterials for biomolecule sensing based on symmetry-broken unit resonators

Terahertz waves have gained attention owing to their potential for various bio-applications, including broadband spectroscopy, imaging, and sensing. For development of practical applications in clinical fields, highly sensitive molecular detection is essential. Notably, the molecular sensitivity of optical sensing can be enhanced by utilizing localized electromagnetic waves in metallic optical resonators. In this study, we theoretically design terahertz (THz) metamaterial sensors based on the Fano resonance, enabling highly sensitive and selective molecular sensing without additional molecular labeling. The metamaterial sensors consisting of symmetry-broken unit resonators are designed to support Fano resonances with strongly localized electromagnetic waves through coupling of the resonators. The key concept behind the design is to match the Fano resonance with the characteristic resonance in the target molecules, leading to pronounced changes in the transmission spectra of THz waves through the metamaterial with the analytes. We numerically demonstrate the sensing performance by considering steroids as the target molecules and explain the sensing mechanism using both temporal coupled-mode theory and FDTD numerical simulations.

Twist Angle-Dependent Intervalley Charge Carrier Transfer and Recombination in Bilayer WS2.

A twist angle at a van der Waals junction provides a handle to tune its optoelectronic properties for a variety of applications, and a comprehensive understanding of how the twist modulates electronic structure, interlayer coupling, and carrier dynamics is needed. We employ time-dependent density functional theory and nonadiabatic molecular dynamics to elucidate angle-dependent intervalley carrier transfer and recombination in bilayer WS2. Repulsion between S atoms in twisted configurations weakens interlayer coupling, increases the interlayer distance, and softens layer breathing modes. Twisting has a minor influence on K valleys while it lowers Γ valleys and raises Q valleys because their wave functions are delocalized between layers. Consequently, the reduced energy gaps between the K and Γ valleys accelerate the hole transfer in the twisted structures. Intervalley electron transfer proceeds nearly an order of magnitude faster than hole transfer. The more localized wave functions at K than Q values and larger bandgaps result in smaller nonadiabatic couplings for intervalley recombination, making it 3-4 times slower in twisted than high-symmetry structures. B2g breathing, E2g in-plane, and A1g out-of-plane modes are most active during intervalley carrier transfer and recombination. The faster intervalley transfer and extended carrier lifetimes in twisted junctions are favorable for optoelectronic device performance.

On the exact soliton solutions and different wave structures to the modified Schrödinger’s equation

Solitons are specialized solutions to certain nonlinear partial differential equations (PDEs) that behave like localized waves. They maintain their shape and speed as they propagate, interacting with other solitons through collision rather than dispersion. Our research aims to explore a wide range of fascinating and diverse soliton solutions for a modified version of Schrödinger’s equation. This modified equation has significant implications for the fields of fluid dynamics and optical fibers. To solve this model, two efficient methods are employed to reveal various forms of soliton behaviors generated by this model. We incorporate a certain combination of Jacobi elliptic functions as a key component of one of these methods to acquire exact solutions for the model. By utilizing this idea, several solutions expressed in terms of these special functions are derived which have great relevance in various areas of mathematical physics. The soliton solutions obtained in this work represent a completely novel set, distinct from those previously derived by other researchers employing alternative techniques. Furthermore, our findings will introduce new and unique configurations of soliton behaviors stemming from this model, providing insights into practical applications like fiber optic communications. Software visualization demonstrates the findings via contour plots, offering insights into potential fiber optic communication implementations. Our employed methodologies hold the potential to significantly advance the field and contribute to the development of new methodologies for tackling these challenging equations.

Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm.

Bilinear auto-Bäcklund transformations and the hybrid localized wave solutions for the ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation

Bilinear auto-Bäcklund transformations and the hybrid localized wave solutions for the ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation

Reflection of internal gravity waves in the form of quasi-axisymmetric beams

Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). This paper provides an explicit description of the leading approximation of the unique Leray solution to the near-critical reflection of internal waves from a slope in the form of a beam wave. More precisely, our beam wave approach allows to construct a fully consistent and Lyapunov stable approximate solution, L2-close to the Leray solution, in the form of a beam wave, within a certain (nonlinear) time-scale. To the best of our knowledge, this is the first result where a mathematical study of internal waves in terms of spatially localized beam waves is performed.A beam wave is a linear superposition of rapidly oscillating plane waves, where the high frequency of oscillation is proportional to the inverse of a power of the small parameter measuring the weak amplitude of waves.Being localized in the physical space thanks to rapid oscillations (and high variations of the modulus of the wavenumber), beams are physically more relevant than plane waves/packets of waves, whose wavenumber is nearly fixed (microlocalized). At the mathematical level, this marks a strong difference between the previous plane waves/packets of waves analysis and our approach.The main novelty of this work is to exploit the spatial localization of beam waves to exhibit a spatially localized, physically relevant solution and to improve the previous mathematical results from a twofold perspective: 1) our beam wave approximate solution is the sum of a finite number of terms, each of them is a consistent solution to the system and there is no artificial/non-physical corrector; 2) thanks to the absence of artificial correctors (used in the previous results) and to the special structure of the nonlinear term, we can push the expansion of our solution to next orders, so improving the accuracy and enlarging the consistency time-scale.Finally, our results provide a set of initial conditions localized on rays, for which the Leray solution maintains approximately in L2 the same localization.

Applicability of Dynamic, Local, and Diffusive Wave Models for Unified Depth-Averaged Fluid Flow Interaction with Porous Media

Applicability of Dynamic, Local, and Diffusive Wave Models for Unified Depth-Averaged Fluid Flow Interaction with Porous Media

An efficient framework for solving forward and inverse problems of nonlinear partial differential equations via enhanced physics-informed neural network based on adaptive learning

In recent years, the advancement of deep learning has led to the utilization of related technologies to enhance the efficiency and accuracy of scientific computing. Physics-Informed Neural Networks (PINNs) are a type of deep learning method applied to scientific computing, widely used to solve various partial differential equations (PDEs), demonstrating tremendous potential. This study improved upon original PINNs and applied them to forward and inverse problems in the nonlinear science field. In addition to incorporating the constraints of PDEs, the improved PINNs added constraints on gradient information, which further enhanced the physical constraints. Moreover, an adaptive learning method was used to update the weight coefficients of the loss function and dynamically adjust the weight proportion of each constraint term. In the experiment, the improved PINNs were used to numerically simulate localized waves and two-dimensional lid-driven cavity flow described by partial differential equations. Meanwhile, we critically evaluate the accuracy of the prediction results. Furthermore, the improved PINNs were utilized to solve the inverse problems of nonlinear PDEs, where the results showed that even with noisy data, the unknown parameters could be discovered satisfactorily. The study results indicated that the improved PINNs were significantly superior to original PINNs, with shorter training time, increased accuracy in prediction results, and greater potential for application.

Wave-impact forces and moments due to random waves on a jacket-type platform for different relative submergence of the deck

Force and moment measurements due to wave impacts were conducted on a jacket platform model under six distinct relative deck submergence conditions. The water depth was carefully chosen to facilitate scenarios ranging from sufficient deck air gaps to partial and complete submergence. For the purpose of our analysis, we focused on peak and average peak wave force and moment values. The study uncovers that the peak wave force towards the shore can escalate to 1.5 times the peak wave force towards the sea. Moreover, the ratio of the peak shoreward force to the average peak shoreward force fluctuates between 3 and 4, contingent upon the relative water level at the deck base and the prevailing wave condition. Remarkably, the peak upward wave force on the deck can reach 5 to 7 times the peak inline wave force. A review of existing guidelines suggests a significant need to enhance research regarding the air gap between the deck and the still water level (SWL), as well as its effect on global and local wave forces and moments on the structures. Our finding establishes that the relative water level from the base of the deck is a crucial parameter in the design process of these structures. This study presents a more in-depth understanding of the physical mechanisms at play by utilizing a realistic jacket platform model. It serves as an initial exploration into the influence of air gap and relative water depth on wave-impact forces and moments. The results obtained from this study shed light on optimal design strategies for jacket-type offshore drilling platforms, considering green water effects. This understanding will enhance the life expectancy and survivability of such platforms.

Interior Route and Seasonal Dynamics of the Meridional Current in the Eastern Indian Ocean Tropical Gyre

AbstractThe eastern boundary current of the tropical Indian Ocean (IO) connects the equatorial/south tropical IO, contributing to the meridional heat and salinity exchange. As a part of the IO tropical gyre, the meridional current in the eastern IO tropical gyre (East Sumatra Current, ESC) flows southward in the mean state. However, the route of this current varies with months. Drifter trajectories display an exceptional route that turns southeastward before reaching Sumatra in the austral winter and spring, considered the interior ESC. This study uses observations and reanalysis data sets to investigate the seasonal structure and forcing mechanisms behind the interior ESC. The velocity is decomposed into geostrophic and wind‐driven components. The results suggest that the geostrophic component plays a dominant role in the ESC recirculating early from April to June. The southward geostrophic currents are mainly caused by positive zonal temperature gradients, which are induced by both the cold anomaly of the Chagos Dome and the warm water carried by the Indonesian Throughflow, particularly in April and May. Meanwhile, the annual Rossby wave contributes to the temperature anomaly of the Chagos Dome. During the monsoon that prevails after July, the wind‐driven component increases and becomes the primary forcing, accompanying the slowdown of geostrophic velocity. Therefore, the local wind stress, wave propagation, and water mass transport account for the formation of the seasonal interior ESC.

Highly localized continuous wave optical vortex with controllable orbital angular momentum orientation and topological charge.

We report an approach to simultaneously control orbital angular momentum (OAM) orientation and topological charge in highly localized optical vortices by employing a 4π focusing system. The required continuous wave illumination field in the pupil planes is derived by superimposing the radiation pattern of only one dipole placed at the focal point of the high numerical aperture lens and the corresponding tailored spiral phase factor. The topological charge and OAM orientation of the obtained focused fields are quantitatively evaluated based on the focal field distributions calculated by the Richards-Wolf vector diffraction integration theory. Results show that the OAM of the generated optical vortices can be tailored by changing the oscillation orientation of the mimic dipole and the topological charge of the superimposed spiral phase term. The presented method may find potential applications in optical trapping, optical tweezers, light-matter interaction, etc.

Nonlinear wave excitations in the (2+1)-D asymmetric Nizhnik-Novikov-Veselov system

The (2+1)-dimensional nonlinear asymmetric Nizhnik-Novikov-Veselov system is one of the extended versions of the Korteweg-de Vries equation, and as such of considerable significance in nonlinear wave dynamics. In this work, it is transformed into a bilinear form by using the Hirota transformation and then treated by the variable separation method. In particular, by separating variables in a specific manner, a class of solutions is obtained, which are constructed with the help of three auxiliary functions, Py, Ry, and Qxt. By selecting the three functions conveniently, we obtain novel nonlinear excitations for the asymmetric Nizhnik-Novikov-Veselov system. To make our results more explicit and interesting, various types of nonlinear profiles were displayed, colloquially named as the parallelogram, walnut, dark breather, half-moon breather, and the top-compressed quadrilateral breather structures. It is found that these local wave packets can be well controlled by appropriately selecting the three auxiliary functions, and that the variable separation approach can be extended to other high-dimensional nonlinear systems.

Domain decoupling implementation for efficient ultrasonic wave simulations using scaled boundary finite elements and the mortar method

We introduce a novel approach that combines the scaled boundary finite element method (SBFEM) with a mortar coupling to enhance the computational modelling of elastic wave propagation and interaction with local features in the ultrasonic range. The key objective is to achieve decoupling between different regions of interest, enabling independent meshes for the zones where waves either propagate or interact with localised discontinuities in the elastic media. This decoupling allows us to exploit the benefits offered by various SBFEM formulations. Thus, we can select the most suitable solution for each specific region. An important concept we emphasise is the differentiation between the near field and far field regions. The near field encompasses zones where the precise representation of small features compared to the wavelength is crucial. At the same time, the far field comprises homogeneous regions where the waves propagate without interactions, eventually radiating towards infinity if the domain is unbounded. By separating these two zones, we can improve the computational performance by employing finer discretisation only where necessary. Furthermore, this decoupling enables the reuse of far field models in parametric analyses, making it highly valuable for scenarios focused particularly on local elastic wave interactions. This approach offers considerable potential in such cases. The modelling technique is validated, and its potential is demonstrated through practical applications.

Regional Features of the 20–30 Day Periodic Behavior in the Southern Hemisphere Summer Circulation

AbstractThe Southern Hemispheric storm tracks exhibit a robust intraseasonal periodicity of 20–30 days as the leading mode of zonal‐mean eddy kinetic energy. To what extent this hemispheric‐scale mode of variability translates to smaller scales remains debated. This work studies the regional features of Southern Hemisphere storm tracks through a filtered variance analysis of local finite‐amplitude wave activity. While the synoptic variance is zonally elongated over the storm track, we find a strong enhancement of intraseasonal variability within the South Pacific. With a minimum strength of the storm track, this region is marked with 20–30 day periodic behavior of local wave activity and precipitation and is driven by enhanced variability of low‐level eddy heat flux on the same timescale. The local nature of 20–30 day periodicity offers a potential source of subseasonal to seasonal predictability for weather analysts and forecasters.