Trapped Waves Research Articles

Strength and timing of austral winter Angolan coastal upwelling

The tropical Angolan upwelling system (tAUS) is a highly productive ecosystem of great socio-economic importance. Productivity peaks in austral winter and is linked to the passage of remotely forced upwelling coastal trapped waves (CTWs), where the strength of the productivity peak is associated with the amplitude of the upwelling CTW. Here, we analyze the year-to-year variability in the timing and amplitude of the austral winter upwelling CTW by examining sea surface temperature, sea level anomaly, and wind fields. Our results show that the timing of the CTW is influenced by variability in the equatorial region and along the southern African coast. Weaker equatorial easterlies from April to July delay the generation of the upwelling Kelvin wave, leading to a later arrival of the upwelling CTW. In contrast, the amplitude of the CTW is primarily influenced by variability in the eastern equatorial Atlantic and the central South Atlantic, where the South Atlantic Anticyclone is located. A cooling in the eastern equatorial Atlantic three to four months before the arrival of the CTW causes stronger zonal winds, ultimately leading to a stronger austral winter upwelling CTW. Our results suggest that the timing and amplitude of the upwelling CTW in the tAUS during austral winter are predictable on seasonal time scales.

Ultra-broadband underwater meta-absorber with gradient impedance-matched composite material

Abstract We have developed an underwater acoustic meta-absorber that exhibits ultra-broadband absorption, with most of absorption coefficients exceeding 0.9 across the frequency range of 1 kHz−20 kHz. This performance is achieved through the localized trapping of acoustic waves and efficient energy dissipation, facilitated by local resonances within meticulously designed, impedance-matched composite materials. The designed gradient structure of the absorber allows for a reduced width of 84 mm (0.05λ at 1 kHz) and a customizable length, determined by the number of unit cells, each with a length of 15 mm (0.01λ at 1 kHz). This different design approach yields an ultra-broadband meta-absorber of compact dimensions, offering a promising alternative for the development of underwater absorption metamaterials and their practical applications.

Rainbow trapping and piezoelectric energy harvesting of flexural waves in a gradient metamaterial waveguide

Metamaterials have provided a new way of controlling classic waves to achieve applications in space. In this work, we construct the gradient waveguide in two-dimensional elastic metamaterial plate to achieve rainbow trapping of flexural waves and then realize piezoelectric energy harvesting. Based on the band gap of flexural waves, the waveguide is formed by the introduction of line defects into the perfect metamaterial plate. The gradient waveguide is designed through the investigation of dispersion curves of guided waves for different geometrical parameters. The elastic flexural waves at different frequencies in the gradient waveguide separate, stop and hence are amplified in different positions. That is, the rainbow trapping is observed. To convert mechanical energy into electrical energy, piezoelectric patches are attached in the proposed metamaterial waveguide. Compared with a reference harvester (i.e., a homogeneous plate without metamaterial structure), the output power from the metamaterial energy harvester is significantly amplified. Besides, the proposed metamaterial harvester exhibits the capacity of multi-frequency energy harvesting.

Topological slow light and rainbow trapping of surface wave in valley photonic crystal bounded by air

Abstract Topological slow light and rainbow trapping tend to rely on large-scale interface structure in previous research work, which have restricted further miniaturization. In this work, we propose a method to realize slow light and rainbow trapping at the zigzag edge of a single valley photonic crystals (VPCs) bounded by air, which is very different from previous studies where rainbow trapping is supported at the interface separating two VPCs with inversion symmetry. By constructing the VPC–air boundaries and VPC–VPC interfaces experimentally, we have observed the topologically protected rainbow trapping simultaneously at the external and internal boundary. This work provides a feasible platform for the miniaturized optical communication devices such as optical buffers, optical storage and optical routing.

Effects of Stratification on Wind‐Driven Upwelling Over a Coastal Valley

AbstractIn‐situ observations indicate variations in stratified conditions over the coastal valley off the Sansha Bay in the northwestern Taiwan Strait across different years. However, dynamic processes and mechanisms governing the upwelling process over the valley, as influenced by stratification, are still unknown. By employing idealized numerical simulations, we demonstrate that compared to the unstratified case, the surface offshore flow intensifies, upwelling flux and net cross‐shore transport are enhanced, upwelling area expands, and the cross‐shore velocity structure is modified over the valley under stratified conditions. The primary factor controlling the vertical velocity within the valley is the relative vorticity change along a streamline (RVC). Further decomposition of the RVC reveals that the depth‐averaged alongshore velocity () and the depth‐averaged alongshore gradient of vorticity () primarily modulate the magnitude and spatial distribution of the vertical velocity. The negative zone of the expands in the valley, resulting in a larger upwelling area. The magnitude of the in the upper layer is slightly enhanced. The combined influence of these two factors leads to increased upwelling flux in the valley under stratified conditions. The net upslope motion over the valley is intensified under stratified conditions. The augmented advection of relative potential vorticity, originating from the increased amplitude of coastal trapped lee waves, primarily contributes to the enhanced net cross‐shore transport in the valley.

A Statistical Examination of Interactions Between 1‐Hz Whistler Waves and Ions in the Earth's Foreshock

AbstractThe 1 Hz whistler wave precursors attached to shock‐like structures are often observed in the foreshock. Using observations from the Magnetospheric Multiscale mission, we investigate the interactions between 1 Hz waves and ions. Incoming solar wind ions do not cyclotron‐resonate with the wave, since typically the wave is right‐handed in their frame. We demonstrate that solar wind ions commonly exhibit 180° gyro‐phase bunching from the wave magnetic field, understanding it with a reconciled linear theory and non‐linear trapping theory for non‐cyclotron‐resonant modulations. Along the longitudinal direction, solar wind ions experience Landau resonance, exhibiting either modulations at small wave potentials or trapping in phase‐space holes at large potentials. The results also improve our understanding of foreshock structure evolution and 1 Hz wave excitation. Shock‐like structures start with having incoming solar wind and remotely reflected ions from further downstream. The ion‐scale 1 Hz waves can already appear during this stage. The excitation may be due to shock‐like dispersive radiation or kinetic instabilities resonant with these remotely reflected ions. Ions reflected by local shock‐like structures occur later, so they are not always necessary for generating 1 Hz waves. The wave leads to ion reflection further upstream, which may cause reformation of shock‐like structures. In one event, locally reflected ions exhibit non‐cyclotron‐resonant modulation in the early stage, and later approach the anomalous cyclotron resonant condition with gyro‐phases ∼270°. The latter is possibly due to nonlinear trapping in regions with an upstream‐pointing magnetic field gradient, linked to reformation. Some additional special features, such as frequency dispersions, are observed, encouraging further investigations.

The Generation of Superinertial Coastally Trapped Waves by Scattering at the Coast

Abstract A series of idealized numerical simulations is used to examine the generation of mode-one superinertial coastally trapped waves (CTWs). In the first set of simulations, CTWs are resonantly generated when freely propagating mode-one internal tides are incident on the coast such that the angle of incidence of the internal wave causes the projected wavenumber of the tide on the coast to satisfy a triad relationship with the wavenumbers of the bathymetry and the CTW. In the second set of simulations, CTWs are generated by the interaction of the barotropic tide with topography that has the same scales as the CTW. Under resonant conditions, superinertial coastally trapped waves are a leading order coastal process, with alongshore current magnitudes that can be larger than the barotropic or internal tides from which they are generated.

A space-adiabatic theorem for longitudinal and transversal wave motion analysis of graded metamaterials

The use of graded metamaterials is widespread in the fields of wave manipulation and energy harvesting. However, they have the drawback of causing energy scattering after a certain period due to wave reflection or trapping, known as the rainbow effect, in some cases. To address this issue, we extend the adiabatic theorem to the spatial modulation field to mitigate the impact of the rainbow effect, thereby enhancing transmission at the interface of graded metamaterials. Firstly, an analytical expression for the limiting gradient in the space-adiabatic theorem is derived. Then, it is applied to study the longitudinal wave motion in a spring-mass with graded resonators (SMGR) system and the transversal wave motion in a beam with graded resonators (BGR) system. The numerical study demonstrates that if the spatial gradient of system properties is small enough to satisfy the adiabatic theorem, wave scattering can almost be neglected, and transmission will experience a significant increase compared to the non-adiabatic case. Finally, the critical boundary between adiabatic and non-adiabatic cases is determined using the fitting method. This study introduces a design strategy for graded metamaterials, offering opportunities for communication, sensing, energy harvesting, and various other applications.

Extracting fault-zone structures using the virtual seismometer method: from theoretical to synthetic test

Summary Rocks near a fault plane are commonly damaged by multiple earthquake ruptures, forming damage zones. The damage zone is important structures controlling various properties of a fault, yet its fine scale (tens to hundreds of meters) structure is difficult to resolve with surface seismic observations. We propose to use earthquakes that occur at depth within a fault zone as virtual seismometers (VSs) and use surface observations to extract Green's function (GFs) between VS pairs (VSGFs) . This method resembles that of ambient noise tomography and the retrieved VSGFs are related to the structures between event pairs. In this study, we develop the theory about how to extract VSGFs using surface stations deployed across a fault zone. Firstly, we use a half-space model and Fresnel zone analysis to determine the upper and lower limits of the GF frequency band, which is controlled by the station spacing and aperture of a given seismic array. Then, for VS in a fault zone, we demonstrate that the VSGF can be retrieved by linear seismic arrays deployed across the fault, and that the VSGF is equivalent to waves emitted simultaneously from an array of mirror sources of one event and received by the other. Secondly, the half-space result is directly adopted to determine the corresponding frequency band in the damage zone situation. Thirdly, we analyze different combinations of VS pair geometry and conclude that a relatively larger VS distance (much larger than the damage zone width) is more effective to recover damage zone structures for the available frequency bands. In this situation, VSGFs are trapped waves, that is represented by the interference of mirror sources. In such a case, the trapped waves are equivalent to surface waves, which have dispersion features to extract damage zone structures. Finally, we adopt the VSGF method to the Ridgecrest earthquake aftershock monitoring array and use a profile of aftershocks to extract 6 pairs of VSGFs. The spatial variation of VSGFs may reflect the depth-dependent variation of damaged zone. Our analysis shows a promising direction to use VSGFs to extract spatial variations of fault damaged zones.

Intraseasonal Variations and Extreme Occurrence in the Local Sea Level Along the Western Coast of India Remotely Controlled by a Basin‐Scale Climate Variability

AbstractThe equatorial Kelvin waves, remotely excited by basin‐scale climate modes, and subsequent coastal trapped waves significantly influence the intraseasonal variations, their low‐frequency modulations, and the frequency of extreme sea level events along the western coast of India. This study demonstrates that the frequency of extreme events are linked to the phase of the Indian Ocean Dipole mode. The temporal changes in the occurrence frequency of extremes are simulated in an eddy‐resolving ocean model consistently with observations. However, a non‐eddying model significantly underestimate the occurrence frequency of extreme sea level events, suggesting the importance of coastal trapped wave propagations regulated by the horizontal scale with the Rossby radius of deformation. This result implies that many state‐of‐the‐art climate models with a one‐degree ocean horizontal resolution may underestimate future coastal sea level variability and the frequency of extreme events under global warming and potential modulations of major internal climate modes.

Rainbow trapping and concentration of surface waves on broad waveguide

Abstract In recent years, topological insulators have been widely designed to manipulate various types of classical waves. The topological edge states characterized by defect and backscattering immunity show great application potential in energy harvesting. This work reports a spin-locked topological surface wave channel, which consists of concrete-filled steel tubes (CFST) placed on foundation soil. Here, the distance between the lattice and the center of the CFST controls the hopping strength between adjacent atoms, determining the topological phase transition. Introducing the surface wave crystal with Dirac cones in the interface, then the robust broad waveguide modes of phononic heterostructure are explored. Notably, incorporating the rainbow effect allows for precise regulation and reliable concentration within the broad waveguide. The proposed broad waveguide surpasses traditional waveguides by simultaneously focusing and segregating energy, enabling applications in low-frequency energy harvesting, sensing, and logic gates. Our work will provide an efficient recovery platform for daily vibration energy, especially for vehicle loads.

A novel approach for using submerged structure as wave-trapping zone

Entrapment of waves is a hydrodynamic phenomenon that occurs under certain incident wave circumstances. The present article, based on potential flow theory, deals with the phenomena of waves interacting with a proposed submerged structure. Focus of this study is on the frequencies for which the wave trapping occurs in the region of the proposed structure. The frequencies presented correspond to significantly higher values of velocity potential in the region. We refer this region as a wave-trapping zone. In scattering problem the reflection coefficient is also investigated with respect to submergence depth, water depth, length and rigidity of the structure and other physical parameters. The optimum values of the structural parameters are also proposed for zero transmission and trapping frequencies. The investigation establishes that for a suitable configuration we can achieve a range of frequencies for which such a geometry can be used as breakwater with total reflection and at certain frequencies also for trapping of waves.

Observation of dynamic non-Hermitian skin effects

Non-Hermitian physics has emerged as a new paradigm that profoundly changes our understanding of non-equilibrium systems, introducing novel concepts such as exceptional points, spectral topology, and non-Hermitian skin effects (NHSEs). Most existing studies focus on non-Hermitian eigenstates, whereas dynamic properties have been discussed only recently, and the dynamic NHSEs are not yet confirmed in experiments. Here, we report the experimental observation of non-Hermitian skin dynamics using tunable one-dimensional nonreciprocal double-chain mechanical systems with glide-time symmetry. Remarkably, dynamic NHSEs are observed with various behaviors in different dynamic phases, which can be understood via the generalized Brillouin zone and the related concepts. Moreover, the observed dynamic NHSEs, amplifications, bulk unidirectional wave propagation, and boundary wave trapping provide promising ways to manipulate waves in a controllable and robust way. Our findings open a new pathway toward non-Hermitian dynamics, which will fertilize the study of non-equilibrium phases of matter.

Study of nonlinear trapped lee waves in the modified β-plane approximation

In the modified β-plane approximation, we derive exact solutions to the nonlinear governing equations of three-dimensional trapped lee waves influenced by Coriolis forces or Coriolis forces and centripetal forces, respectively. Further, we obtain the dispersion relation and qualitatively analyze the pressure, density, and vorticity in two cases. In this process, we find more accurate representations of solutions caused by the incorporation of a gravitational-correction term and investigate the influence of centripetal forces on trapped lee waves.

Research on data analysis method of oscillating water column wave energy converters

Abstract Taking the floating oscillating water column central tube wave energy converters (OWC WECs) as the research goal, the Fourier transform (FFT), and the ensemble empirical mode decomposition method (EEMD) were used to statistically analyze the wave height, motion acceleration, velocity and displacement of the device in the physical model test from the perspective of a frequency domain. Through the Fourier transform, the energy spectrum of the incident wave and the motion of the WEC is obtained, and it is found that the peak frequency of the two is the same, that is, the period is 1.138s, but the peak energy of the former is slightly greater than that of the latter. Through the ensemble empirical mode decomposition method, the 1-8 intrinsic mode functions of the incident wave and the displacement of the device are obtained, which shows that the device efficiently captures the dominant frequency wave in the incident wave, that is, the wave height is 0.0628m, the period is 1.1s, and the motion displacement of the vertical direction obtained by the device is 0.0585mm, and the period is 1.1119s. At the same time, it absorbs low-frequency, long-period reflected waves in the pool. The analysis results of the two methods are highly consistent, and the OWC WEC shows good hydrodynamic performance, with efficient wave trapping ability and fast wave responsability. This paper’s research methods and results provide a basis for the later optimization of the device and a new idea for the data processing method of the WECs.

Effect of a harmonic surface pressure on wave propagation over a beach

The objective is to study the harmonic forced wave motion over a beach by a finite Fourier transform technique. The constructed approximate solution has a logarithmic singularity at the shoreline. It accounts for reflexion and local perturbations. Trapping of waves may take place for particular choices of the applied surface pressure excess. The case of a wave incident against a cliff with horizontal bottom is solved exactly. The method deals invariably with a variety of bottom shapes, including the case where there is an additional corrugation of the bottom on a finite interval. Other bottom boundary conditions than impermeability can be treated as well. The results may be of interest in several practical applications, in particular the evaluation of the reflected wave. Numerical applications for a plane sloping beach, a parabolic-type beach and a shelf-type beach are presented and the systems of streamlines have been drawn over and in the proximity of the beach.

Wave trapping by porous breakwater near a rigid wall under the influence of ocean current

The present work investigates the water wave interaction with bottom-standing thick porous trapezoidal-shaped structures and shore-side vertical rigid wall in the presence of uniform ocean currents. This study has been done to understand the impact of different physical parameters like friction, porosity, and ocean currents along with different structural parameters (width and height) on different phenomena like wave energy reflection, wave forces, wave energy dissipation, etc. The quadratic boundary element method-based numerical technique has been used to solve the boundary value problem. The structural porosity is modeled using Sollitt and Cross’s model of water wave interaction with thick porous structures. Several results associated with the wave energy reflection and energy dissipation have been analyzed. Also, the wave force exerted by the incoming waves has been investigated to check the stability and sustainability of the right vertical rigid wall and porous structure. The Doppler-shift effect is observed in wave transformation characteristics due to the presence of ocean currents. The impact of following and opposing ocean currents can be seen in the graph of wave energy reflection, dissipation, and wave forces. The periodic patterns can be observed clearly in wave characteristics like wave energy reflection, dissipation, and wave forces when plotted against the non-dimensional separation gap between the porous breakwater and shore-side rigid seawall.

Coupled topological rainbow trapping of elastic waves in two-dimensional phononic crystals

Rainbow trapping, observed in elastic waves, has attracted considerable scientific interest owing to its potential applications in energy harvesting, buffering, and wavelength-division multiplexing devices. However, previous approaches have often necessitated complex geometric modifications to the scatterer, such as altering dimensions or shifting along diagonals to corners, limiting practical utility. Here, we realize the coupled topological edge states (CTESs) of elastic waves in a two-dimensional (2D) solid phononic crystal (PC) with inversion center changes. Changing the inversion center along the x or y directions by a specific distance can induce the topological phase transition. The topological edge states (TESs) arise at the interface by combining PCs with different topologies positioned adjacent to each other. Furthermore, it is demonstrated that TES exhibits topological robustness against defects. By introducing a gradient into the PC structure by altering the geometrical parameters of scatterers along the interface, the topological rainbow trapping of elastic waves is achieved. Finally, the CTES are generated by the interaction between TESs of different interfaces, which can lead to coupled topological rainbow trapping in phononic heterostructures with different displacement parameters along the multiple interface gradient. Our results pave the way for manipulating the symmetric and antisymmetric topological modes of elastic waves in topologically coupled waveguides, which offers potential applications in selective filtering and multiband waveguiding.

Drivers and impact of the 2021 extreme warm event in the tropical Angolan upwelling system

Benguela Niños are extreme warm events that typically occur during the main downwelling season (austral fall) in the tropical Angolan upwelling system when the biological productivity is low. However, the extreme warm event that occurred between April and August 2021 stands out due to its late timing. It occurred and peaked during the main upwelling season in austral winter with sea surface temperature anomalies exceeding 2 °C in the Angola-Benguela area in June 2021. This led to an unprecedented reduction of the net primary production off southern Angola. Both local atmospheric processes and remote influences (via downwelling coastal trapped wave propagations) have contributed to the onset of the extreme warm event in April and its intensification towards the peak phase in June. Moreover, the poleward advection of warm equatorial waters toward the Angola-Benguela area in May 2021 might have contributed to the warming, since the transport of the Angola Current, as estimated from observations, was notably elevated, amounting to 2.1 Sv.

Internal Tides at the Coast: Energy Flux of Baroclinic Tides Propagating into the Deep Ocean in the Presence of Supercritical Shelf Topography

Abstract The generation of internal tides at coastal margins is an important mechanism for the loss of energy from the barotropic tide. Although some previous studies attempted to quantify energy loss from the barotropic tides into the deep ocean, global estimates are complicated by the coastal geometry and spatially and temporally variable stratification. Here, we explore the effects of supercritical, finite amplitude bottom topography, which is difficult to solve analytically. We conduct a suite of 2D linear numerical simulations of the barotropic tide interacting with a uniform alongshore coastal shelf, representing the tidal forcing by a body force derived from the vertical displacement of the isopycnals by the gravest coastal trapped wave (of which a Kelvin wave is a close approximation). We explore the effects of latitude, topographic parameters, and nonuniform stratification on the baroclinic tidal energy flux propagating into the deep ocean away from the shelf. By varying the pycnocline depth and thickness, we extend previous studies of shallow and infinitesimally thin pycnoclines to include deep permanent pycnoclines. We find that scaling laws previously derived in terms of continental shelf width and depth for shallow and thin pycnoclines generally hold for the deeper and thicker pycnoclines considered in this study. We also find that baroclinic tidal energy flux is more sensitive to topographic than stratification parameters. Interestingly, we find that the slope of the shelf itself is an important parameter but not the width of the continental slope in the case of these steep topographies. Significance Statement The objective of this study is to better understand how vertical density stratification, which can vary seasonally in the ocean, affects the interaction of tides with steep coastal topography and the generation of waves that travel away from the coast in the ocean interior. These waves in the interior can travel over long distances, carrying energy offshore into the deep ocean. Our results suggest that the amount of energy in these internal waves is more sensitive to changes in topography and latitude than to the vertical density profile. The scaling laws found in this study suggest which parameters are important for calculating global estimates of the energy lost from the tide to the ocean interior at the coastal margins.