Wave Period Research Articles

CanESM5-derived ocean wave projections — Considerations for coarse resolution climate models

This study presents the first set of CanESM5-driven wave projections for two emission scenarios (SSP5-8.5 and SSP2-4.5) and two time periods for mid- and end-century. While coarse resolution climate models, like CanESM5, might be less attractive for development of ocean wave projections, their results are needed to explore the full range of inter-model uncertainty in CMIP6 projections. Considering the coarse resolution limitation, wave simulations were obtained with a proposed computationally efficient 2-step bias-correction approach that consists of (i) calibrating the wind-to-wave energy transfer in the ocean wave model to reduce the underestimation of extremes resulting from coarse resolution, and (ii) bias-correcting the surface winds with a multivariate bias-correction to reduce remaining systematic biases. Results showed overall good performance in comparison with state of the art reanalysis and satellite data. Resulting projections provide increased understanding of future changes in wave conditions, confirming previously reported global-scale changes, such as higher waves in the eastern tropical Pacific and lower waves in the North Atlantic. They also provide more detailed information for areas affected by sea ice conditions in comparison to the latest CMIP5-based wave ensembles, which is critical for the Arctic region, a hotspot for ocean wave changes. Moreover, while the largest changes are typically seen by the end-century under SSP5-8.5, this study reveals that for some variables and areas, such as the mean wave period, larger changes occur for lower warming levels as a result of competing driving factors. Finally, the presented projections can contribute to ongoing efforts to generate a large multi-model ensemble of wave projections based on CMIP6.

Solitary wave solutions and their limits to the fractional Schrödinger system

This study is concerned with solitary wave solutions and the dynamic behavior of the (2+1)-dimensional nonlinear fractional Schrödinger system. By exploring the dynamic properties of the equilibrium levels to the corresponding Hamiltonian, the expressions of exact solutions of the above system are obtained, including solitary wave solutions, periodic wave solutions, singular periodic wave solutions, singular wave solutions, kink wave solutions, and anti-kink wave solutions. Moreover, the linear stability, geometric characteristics, and limiting behavior of these solutions to the nonlinear fractional Schrödinger system were investigated.

Crisis and Emergency Risk Communication and Emotional Appeals in COVID-19 Public Health Messaging: Quantitative Content Analysis.

Although COVID-19 is no longer a global health emergency, it remains pervasive in Singapore, a city-state situated in Southeast Asia, with periodic waves of infection. In addition to disease management, strong communication strategies are critical in the government's response to the pandemic to keep the public updated and equip them in protecting themselves. Grounded in the crisis and emergency risk communication (CERC) framework and emotional appeals, this study aimed to analyze public health communication strategies in Singapore during the COVID-19 pandemic. Quantitative content analysis was conducted on 696 Facebook (Meta Platforms Inc) posts and 83 website articles published by Singapore-based public health institutions between January 2020 and September 2022. The results showed that increasing communication on message themes, such as inquisitive messaging and clarification, can enhance communication strategies. The use of emotional appeals also varies with time and should be carefully used as they are context-specific. Theoretically, this study contributes to advancements in the CERC framework and concepts of emotional appeals by exploring the applications and changes of CERC message types and emotional appeals at different phases. The findings can provide practical guidance for authorities and communication practitioners in developing effective communication strategies.

Volcano tsunamis and their effects on moored vessel safety: the 2022 Tonga event

Abstract. The explosion of the Hunga Tonga–Hunga Ha'apai volcano on 15 January 2022 (Tonga 2022) was the origin of a volcano-meteorological tsunami (VMT) recorded worldwide. At a distance exceeding 10 000 km from the volcano and 15 h after its eruption, the moorings of a ship in the port of La Pampilla, Callao (Peru), failed, releasing over 11 000 barrels of crude oil. This study delves into the profound implications of the Tonga 2022 event, investigating whether it could have led to the breaking of the mooring system. We conducted a comprehensive analysis of this significant event, examining the frequency content of the time series recorded at tide gauges, DART (Deep-ocean Assessment and Reporting of Tsunamis) buoys, and barometers in the southern Pacific Ocean. Our findings revealed that the maximum energy of the spectra corresponds to the 120 min wave period off the coast of Peru, with the arrival time of these waves coinciding with the time of the accident in the port. We used a Boussinesq model to simulate the propagation of the volcano-meteorological tsunami from the source to the port in Peru to study the impact of those waves on the mooring system. We used the synthetic tsunami recorded in the port as input for the model that simulates mooring line loads based on the ship's degrees of freedom. The results suggest that the 120 min wave triggered by the VMT could significantly increase mooring stresses due to the resulting hydrodynamic effects, exceeding the minimum breaking load (MBL). We conclude that the propagation of the long wave period generated by the VMT caused overstresses in moored lines that triggered accidents in port environments. This event showed the need to prepare tsunami early warning systems and port authorities for detecting and managing VMTs induced by atmospheric acoustic waves. The work provides new insights into the far-reaching impacts of the Tonga 2022 tsunami.

Assessment of the inundation probability caused by tsunamis along the eastern coast of Hainan Island

ABSTRACT Coastal areas around the South China Sea are threatened by potential tsunamis triggered by large earthquakes in the Manila Trench. To quantitively assess the inundation probability caused by tsunamis is crucial for coastal disaster prevention and mitigation. This study focuses on the eastern coast of Hainan Island, which is located to the west of the Manila Trench and may directly face tsunami impact. More than one million tsunami scenarios are simulated considering the randomness of earthquake magnitude, epicenter location, and focal depth. The simulation of numerous tsunami scenarios is based on the unit source superposition method in deep water, which provides boundary conditions for the local model with high spatial resolution for nearshore wave propagation and inundation. Representative waves with different heights and periods are adopted as incident waves in the local model. By involving the joint probability density of incident wave height and period, the spatial distribution of inundation probability is given along the eastern coast of Hainan Island. This study provided an assessment method for the inundation probability, which can more comprehensively consider the uncertainty of earthquakes and provide a more reliable assessment result than that based on refined simulation of several typical scenarios.

Cell cycle regulated expression of the WHI7 Start repressor gene

ABSTRACT Periodic transcriptional waves along the cell cycle ensure the accurate progression of the different cell cycle phases through the timely regulated expression of cell cycle proteins. The G1/S transition (Start) consists in the activation of a transcriptional program by G1 CDKs through the inactivation of Start transcriptional repressors, Whi5 and Whi7 in yeast or Rb in mammals. Here, we provide a comprehensive characterization of the transcriptional regulation of the Start repressor Whi7 in budding yeast. We found that WHI7 is a cell cycle regulated gene that shows periodic expression peaking in G1. Our results demonstrate that the three cell cycle transcriptional programs related to G1 and their corresponding transcription factors are involved in the transcriptional control of WHI7. Specifically, we identified that the transcriptional regulators Swi5 and Mcm1-Yox1, which are involved in late M and early G1 expression, and the transcription factors MBF and SBF, which are responsible for G1/S expression, are able to associate and regulate the WHI7 gene. In summary, in this work, we provide new mechanisms for the regulation of the Start repressor Whi7, which highlights the precise and complex control of the cell cycle machinery governing the G1/S transition.

Investigation of a new similarity solution for the (2+1)-dimensional Schwarzian Korteweg–de Vries equation

We study the (2+1)-dimensional Schwarzian Korteweg–de Vries equation (SKdV). The explored solutions describe new Lump soliton colliding with visible soliton, an interaction between multi-soliton waves with one soliton, multi peaks of waves moving in a curved path, two hyperbolic waves moving together without interaction and some of periodic waves. We examine the commutative product between multi unknown Lie infinitesimals for the (2+1)-dimensional (SKdV) equation, and this study result in some new Lie vectors. The commutative product generates a system of nonlinear ODEs which had been solved manually. Through two stages of Lie symmetry reduction, SKdV equation is reduced to non-solvable nonlinear ODEs using various combinations of optimal Lie vectors. Using the Riccati–Bernoulli sub-ODE and Integration methods, we investigate new analytical solutions for these ODEs. Back substituting for the original variables generates new solutions for SKdV. Some selected solutions are illustrated through three-dimensional plots.

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves

We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.

Variabilities in the estimate of 100-year return period wave height in the Indian shelf seas

Variabilities in the estimate of 100-year return period wave height in the Indian shelf seas

Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation

The Klein–Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.

Nonlinear Subharmonic Dynamics of Spectrally Stable Lugiato–Lefever Periodic Waves

Nonlinear Subharmonic Dynamics of Spectrally Stable Lugiato–Lefever Periodic Waves

Research on dynamic responses of multi-float systems during wet towing

Very large floating structures (VLFS) are substantial in scale, typically comprising dozens to hundreds of interconnected modules. This paper utilizes a multi-float towing approach to enhance transport efficiency. A numerical model of multi-float system, based on potential flow theory and multi-body hydrodynamic interaction, is developed and validated. The dynamic responses for six towing configurations under various wave periods and environmental load directions are investigated by using this model. In addition, a selection method is proposed to determine the optimal towing configuration that meets the towing stability criteria while maximizing efficiency, cost-effectiveness, and minimizing environmental impact. Results indicate that during towing multi-float systems, the rear module's vertical motion caused by the combination of heave and pitch is significantly greater than that of the front module, especially in long wave periods. When the number of longitudinal tandem modules reaches four, the low-frequency motion modes with sway and yaw as the main motions are excited, leading to a significant lateral displacement and horizontal rotation of the multi-float system. This also results in uneven tensions of the symmetrical cables. Additionally, the dynamic behaviors of the towing configurations are more pronounced in oblique or lateral waves than in forward waves. As the current direction shifts from forward to lateral, the sway amplitude of the system with four longitudinal tandem modules decreases. Furthermore, an optimal towing configuration is determined by the selection method, which has good stability in moderate sea conditions. The findings of this paper provide valuable insights for towing multi-float systems and have implications for future VLFS construction.

Multiple solitons and breathers on periodic backgrounds in the complex modified Korteweg–de Vries equation

This study explores multiple soliton and breather solutions on periodic backgrounds in the complex modified Korteweg–de Vries equation. The compact determinant formulas and their detailed derivation process for these solutions are provided via the bilinear method. We confirm that on periodic backgrounds, soliton amplitudes exhibit regular periodic behaviors, while breather amplitudes display quasi-periodic behaviors, as is expected for a breather with one period propagating over a periodic wave with another period. The asymptotic expressions for the solitons and breathers, which establish the high accuracy of the derived solutions, are provided to reveal the soliton and breather dynamics on the periodic backgrounds.

Modeling Rip Current Systems around Multiple Submerged Breakwaters

Multiple submerged breakwaters (MSBWs) are commonly used coastal protection structures due to their specific advantages over the emerged ones. Rip currents, as the inevitable natural hazard in the gaps of these constructions, are investigated numerically in the present study. A fully nonlinear mild-slope equation (NMSE) model possessing both fully nonlinear and fully dispersive properties is validated and adopted in the simulations. With four monochromatic wave conditions of different wave heights, periods and incidences representing low-energy, typical, storm and oblique waves tested, the flow patterns and the low-frequency oscillations of the rip currents are studied. For the convenience of risk assessment, the rip risk level is divided into three degrees according to the maximum rip flow speed. The effects of the configurations of the MSBWs on the rip current system as well as the rip risk level are examined, considering different breakwater widths, heights, forms, gap widths and gap numbers. Simulation results suggest that the cross-shore configurations of MSBWs influence the rip risk level by inducing different wave energy dissipations but the longshore configurations of MSBWs by changing flow field patterns.

Trapezoidal breakwater on reducing resonant wave amplitude on a rectangular basin

In this study, we delve into the effectiveness of trapezoidal breakwaters in mitigating resonance phenomena. The challenge at hand is to identify the optimal configuration capable of halting resonance. Employing Shallow Water Equations with a friction term to encapsulate the breakwater’s roughness, we analytically solve the model to determine the natural wave period. This period serves as the instigator of an unstoppable harmonic oscillation. Numerically, we use the Finite Volume Method on a Staggered Grid to simulate the model for several cases to pinpoint the infimum value of the natural wave period required to impede resonance phenomena. This research holds significance for those involved in coastal protection design, particularly in the context of trapezoidal breakwaters. The findings contribute to the effective reduction, rather than amplification, of wave height, thereby enhancing the reliability of such coastal protection structures.

Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles

The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.

Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields

While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This study aims to shed light on this topic by investigating the combined influence of a horizontal electric field and constant vorticity on the free surface and the emergence of stagnation points. Using the Euler equations framework, we employ conformal mapping and pseudo-spectral numerical methods. Our findings reveal that increasing the electric field intensity eliminates stagnation points and smoothen the wave profile. This implies that a horizontal electric field acts as a mechanism for the elimination of stagnation points within the fluid body. Besides, we have identified regimes where three stagnation points appear on the free surface — something that cannot occur in purely gravity rotational waves.

Residual Symmetry and Interaction Solutions of the (2+1)-Dimensional Generalized Calogero–Bogoyavlenskii–Schiff Equation

In this paper, we investigate the (2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff (gCBS) equation by using the residual symmetry analysis and consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the gCBS equation is localized into a Lie point symmetry in a prolonged system and a new Bäcklund transformation of this equation is obtained. By applying the standard Lie symmetry method to the prolonged gCBS system, new symmetry reduction solutions of the gCBS equation are obtained. The gCBS equation is proved to be CRE integrable and new Bäcklund transformations of it are obtained, from which interaction solutions between solitons and periodic waves are generated and analyzed.

Breathers and rogue waves on the periodic wave background of the nonlocal higher-order Chen-Lee-Liu equation

Breathers and rogue waves on the periodic wave background of the nonlocal higher-order Chen-Lee-Liu equation

The localized excitation on the Weierstrass elliptic function periodic background for the (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation

In this paper, the linear spectral problem associated with the (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (gvcKP) equation with the Weierstrass function as the external potential is investigated based on the Lamé function, from which some new localized nonlinear wave solutions on the Weierstrass elliptic ℘-function periodic background are obtained by the Darboux transformation. The degenerate solutions on the ℘-function periodic background for the gvcKP equation can be derived by taking the limits of the half-periods ω 1, ω 2 of ℘(x), whose evolution and corresponding dynamics are also discussed. The findings show that nonlinear waves on the ℘-function periodic background behave as different types of nonlinear waves in different spaces, including periodic waves, vortex solitons and interaction solutions, aiding in elucidating some physical phenomena in the related fields, such as the physical ocean and nonlinear optics.