Local Wave Research Articles

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

To better understand the mechanisms underlying the formation of blocking highs over the North Atlantic as a type of large-amplitude disturbance, this paper reports results from numerical experiments within the framework of local finite-amplitude wave activity (LWA). The numerical model employed in this study explicitly depicts two important atmospheric internal dynamic processes—nonlinear zonal eddy flux and Rossby wave packet propagation—which have been individually emphasized by different previous studies. The simulation results reveal that these two dynamic processes are the dominant contributors to the formation of Atlantic blocking cases. However, they exert different influences over different regions. The southern and northern parts of the primary LWA associated with the blocking cases are mainly induced by the nonlinear zonal eddy flux and Rossby wave packet propagation, respectively. Thus, this study reconciles and integrates insights from previous studies on Atlantic blocking events, providing a cohesive understanding of their formation.摘要为研究北大西洋阻高的形成机制, 本文在局部有限振幅波活动 (LWA) 框架下进行了一系列数值实验. 采用的数值模型能显式地描绘出两种重要的大气内部动力过程, 即非线性纬向位涡通量和Rossby波包传播. 模拟结果显示, 这两种动力学过程均是形成大西洋阻高的重要机理. 具体地, 非线性纬向位涡通量和Rossby波包传播, 分别是大西洋阻高南部和北部LWA形成的主导因子. 因此, 本研究综合了前人关于大西洋阻高的研究成果, 为其形成机理提供了新的认识.

The Earliest Stages of Wind Wave Generation in the Open Sea

Abstract We have explored the earliest stages of wind wave generation in the open sea, from the first initial wavelets appearing on an otherwise flat surface or low, smooth undulations until the practically fully developed conditions for the very low range of wind speeds we have considered. We suggest the minimal wind speed for the appearance of the first wavelets to be close to 1.8 m s−1. The peculiar conditions associated with the development of coastal sea breezes allow us to consider the local waves as generated under time-limited conditions. The 2D spectra measured during these very early stages provide the first evidence of an active Phillips process generation in the field. After appearing in these very early stages, wavelets quickly disappear as soon as the developing wind waves take a leading role. We suggest that this process is due to the strong spatial gradients in the surface orbital velocity, which impedes the instability mechanism at the base of their formation, while at a later stage of development, these gradients decrease and wavelets reappear. On a decadal perspective, the progressive decrease of the intensity of the sea breezes in the northern Adriatic Sea, where we have carried out our measurements, is associated with the steadily milder winters, and therefore not sufficiently cold local sea temperatures in early summer. Significance Statement We have explored for the first time the earliest stages of wind wave generation (millimeter scale) in the open sea. This was possible with the combination of the daily sea breeze development and the availability of an oceanographic tower 15 km offshore. The minimum wind speed for wave generation was 1.8 m s−1, lower than previously assumed. The data provide strong indications on the different stages of the generation process, offering measured and visual evidence, under these very light wind conditions, of the Phillips one. The presence of wind-related ripples, essential for remote sensing measurements, turns out to be dependent on the stage of generation.

Numerical investigation of optical distortions by turbulent wake and shock wave in the transonic flow

Large eddy simulation with the explicit fifth-order weighted compact nonlinear schemes is performed to investigate the aero-optical distortion caused by a transonic flow over a cylinder at Reynolds numbers of Re = 1 × 105, Re = 2 × 105, and Re = 4 × 105. Proper orthogonal decomposition identifies two dominant modes: the antisymmetric “shifting” mode and the symmetric “breathing” mode, both peaking at the non-dimensionalized Strouhal number StD = 0.18. Optical distortion refers to the phenomenon where a beam passes through a non-uniform and fluctuating flow field, resulting in defocus, jitter, and significant energy reduction. Optical calculations for 12 cases demonstrate that local shock waves and turbulent wakes notably exacerbate optical distortion. In terms of temporal results, the peak frequency of the beam aligns with StD = 0.18 when passing through the cylinder shockwave and falls within StD = 0.16–0.42 as it crosses the shear layer. Significant fluctuations are observed in the turbulent wake and local shock wave, with frequency peaks ranging from StD = 0.12–0.72. Additionally, streamwise flow structures are found to primarily impact optical distortion. Comparative analysis across the three Reynolds numbers indicates that optical distortion is insensitive to Reynolds number variations within the same order of magnitude. The employed grid sufficiently resolves key flow structures impacting beam transmission.

Rogue wave excitations and hybrid wave structures of the Heisenberg ferromagnet equation with time-dependent inhomogeneous bilinear interaction and spin-transfer torque.

In this paper, we focus on the localized rational waves of the variable-coefficient Heisenberg spin chain equation, which models the local magnetization in ferromagnet with time-dependent inhomogeneous bilinear interaction and spin-transfer torque. First, we establish the iterative generalized (m,N-m)-fold Darboux transformation of the Heisenberg spin chain equation. Then, the novel localized rational solutions (LRSs), rogue waves (RWs), periodic waves, and hybrid wave structures on the periodic, zero, and nonzero constant backgrounds with the time-dependent coefficients α(t) and β(t) are obtained explicitly. Additionally, we provide the trajectory curves of magnetization and the variation of the magnetization direction for the obtained nonlinear waves at different times. These phenomena imply that the LRSs and RWs play the crucial roles in changing the circular motion of the magnetization. Finally, we also numerically simulate the wave propagations of some localized semi-rational solutions and RWs.

Theoretical modeling and dynamic analysis of designable grillages for repairing material surface defect

Designing structural grillages is an innovative solution to repair material surface defects. The grillages have advantages as lightweight and directionally enhanced, but their stability and stress concentration under dynamic loads may pose significant risks. Three analytical models of grillages above a semicircular defect are constructed. The analytical solution of the frequency-domain wave field around the semicircular defect under SH wave incidence is solved. The complex variable function method is introduced to simplify the wave field expression. The accuracy is verified by comparing it with classic examples. Applying the Modified Time-Frequency Transform to obtain the time-domain wave field. Based on the Multipoint Transient Input Method (MTIM), the transient surface displacement response of the grillage above the defect is derived, mainly discussing the superposition behavior of input waves in the grillage. MTIM is based on the analytical solution of local time-domain wave field and takes the time histories of the surface characteristic points as the wave input. It has been validated as an effective method for studying the dynamic response of structures. The numerical results show that grillage form, incident angle, and wave velocity ratio are important factors affecting the structural responses of grillage above the defect. This research aims to reveal the propagation characteristics of waves in grillages in filling material defects, providing theoretical guidance for the design and application of grillages in this field.

Ultrasonic characterization of material anisotropy in additively manufactured AlSi10Mg

Metal additive manufacturing (AM) based on laser powder bed fusion (LPBF) generates components by melting metal powder on a layer-by-layer basis. The melting and cooling process often generates samples with a preferred material symmetry aligned with the build direction. This anisotropy affects mechanical performance and can be challenging to characterize nondestructively. Here, LPBF was used to create samples of AlSi10Mg with specific geometries to affect the overall anisotropy. In addition, the hybrid AM process of interlayer milling was used to impact the microstructure and residual stress of some samples. Ultrasonic measurements were used to characterize the samples using both coherent wave and diffuse wave experiments to capture the anisotropic nature of the wave speed and scattering. The material symmetry and morphology of the grains affect the wave speed, attenuation, and backscatter with respect to direction. Furthermore, spatially resolved acoustic spectroscopy was used to provide insight regarding the localized wave speeds with respect to sample location and propagation direction. The experimental data were used collectively to quantify differences between the AM processes used to create the samples. Such information can be used to guide AM process parameters to optimize sample performance. Finally, prospects for characterization of residual stresses will be discussed.

Dark Localized Waves in Shallow Waters: Analysis within an Extended Boussinesq System

We study dark localized waves within a nonlinear system based on the Boussinesq approximation, describing the dynamics of shallow water waves. Employing symbolic calculus, we apply the Hirota bilinear method to transform an extended Boussinesq system into a bilinear form, and then use the multiple rogue wave method to obtain its dark rational solutions. Exploring the first- and second-order dark solutions, we examine the conditions under which these localized solutions exist and their spatiotemporal distributions. Through the selection of various parameters and by utilizing different visualization techniques (intensity distributions and contour plots), we explore the dynamical properties of dark solutions found: in particular, the first- and second-order dark rogue waves. We also explore the methods of their control. The findings presented here not only deepen the understanding of physical phenomena described by the (1+1)-dimensional Boussinesq equation, but also expand avenues for further research. Our method can be extended to other nonlinear systems, to conceivably obtain higher-order dark rogue waves.

Chirped self-similar optical solitons with cubic–quintic–septic–nonic form of self-phase modulation

This study investigates the dynamics of ultrashort light pulses in an inhomogeneous optical medium exhibiting all orders of nonlinearity up to the ninth order. The research focuses on exploring the existence and properties of self-similar solitons while varying cubic, quintic, septic, and nonic nonlinearities, group velocity dispersion, and loss or gain. It is found that the transmission system supports the existence of novel types of self-similar bright and dark pulses in the presence of various physical processes. Importantly, these self-similar localized waves exhibit a linear chirp, a crucial factor for achieving effective pulse amplification or compression. Based on the chirp property, the dynamical behaviors of these self-similar waveforms are discussed in a periodically distributed amplification system. The findings highlight that the shape and dynamics of these chirped self-similar pulses can be precisely controlled by selecting appropriate profiles for gain or loss, nonlinearity, and dispersion. Additionally, the research numerically discusses the interaction dynamics between two and three adjacent solitons.

Localized waves and interaction solutions to an integrable variable coefficient Date-Jimbo-Kashiwara-Miwa equation

This paper initiates an exploration into the exact solutions of the variable coefficient Date-Jimbo-Kashiwara-Miwa equation, first utilizing the Painlevé analysis method to discuss the integrability of the equation. Subsequently, By employing the Hirota bilinear method, N-soliton solutions for the equation are constructed. The application of the Long wave limit method to these N-soliton solutions yields rational and semirational solutions. Various types of localized waves, encompassing solitons, lumps, breather waves, and others, emerge through the careful selection of specific parameters. By analyzing the image of the solutions, the evolution process and its dynamical behavior are studied.

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

AbstractThis study investigates the localized wave propagation at the free edge of a thin semi‐infinite Magneto‐Electro‐Elastic (MEE) plate. The plate is supported by a two‐parameters elastic foundation. Biot's porosity theory is considered to formulate the porosity in the model, and the pore structure is saturated with an incompressible fluid. The Kirchhoff–Love plate theory determines the plate displacement field. A non‐homogeneity in the material parameters is considered, which varies with the spatial coordinate along the thickness direction of the plate. In order to illustrate the impacts of the surface elements on bending wave propagation, the model incorporates the surface elasticity theory. The short circuit boundary conditions are implemented to derive the general form of the potential function connected with the electric and magnetic fields, respectively. The dispersion relation for bending edge wave on a MEE fluid‐saturated porous plate is obtained by considering a sinusoidal waveform, which propagates along the free edge of the plate. A numerical method named Finite Difference (FD) scheme is employed to analyze the stability of the numerical scheme and also extract the expression of the velocity profiles of the bending edge wave in the absence of the pore structure. The impacts of the various parameters included in the considered model are examined using a numerical example, from which conclusions regarding their sensitivity are derived.

Strong interactions between solitons and background light in Brillouin-Kerr microcombs.

Dissipative Kerr-soliton combs are laser pulses regularly sustained by a localized solitary wave on top of a continuous-wave background inside a nonlinear resonator. Usually, the intrinsic interactions between the background light and solitons are weak and localized. Here, we demonstrate a strong interaction between the generated soliton comb and the background light in a Brillouin-Kerr microcomb system. This strong interaction enables the generation of a monostable single-soliton microcomb on a silicon chip. Also, new phenomena related to soliton physics including solitons hopping between different states as well as controlling the formations of the soliton states by the pump power, are observed owing to such strong interaction. Utilizing this monostable single-soliton microcomb, we achieve the 100% deterministic turnkey operation successfully without any feedback controls. Importantly, it allows to output turnkey ultra-low-noise microwave signals using a free-running pump.

The influence of carotid plaque on carotid artery stiffness indicators in hypertensive patients with and without accompanying type 2 diabetes

Aim. To compare the elastic properties of the common carotid arteries (CCA) in patients with stage II hypertension (HTN) depending on the presence of diabetes mellitus (DM) and atherosclerotic plaque (ASP) <50 % of carotid arteries (CA). Materials and methods. The study included 80 patients with stage II HTN, 43 of them without type 2 DM, 37 with type 2 DM, average age – 57.7, 55.3 % men. Basic anthropometric data, laboratory indicators of lipid and carbohydrate metabolism, creatinine, data of daily blood pressure monitoring, echocardiography, intima-media thickness, local stiffness indicators: artery diameter, distensibility, the distensibility coefficient (DC), and compliance coefficient (CC), stiffness indices α, β, local pulse wave velocity (PWV), pressure and augmentation index (using radiofrequency-based technologies) were studied. Statistical analysis was performed; the probability of differences is at the level of p < 0.05. Results. The prevalence of ASP in the carotid basin in the group of patients with HTN without DM was 51.1 %, with DM – 54.0 % (p = 0.79). While comparing the elastic properties of CCA of patients without ASP, no reliable similarities were found in the studied indicators. In patients with HTN, accompanying type 2 DM with ASP, the diameter of the CCA was significantly larger by 11.8 % (p = 0.03), and the CC was also higher by 23.6 % (p = 0.049) than in patients with HTN without DM. In patients with HTN with and without DM the limit levels for the intima-media thickness of the left CCA associated with the presence of atheroma were determined, however, the comparison of the areas under the ROC curves did not reveal a statistical difference in the cut-off values in the studied groups (р = 0.681). Conclusions. A feature of CCA remodeling in HTN patients with DM at the stage of ASP presence should be considered a more substantial increase in the diameter of the CCA with preservation of the distensibility of the plaque-free vascular wall. The addition of a second factor (DM) to one risk factor (HTN) is not accompanied by a further statistically significant increase in IMT as a mandatory prerequisite for the appearance of ASP.

Quasi-classical dynamics of a charged particle under conditions of ionization losses in a weak magnetic field

The quasi-classical dynamics of a charged particle in a weak magnetic field in the presence of dissipative losses caused by ionization of the medium is studied. The approximate approach proposed here is a generalization of the Caldirola—Kanai method for quantizing the translational motion of particles in dissipative media. It is shown that a weak curvature of a classical trajectory by the magnetic field is accompanied by an isotropic increase of uncertainty of the particle coordinates to the some maximum value at the moment the localized probability density wave packet stops. The limitation of the increase of coordinate uncertainty is due to irreversible ionization losses.

Feasibility study of a method for tuning wave energy converters

A Wave Energy Converter (WEC) cannot operate efficiently if left alone floating to the mercy of the random sea surface. For a WEC to be efficient, its natural frequency should be close to the peak frequency of the local dominant waves. This paper introduces a method for tuning any natural frequency of a WEC to the peak frequency of a wave spectrum and converting dynamic responses into mechanical power. An innovative lightweight and dual-drag force subsea structure with a huge amount of entrapped seawater can be attached to any vessel using cables. This structure increases the roll mass moment of inertia of a medium size barge, and the mass of a small heaving floater, reducing their natural frequencies. The tension in the cables is converted into mechanical power. The study focuses on the Galápagos Islands, where swells with a typical 13 s peak period and significant wave height between 1 to 3 m dominate the wave climate. For the dynamic systems based on roll and heave responses, annual averages of mechanical power are 178 and 73 kW with efficiencies of 49 and 67% respectively. The method developed in this paper can improve the efficiency of existing and novel WECs.

The Role of Climatological State in Supporting US Heat Waves Through Rossby Waves Packets

AbstractWhile heat waves are local extreme weather events, a slowly propagating planetary‐scale Rossby wave pattern is statistically correlated to the occurrence of heat waves in the US. However, whether this correlation indicates that such planetary wave patterns physically cause the enhanced statistics of local heat waves is debatable. In this work, we hypothesize that the atmospheric climatological state controls the slowly propagating wave pattern, setting up a conducive large‐scale environment for local US heat waves. We implement an idealized dry dynamic core model with an iterative approach to simulate the realistic North American summer climatological state. As the idealized atmospheric model can generate similar zonal wavenumber five planetary wave patterns propagating throughout North America, significantly more heat waves are generated, and the statistics of heat waves become consistent with those estimated in reanalysis products. The slowly propagating Rossby wave packets with a timescale of 20–30 days may serve as a new source of intraseasonal predictability in the midlatitudes.

Thermodynamic characteristics of extreme heat waves over the middle and lower reaches of the Yangtze River Basin

In August 2022, an exceptionally long-lasting heat wave (HW) affected the middle and lower reaches of the Yangtze River basin. This study uses the JRA55 daily reanalysis datasets to elucidate the thermodynamic characteristics of the daily evolution of historical extreme HWs in this region via the heat budget equation. HWs are generally characterized by the occurrence of anticyclonic circulation anomaly throughout the troposphere and positive air temperature anomaly with the maximum amplitude in the boundary layer. The anticyclonic anomaly can induce compression heating in the entire troposphere and warm zonal advection in the boundary layer. Meanwhile, due to the reduced cloud cover, more shortwave radiation reaches the ground surface, and the sensible heat flux becomes an important source of diabatic heating before the onset of HWs. The accumulated excessive heat in the HWs is primarily damped through the emission of longwave radiation and meridional thermal advection. For the HW in August 2022, its extreme persistence is mainly caused by prolonged adiabatic heating, enhanced diabatic heating during the developing stage and weakened diabatic cooling during the decay stage. The upper-level portion of the anticyclonic circulation anomalies is linked to the strengthened South Asia High. After applying the state-of-the-art dynamic metric, i.e., local finite wave activity, we reveal that the formation of the anomalous South Asia High in August 2022 is associated with the Stokes drift flux rather than the dispersion of Rossby wave energy. This characteristic sets it apart from other extreme HWs.

Interactions of certain localized waves for an extended (3+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics

Currently, there is much interest in the study on the localized waves and their interactions in fluid mechanics. An extended (3+1)-dimensional Kadomtsev-Petviashvili equation is considered here. By means of the Hirota method, we obtain the N-soliton solutions, with N as a positive integer. The higher-order breather solutions are obtained from the N-soliton solutions through the complex conjugated transformations. Making use of the long-wave limit method, we determine the higher-order lump solutions via the N-soliton solutions. Besides, some hybrid solutions are presented. Three kinds of the localized waves, namely, the solitons, breathers and lumps, along with their interactions, are investigated via the above solutions. Amplitudes, shapes and velocities of those localized waves remain invariant after the interactions, which indicate that the interactions are elastic. Fluid-mechanically meaningful, all our results rely on the coefficients in that equation.

The excitation of high-order localized waves in (3+1)-dimensional Kudryashov-Sinelshchikov equation

The aim of this work is to explore the excitation of high-order localized waves in the (3+1)-dimensional Kudryashov-Sinelshchikov equation, which is used to describe the dynamic of liquid with gas bubble. First of all, classical N-soliton solutions are constructed by means of Hirota bilinear form and symbolic calculation. What’s more, the high-order breather waves are derived through the degeneration process of the N-soliton solutions with conjugate parameter. Then, high-order lump waves are constructed by taking long wave limit technique on N-soliton solutions. Finally, the high-order mixed localized waves involving resonant Y-type solitons, high-order breather waves and high-order lump waves are obtained by utilizing some comprehensive methods. Abundant dynamical and evolutionary behaviors of these results are investigated specifically, some figures are presented to shed light on the nonlinear phenomena hidden in the high-order localized waves vividly.

Effect of Broadness of Wave Spectrum on Significant Wave Height and Wave Power for Open Ocean Conditions of the Peru Basin

Abstract When estimating significant wave height and wave power, it is regularly assumed 4 for the spectral estimate factor. It means considering a narrowband wave spectrum. That approach is accurate enough when the spectral broadness parameter is near zero. Since the Peru Basin is an open ocean: swells and local wind waves can overlap; therefore, its wave spectrum should be considered broadband. This work aims to demonstrate that the wave spectrum in the Peru Basin has waves in a broad band of frequencies and also discuss how this characteristic affects estimating the significant wave height and wave power. The methodology comprises numerical methods, inferential statistics, and spectral analysis applied to ocean data. The paper's conclusions declare the Peru Basin wave spectrum as broadband. The estimated significant wave height for broadband wave spectrum is 7% lower than if the wave spectrum was considered narrowband. We propose 3.7 as the spectral estimate factor for calculating the significant wave height in the Peru Basin instead of the commonly used 4. The significant wave height error when assuming a narrowband wave spectrum slightly affects the spectral parametric wave power calculation, causing a maximum overestimation of 5%. Nevertheless, accurately estimating significant wave height is critical for diverse marine technologies.

Dependence of local carotid arterial stiffness on the presence of atherosclerotic plaque in the carotid basin in hypertensive patients

Aim. To evaluate the viscoelastic properties of the common carotid arteries (CCA) in patients with stage II hypertension (HTN) and to compare these indicators between groups with and without carotid artery (CA) stenosis <50 %. Materials and methods. The study included 48 patients with stage II HTN, mean age – 55.9 years, 45.8 % men. Basic anthropometric data, laboratory parameters of lipid and carbohydrate metabolism, creatinine, quality intima-media thickness (QIMT), local stiffness indicators: artery diameter, distensibility, distensibility coefficient (DC), compliance coefficient (CC), stiffness indices α, β, local pulse wave velocity (PWV), pressure and augmentation index (using RF-QIMT, RF-QAS technologies) were studied. Statistical analysis was performed, p values of < 0.05 were considered statistically significant. Results. CA atheromas with stenosis up to 50 % were found in 48 % of the examined, they were older with higher parameters of vessel diameter by 4.6 %, QIMT – by 12.5 %, α index – by 28.0 %, β index – by 27.7 %, and PWV – by 14.7 %. A medium-strength positive correlation has been revealed for age, QIMT, HDL, creatinine level and local stiffness parameters (distensibility, CC, PWV, indices α, β). The atherosclerotic plaque (ASP) presence in the CA was associated with the limit levels of the left CCA QIMT over 698 μm (sensitivity 65.2 %, specificity 86.6 %, p < 0.01), of the right – over 598 μm (sensitivity 73.9 %, specificity 66.6 %, p < 0.01). However, a greater dependence on age than on the presence of atheroma has been proven. At the same time, the odds ratio of the ASP presence was 2.99-fold higher (p = 0.0065) with an increase in the CCA diameter of more than 7.94 mm, and in the multivariate model incorporating age – 2.6-fold higher (p = 0.036), while age has not impacted significantly (p = 0.301) the prognosis. Conclusions. In individuals with stage II HTN, the presence of CA atherosclerosis with stenosis up to 50 % is associated with a significant increase in vessel diameter regardless of age. CCA intima media thickness depends more on the age of hypertensive patients.