Wave Period Research Articles

Propagation Dynamics in Time‐Periodic Reaction–Diffusion Systems with Network Structures

ABSTRACTThe main purpose of this paper is to study the propagation dynamics for a class of time‐periodic reaction–diffusion systems with network structures. In the first part, by using the persistence theory, we obtain threshold results for the extinction and uniform persistence of the corresponding periodic ordinary differential system. The second part is concerned with the asymptotic speed of spread and traveling wave solutions. The uniform boundedness of solutions is proved by employing the refined high‐dimensional local ‐estimate and abstract periodic evolution theories and the spreading properties of the corresponding solutions are established. We also prove the existence of the critical periodic traveling wave with wave speed by using a delicate limitation argument. Finally, these results are applied to a multistage epidemiological model.

Internal Doubly Periodic Gravity-Capillary Waves with Vorticity

Internal Doubly Periodic Gravity-Capillary Waves with Vorticity

Spectra of solar shallow-water waves from bright point observations

Rossby waves, large-scale meandering patterns drifting in longitude, detected in the Sun, were recently shown to a play a crucial role in understanding “seasons” of space weather. Unlike Earth's purely classical atmospheric Rossby waves, the solar counterparts are strongly magnetized and most likely originate in the tachocline. Because of their deeper origin, detecting these magnetized Rossby waves is a challenging task that relies on careful observations of long-lived longitudinally drifting magnetic patterns at the surface and above. Here, we have utilized 3 years of global, synchronous observations of coronal bright point densities to obtain empirical signatures of dispersion relations that can be attributed to the simulated waves in the tachocline. By tracking the bright point densities at selected latitudes, we computed their wave-numbertimes frequency spectra. Wave-numbertimes frequency spectra were computed utilizing the Wheeler-Kiladis method. This method has been extensively used in the identification of equatorial waves in Earth's atmosphere by highlighting spectral peaks in the wave-numbertimes frequency space. Our results are compatible with the predictions of magneto-Rossby waves with typical periods of several months and inertio-gravity waves with typical periods of a few weeks, depending on the background magnetic field's strength and stratification at the convection zone base. Our analysis suggests that magnetized Rossby waves originate from the tachocline toroidal field of lesssim 15 kG. Global observations of bright points over extended periods will allow us to better constrain the stratification and magnetic field strength in the tachocline.

Impact of relativistic positron beam on ion-acoustic solitary, periodic and breather waves in Earths’ ionospheric region through the framework of KdV and modified KdV equation

Abstract This study explores the propagation characteristics of ion-acoustic periodic, soliton, and breather waves in electron-positron-ion (EPI) plasma with a relativistic positron beam. The Korteweg–de Vries (KdV) equation is obtained by applying the traditional reductive perturbation method (RPM) to the fundamental set of fluid equations. When the KdV model is unable to accurately represent the nonlinear system’s evolution, a modified Korteweg–de Vries (mKdV) equation is constructed. In both models, Jacobi elliptic functions are used to derive periodic solutions, and a connection between periodic waves and soliton solutions is established. Hirota’s bilinear method is used to generate breathers directly from the KdV type framework without utilizing the modified Schrödinger framework inferred from the KdV type framework, which is a prevalent method in studies of nonlinear waves. Numerical knowledge of various physical factors in the ionospheric region is incorporated into the model to elucidate wave propagation in the Earth’s upper atmosphere.

From “open ocean” to “exposed aquaculture”: why and how we are changing the standard terminology describing “offshore aquaculture”

The term “offshore” with regards to aquaculture has hitherto encompassed various perspectives, including technology, geographic location, legal jurisdiction, and more. To resolve the ambiguity in this term and understand its implications for current and future aquaculture development, “offshore” should be resolved into two separate metrics: distance from shore and energy exposure. The United Nations Convention on the Law of the Sea (UNCLOS) distinguishes between internal waters, territorial sea, contiguous zone, exclusive economic zone (EEZ), and the high seas, but currently has no precise definition for “offshore” in its provisions, and therefore no applicable laws pertaining to “offshore” aquaculture. Regulating a multi-technology aquaculture sector may require integrating new spatial concepts into the law rather than merely adapting and extending current regulatory designs to include new production concepts. The metrics of distance from shore and exposure are seen as a range rather than a specific threshold, allowing for a continuum. Distance from shore is readily quantified as a distance from a baseline. To rigorously quantify the exposure, the influence and interactions of oceanic parameters (water depth, water current, and wave height and period) we utilized to generate six indices. These oceanic parameters are seen as the main contributions which influence the physical and some biological parameters required for site, species, and technology selection. Four shellfish, three seaweed, and three finfish sites along with 20 potential aquaculture sites were examined using the indices in association with the energy index to determine tolerances of the structures and their ability to cultivate their relevant species. Two indices, Specific Exposure Energy (SEE) and Exposure Velocity (EV), were selected for utilization in the analysis of sites based on their ease of use and applicability. The interaction between the energy indices and various aspects of farm operations and performance were explored. The indices developed and used in the case studies presented have been shown to be useful tools in the general assessment of the energy that will influence the species and equipment selection at potential aquaculture sites. The indices do not provide a definitive answer as to the potential financial success of a site as this requires other inputs relating to infrastructure costs, annual production, distance from port, sales strategy, etc. However, the Specific Exposure Energy index creates a useful tool to describe site energy and be comprehensible to a wide range of stakeholders. We recommend the SEE index be adopted as the predominant tool to communicate the exposure level of aquaculture sites.

New analytical wave structures for generalized B-type Kadomtsev–Petviashvili equation by improved modified extended tanh function method

Abstract Recently, solving the complicated nonlinear partial differential equations has become very important demand in order to simulate their physical phenomena. This manuscript focuses on extracting the wave solutions of (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation (GBKPE), which demonstrates the behavior of nonlinear waves in fluid mechanics. The improved modified extended Tanh function (IMETF) method is the suggested method to do this task as it gives different types of solutions. This method enables us to obtain many solutions, such as Jacobi elliptic, dark soliton, and singular soliton, exponential, and singular periodic wave solutions. Additionally, for more illustrations graphical visual representations of some solutions are provided.

Nonlinear waves in a sheared liquid film on a horizontal plane at small Reynolds numbers

The nonlinear waves in a sheared liquid film on a horizontal plate at small Reynolds numbers are examined by theoretical and numerical approaches. The analysis employs the long-wave approximation along with finite difference schemes. The results show that the surface tension can suppress disturbances and prevent the occurrence of singularities. While the film flow is driven by the shear stress on the interface, its instability highly depends on the magnitude and direction of gravity. Specifically, when the direction of gravity is opposite to the wall-normal direction, perturbations are stabilized by gravity. In contrast, when these two directions are the same, the gravitational force is destabilizing, and stationary travelling waves can exist if a balance is reached between the effects of gravity and surface tension. For the steady solitary waves, there are quasi-periodic oscillations occurring between two stationary points, indicating the presence of heteroclinic trajectories. For periodic waves, the evolutions are sensitive to several parameters and initial disturbances, while one steady-state wave exhibits a sine function-like behaviour.

Performance Characteristics of Newly Developed Real-Time Wave Measurement Buoy Using the Variometric Approach

Accurate measurement of ocean wave parameters is critical for applications including ocean modeling, coastal engineering, and disaster management. This article introduces a novel global navigation satellite system (GNSS) drifting buoy for surface wave measurements that addresses the challenges of performing real-time, high-precision measurements and realizing cost-effective large-scale deployment. Unlike traditional approaches, this buoy uses the kinematic extension of the variometric approach for displacement analysis stand-alone engine (Kin-VADASE) velocity measurement method, thus eliminating the need for additional high-precision measurement units and an expensive complement of satellite orbital products. Through testing in the South China Sea and Laoshan Bay, the results showed good consistency in significant wave height and main wave direction between the novel buoy and a Datawell DWR-G4, even under mild wind and wave conditions. However, wave mean period disparities were observed partially because of sampling frequency differences. To validate this idea, we used Joint North Sea Wave Project (Jonswap) spectral waves as input signals, the bias characteristics of the mean periods of the spectral calculations were compared under conditions of identical input signals and gradient-distributed wind speeds. Results showed an average difference of 0.28 s between the sampling frequencies of 1.28 Hz and 5 Hz. The consequence that high-frequency signals have considerable effects on the mean wave period calculations indicates the necessity of the buoy’s high-frequency operation mode. This GNSS drifting buoy offers a cost-effective, globally deployable solution for ocean wave measurement. Its potential for large-scale networked ocean wave observation makes it a valuable oceanic research and monitoring instrument.

Residual symmetry and interactions between solitons and periodic waves of the Drinfeld–Sokolov–Satsuma–Hirota system

In this paper, the Drinfeld–Sokolov–Satsuma–Hirota (DSSH) system is studied by using residual symmetry and the consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the DSSH system is localized to Lie point symmetry in a properly prolonged system, based on which we get a new Bäcklund transformation for this system. New symmetry reduction solutions of the DSSH system are obtained by applying the classical Lie group approach on the prolonged system. Moreover, the DSSH system proves to be CRE integrable and new interesting interaction solutions between solitons and periodic waves are generated and analyzed.

Numerical Analysis and Validation of Horizontal and Vertical Displacements of a Floating Body for Different Wave Periods

This study concentrates on numerically evaluating the behavior of a floating body with a box format. Although research on floating objects has been conducted, the numerical modeling of Wave Energy Converter (WEC) devices, considering the effects of fluctuations, remains underexplored. Therefore, this research intends to facilitate the analysis of floating devices. First, the experimental data served as a benchmark for evaluating the motion paths of the floating box’s centroid. Second, the effects of various wave periods and heights on the floating body’s movement were analyzed. The Volume of Fluid (VOF) multiphase model was applied to simulate the interactions between phases. The computational model involved solving governing equations of mass conservation, volumetric fraction transport, and momentum, employing the Finite Volume Method (FVM). The validation demonstrated that the Normalized Root Mean Square Error (NRMSE) for the x/h ratio was 3.3% for a wave height of 0.04 m and 4.4% for a wave height of 0.1 m. Moreover, the NRMSE for the z-coordinate to the depth of water (z/h) was higher, at 5% for a wave height of 0.04 m and 5.8% for a wave height of 0.1 m. The overall NRMSE remained within acceptable ranges, indicating the reliability of the numerical solutions. Additionally, the analysis of horizontal and vertical velocities at different wave periods and heights showed that for H = 0.04 m, the wave periods had a minimal impact on the amplitude, but the oscillation frequency varied. At H = 0.1 m, both velocities exhibited significantly larger amplitudes, especially for T = 1.2 s and T = 2.0 s, indicating stronger motion with higher wave heights.

Regionalized ensemble estimation of wave periods for assessing wave energy resources across Canada. Part II: Wave-period and wave-energy analyses

The cornerstone for harnessing and utilizing wave energy resources lies in the precise and thorough estimation and assessment of wave energy fluxes through advanced modeling of wave periods. This study implements the developed macroscale regionalized ensemble wave-period modeling (MREWPM) method to accomplish the initial integrated estimation and analysis of wave periods and wave energy fluxes across Canada, complemented by advanced estimations of wave heights and wind speeds. The results indicate that Canadian wave periods lengthen in shallow, low-backscatter, southern, remote, or eastern waters, and exhibit temporal variability in breezy, low-backscatter, southern, remote, or eastern regions. The trend of wave periods exhibited fluctuations, decreasing before and increasing after the trough (9.06 s in 2004) during cool seasons. Temporal variabilities and trends of wave periods were more fragmented and heterogeneous compared to averages. Canadian wave energy fluxes generally exhibit an increase southward with latitudes. The wave energy typically diminishes from offshore (deep waters) to nearshore areas (shallow waters), with this attenuation being more pronounced in winter months. There is a rough decrease from winter, autumn, and spring to summer months, mirroring the seasonal variations of wave periods. This seasonality tends to be more pronounced in highly energetic regions, such as the Pacific and Atlantic oceans. This study enhances reliability and feasibility of macroscale wave-period and wave-energy estimation and analyses, offering scientific support for wave energy development, wave climatology, and ocean engineering.

A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.

Input / Output Relationships for the Primary Hippocampal Circuit.

The hippocampus is the most studied brain region but little is known about signal throughput -- the simplest, yet most essential of circuit operations -- across its multiple stages from perforant path input to CA1 output. Using hippocampal slices derived from male mice, we have found that single-pulse lateral perforant path (LPP) stimulation produces a two-part CA1 response generated by LPP projections to CA3 ('direct path') and the dentate gyrus ('indirect path'). The latter, indirect path was far more potent in driving CA1 but did so only after a lengthy delay. Rather than operating as expected from the much discussed trisynaptic circuit argument, the indirect path used the massive CA3 recurrent collateral system to trigger a high frequency sequence of fEPSPs and spikes. The latter events promoted reliable signal transfer to CA1 but the mobilization time for the stereotyped, CA3 response resulted in surprisingly slow throughput. The circuit transmitted theta (5Hz) but not gamma (50Hz) frequency input, thus acting as a low-pass filter. It reliably transmitted short bursts of gamma input separated by the period of theta wave - CA1 spiking output under these conditions closely resembled the input signal. In all, the primary hippocampal circuit does not behave as a linear, three-part system but instead uses novel filtering and amplification steps to shape throughput and restrict effective input to select patterns. We suggest that the operations described here constitute a default mode for processing cortical inputs with other types of functions being enabled by projections from outside the extended hippocampus.Significance statement Despite intense interest in hippocampal contributions to behavior, surprisingly little is known about how signals are processed across the network linking cortical input to CA1 output. Here, we describe the first input/output relationship for the system with results challenging the traditional tri-synaptic circuit concept. Signal throughput requires mobilization of recurrent activity within CA3 to amplify sparse input from the dentate gyrus into an unexpectedly stereotyped composite response. Potent low-pass filters determine effective input patterns. These results open the way to new analyses of how variables such as aging affect hippocampus and its contributions to behavior while providing material needed for biologically realistic models of the structure.

Seven Years of Monitoring the Development of an Oyster Reef Living Shoreline

The implementation of nature-based solutions (NbS), including living shorelines, to mitigate estuarine habitat loss is increasing at a pace exceeding the evaluation of their long-term success. Constructed oyster reefs (CORs) made of shell, concrete, stone, and other materials are one living shoreline tactic that is widely utilized, yet few studies have been conducted to understand the development of CORs within the context of both physical and ecological parameters over longer time scales (4 + years). A COR-based living shoreline project at the Gandy’s Beach Preserve (GBP) in Delaware Bay, NJ, USA, had dual goals of coastal protection and habitat provisioning, which prompted the development of a goal-driven monitoring framework to track project objectives. Methods were developed to quantify the following multi-disciplinary metrics over 7 years: elevations of CORs, waves (height, period, and direction), shoreline elevations, change in extent of vegetation patches, oyster density and size, nekton richness and community composition, and horseshoe crab impingement. The CORs met most of their habitat provisioning objectives as they were colonized by a multi-generational population of shellfish and created habitat for nekton, while posing negligible hazards to horseshoe crabs. However, none of the coastal protection objectives was fully achieved including material stability, wave attenuation, and sediment elevation increase. Results highlight the value of longer-term monitoring to understand performance and the need to match the scale and type of NbS tactic(s) with both the scale of the landscape and the site-specific hydrodynamic conditions to meet project goals.

Superposition and Interaction Dynamics of Complexitons, Breathers, and Rogue Waves in a Landau–Ginzburg–Higgs Model for Drift Cyclotron Waves in Superconductors

This article implements the Hirota bilinear (HB) transformation technique to the Landau–Ginzburg–Higgs (LGH) model to explore the nonlinear evolution behavior of the equation, which describes drift cyclotron waves in superconductivity. Utilizing the Cole–Hopf transform, the HB equation is derived, and symbolic manipulation combined with various auxiliary functions (AFs) are employed to uncover a diverse set of analytical solutions. The study reveals novel results, including multi-wave complexitons, breather waves, rogue waves, periodic lump solutions, and their interaction phenomena. Additionally, a range of traveling wave solutions, such as dark, bright, periodic waves, and kink soliton solutions, are developed using an efficient expansion technique. The nonlinear dynamics of these solutions are illustrated through 3D and contour maps, accompanied by detailed explanations of their physical characteristics.

Floquet theory and stability analysis for Hamiltonian PDEs

Abstract We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third order), the nonlinear Schrödinger and Boussinesq equations (fourth order), and the Kawahara equation (fifth order). Our analysis reveals that the characteristic polynomial of the monodromy matrix inherits symmetry from the underlying PDE, enabling us to determine the essential spectrum along the imaginary axis and bifurcations of the spectrum away from the axis, employing the Floquet discriminant. We present numerical evidence to support our analytical findings.

Wind-wave characteristics in the coastal area between Damietta and Port Said, Egypt

This study attempts to investigate the wind-wave characteristics in the region between Damietta and Port Said from 2011 to 2020 using the ERA5 data set for the considered area. Fourteen stations were used for data collection to represent the study area. The ERA5 data were compared with measured wave data from a directional wave buoy from February 1999 to February 2000. The following error statistics were obtained: bias = - 0.014 m and RMSE = 0.3 m. The ERA5 data were then used to create seasonal maps to simulate wind speed and direction, significant wave height (Hs), wave direction, and wave period. Results showed that the annual average Hs was 0.42 m, and the annual mean wind speed was 5.13 m/s. According to the Mann-Kendall test, the average Hs exhibited increasing trends of 0.0014 m/year and 0.0024 m/year with 70–80 % significance levels, respectively, in winter and autumn. In the spring, the Hs trend was 0.0013 m/year with an 80–90 % significance. During summer, this trend decreased to −0.00037 m/year, with a 70–80 % significance level. The average wind speed had increasing trends in winter, spring, and autumn of 0.009 m/s/year and 0.016 m/s/year with a 70–80 % level of significance and 0.0026 m/s/year with 80–90 % significance level, respectively. Meanwhile, the summer average wind speed showed a weak, insignificant trend of increase of as low as 0.0001 m/s/year. The study recommends using simulated wave characteristics to fill the gap in wave data along the Southeastern Mediterranean coast and using the southeast zone of the study area for economic activities.

Regionalized ensemble estimation of wave periods for assessing wave energy resources across Canada. Part I: Improved wave-period modelling methodology

Large-scale estimations of wave periods are desired for wave energy assessment, ocean engineering, and wave climate research. Long-term global wave data from satellite altimeters are routinely applied to the estimations. However, this is challenged by uncertainties in wave-period models (WPMs), inaccuracies in data, and simplifications in modeling. Additionally, there exists a gap in the comprehensive examination of the variational mechanisms governing wave periods or model performances. As an effort to address them, we innovate a macroscale regionalized ensemble wave-period modeling (MREWPM) method by optimizing four wave-period models, driven by enhanced altimeter-based REWS (regionalized ensemble wave simulation) estimates of wave heights and wind speeds, within a regionalization framework in macroscale water environments. Results show that MREWPM driven by REWS dataset outperforms existing methods and performs better at larger scales (e.g., in eliminating local-scale overestimation). WPMs are more accurate over remote, deep, and windy regions in cool seasons under metrics-, scale- and data-dependent variations of performances with driving factors (mainly geographical features). This study serves as a foundational contribution towards the enhancement of wave-period simulations, the advancement of understanding wave-period dynamics, and the scientific evaluation of wave energy at macroscales.

Exploring the Status and Experiences of School Nurses’ Response to the COVID-19 Pandemic: A Mixed Method Study

PurposeThis study aimed to provide a deeper understanding of the response status and school nurses’ experience of the prolonged COVID-19 pandemic in Korea. MethodRecognizing the limitations of existing tools in capturing prolonged COVID-19 response, we divided the COVID-19 pandemic into different wave periods and adopted a mixed-methods design enrolling school nurses in elementary, middle, and high schools in Korea to gain a comprehensive view. A quantitative survey was conducted among 153 school nurses nationwide and in-depth interviews were conducted with nine, using Van Kaam’s phenomenological analysis. ResultsIn 56.9% of the cases, multiple persons in charge of COVID-19 management were not designated, and there was no significant difference in response by school level. Excessive work, coping with civil complaints, unilateral work burden, difficulties communicating with related organizations, lack of concreteness in manuals, lack of cooperation among school members, and frequent changes in guidelines were continuous difficulties encountered during the pandemic. From the in-depth interviews, we extracted 189 meaningful statements, 22 subthemes, and 8 themes. The eight themes were divided into three categories: beginning of COVID-19 response, process of response to COVID-19, and lessons learned from the COVID-19 response experience. ConclusionA specific and systematic infectious disease response manual should be established, as well as an educational and training program to strengthen the capacity of educational personnel to cope with new infectious diseases.

Dynamic Formulation of the Double Multiple Stream Tube Model of Offshore Vertical Axis Wind Turbines

Abstract The paper proposes a novel algorithm to simulate Vertical Axis Wind Turbines in floating motion based on a low-fidelity approach. The conventional Double Multiple Stream Tube Model is formulated as a steady state model to deal with the inherent unsteady aerodynamics of VAWTs. The Double Multiple Stream Tube Model makes use of an average contribution of the blade passages over a revolution to solve the Blade Element Momentum equation. The model reduces the dependence of the solution (the induction field) to a space variable. Floating Vertical Axis Wind Turbines undergoes a variation of aerodynamic quantities according to wave periods, also different from the rotor period. This paper provides a new formulation of the Double Multiple Stream Tube Model to solve the turbine rotation in time and space, introducing the variation of the platform velocity and a revised approach to the downstream actuator disc. The most impactful parameter is found to be the wave frequency: wave periods at full-scale are lower than the ones of the turbine rotor, featuring optimal operating points at low tip speed ratios. The increase of the wave frequency highlights the differences of the average torque prediction for a single blade up to 10% between the unsteady and the standard formulation. In this context, the development of fast low-fidelity computational tools play a key role in the assessment of the preliminary designs of Floating Offshore Vertical Axis Wind Turbines and it will be used to optimise the aerodynamic design of the laboratory scaled model under surge motion.