Damping Of Waves Research Articles

Stability for the 2D magnetic Bénard system with partial dissipation and thermal damping near an equilibrium

In this paper, we focus on the Boussinesq equations with magnetohydrodynamics convection, in which the temperature obeys degenerate damped wave equations. Under the influence of an equilibrium, we prove that the 2D magnetic Bénard system remains stable in the whole space . In particular, we obtain the decay rate and large‐time behavior. Without the coupling, the 2D MHD system with only vertical dissipation is not known to be stable. It is revealed that both the thermal damping and the horizontal background magnetic field are indispensable.

Propagation of eigenwaves in plane three-layer media

The paper considers the problem of propagation of natural stress waves in a strip that is in contact with an unbounded isotropic viscoelastic medium made of another material. It is assumed that there are no external influences during the propagation of natural waves. In some cases, the physical properties of viscoelastic materials are described by linear hereditary Boltzmann–Voltaire relations with integral differences of heredity kernels. Some of the layers can be elastic. In this case, the heredity kernels describing the rheological properties of the layers are identically zero. A system in which the rheological properties of the layers are identical (the nuclei of heredity of elements are equal to each other) will be called dissipatively homogeneous. In the particular case, when there are no external influences, the propagation of damped waves of the system is considered; — in the presence of external influences — forced. The main problem is the study of the dissipative (damping) properties of the system as a whole, as well as its stress-strain state.

Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain

Lifespan estimates for semilinear damped wave equations of the form ∂t2u-Δu+∂tu=|u|p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial _t^2u-\\Delta u+\\partial _tu=|u|^p$$\\end{document} in a two dimensional exterior domain endowed with the Dirichlet boundary condition are dealt with. For the critical case of the semilinear heat equation ∂tv-Δv=v2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial _tv-\\Delta v=v^2$$\\end{document} with the Dirichlet boundary condition and the initial condition v(0)=εf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v(0)=\\varepsilon f$$\\end{document}, the corresponding lifespan can be estimated from below and above by exp(exp(Cε-1))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (\\exp (C\\varepsilon ^{-1}))$$\\end{document} with different constants C. This paper clarifies that the same estimates hold even for the critical semilinear damped wave equation in the exterior of the unit ball under the restriction of radial symmetry. To achieve this result, a new technique to control L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document}-type norm and a new Gagliardo–Nirenberg type estimate with logarithmic weight are introduced.

Recovery of a coefficient in a diffusion equation from large time data

Abstract This paper considers the determination of a spatially varying coefficient in a parabolic equation from time trace data. There are many uniqueness theorems known for such problems but the reconstruction step is severally ill-posed: essentially the problem comes down to trying to reconstruct an analytic function from values on a strip. However, we look at an even more restricted data where the measurements are not made on the whole time axis but only for large values adding further to the ill-conditioning situation. In addition, we do not assume the initial state is known. Uniqueness is restored by making changes to the boundary condition, in particular, to the impedance parameter, for each of a series of measurements. We show that an implementation of the above paradigm leads to both uniqueness and an effective reconstruction algorithm. Extension is also made to the case of fractional model and to replacing the parabolic equation with a damped wave equation.

Damping of spin waves

We show that, in ideal-spin hydrodynamics, the components of the spin tensor follow damped wave equations. The damping rate is related to nonlocal collisions of the particles in the fluid, which enter at first order in ℏ in a semiclassical expansion. This rate provides an estimate for the timescale of spin equilibration and is computed by considering a system of spin-1/2 fermions interacting via a quartic self-interaction as well as via (screened) one-gluon exchange. It is found that the relaxation times of the components of the spin tensor can become very large compared to the usual dissipative timescales of the system. Our results suggest that the spin degrees of freedom in a heavy-ion collision may not be in equilibrium by the time of freeze-out, and thus should be treated dynamically. Published by the American Physical Society 2024

Damping of Strong GHz Waves near Magnetars and the Origin of Fast Radio Bursts

We investigate how a fast radio burst (FRB) emitted near a magnetar would propagate through its surrounding dipole magnetosphere at radii r = 107–109 cm. First, we show that a GHz burst emitted in the O-mode with luminosity L ≫ 1040 erg s−1 is immediately damped for all propagation directions except a narrow cone along the magnetic axis. Then, we examine bursts in the X-mode. GHz waves propagating near the magnetic equator behave as magnetohydrodynamic (MHD) waves if they have L ≫ 1040 erg s−1. The waves develop plasma shocks in each oscillation and dissipate at r∼3×108L42−1/4 cm. Waves with lower L or propagation directions closer to the magnetic axis do not obey MHD. Instead, they interact with individual particles and require a kinetic description. The kinetic interaction quickly accelerates particles to Lorentz factors 104–105 at the expense of the wave energy, which again results in strong damping of the wave. In either propagation regime, MHD or kinetic, the dipole magnetosphere surrounding the FRB source acts as a pillow absorbing the radio burst and reradiating the absorbed energy in X-rays. These results constrain the origin of observed FRBs. We argue that the observed FRBs avoid damping because they are emitted by relativistic outflows from magnetospheric explosions, so that the GHz waves do not need to propagate through the outer equilibrium magnetosphere surrounding the magnetar.

The suppression of ocean waves by biogenic slicks

Ocean waves are significantly damped by biogenic surfactants, which accumulate at the sea surface in every ocean basin. The growth, development, and breaking of short wind-driven surface waves are key mediators of the air–sea exchange of momentum, heat and trace gases. The mechanisms through which surfactants suppress waves have been studied in great detail through careful laboratory experimentation in quasi-one-dimensional wave tanks. However, the spatial scales over which this damping occurs in structurally complex surfactant slicks on the real ocean have not been resolved. Here, we present the results of field observations of the spatial response of decimetre- to millimetre-scale waves to biogenic surfactant slicks. We found that wave damping in organic material-rich coastal waters resulted in a net (spatio-temporally averaged) reduction of approximately 50% in wave slope variance relative to the open ocean for low to moderate wind speeds. This reduction of wave slope variance is understood to result in a corresponding reduction in momentum input to the wave field. This significant effect had thus far evaded quantification due in large part to the enormous range of scales required for its description—spanning the sea surface microlayer to the ocean submesoscale.

Thermal Performance of Novel Eco-Friendly Prefabricated Walls for Thermal Comfort in Temperate Climates

The global threat of climate change has become increasingly severe, with the efficiency of buildings and the environment being significantly impacted. It is necessary to develop bioclimatic architectural systems that can effectively reduce energy consumption while bringing thermal comfort, reducing the impact of external temperatures. This study presents the results of a real-scale experimental house prototype, MHTITCA, using a unique design composed of novel eco-friendly prefabricated channel walls filled with a blend of soil, sawdust, and cement for walls and roofs. The experimental analysis performed in this study was based on dynamic climatology. A solar orientation chart of the place was constructed to identify the solar radiation intensity acting on the house. Measurements of roof surface temperatures were conducted to determine temperature damping and temperature wave lag. Monthly average temperature and direct solar radiation data of the site were considered. Compared to other alternative house prototypes, the system maximizes thermal comfort in high-oscillation temperate climates. Temperature measurements were taken inside and outside to evaluate the thermal performance. A thermal insulating layer was added outside the wall and the envelope to improve the prototype’s thermal comfort and reduce the decrement factor even more. This MHTITCA house prototype had 85% thermal comfort, 0% overheating, and 15% low heating. This eco-friendly prototype design had the best thermal performance, achieving a thermal lag of twelve hours, a reduced decrement factor of 0.109, and preventing overheating in areas with high thermal fluctuations. Comparatively, the other prototypes examined provided inferior thermal comfort. The suggested MHTITCA system can be an energy-saving and passive cooling option for thermal comfort in low-cost houses in temperate climates with high thermal oscillations in urban or rural settings.

Pseudomodes of Schrödinger operators

Pseudomodes of non-self-adjoint Schrödinger operators corresponding to large pseudoeigenvalues are constructed. The approach is non-semiclassical and extendable to other types of models including the damped wave equation and Dirac operators.

Stabilisation of linear waves with inhomogeneous Neumann boundary conditions

ABSTRACT We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of these models presents additional interesting features and challenges compared to their homogeneous counterparts. In the present context, energy depends on the boundary trace of velocity. It is not clear in advance how this quantity should be controlled based on the given data, due to regularity issues. However, we establish global existence and also prove uniform stabilisation of solutions with decay rates characterised by the Neumann input. We supplement these results with numerical simulations in which the data do not necessarily satisfy the given assumptions for decay. These simulations provide, at a numerical level, insights into how energy could possibly change in the presence of, for example, improper data.

Numerical Investigation of the Sediment Load Exchange between a Coastal Mud Bank and Its Neighbouring Estuary

Muddy coastlines cover much of the world’s shores, yet studies on the interaction between mud-affected coasts and estuaries are limited. This study focuses on the Mahury River estuary and its interaction with the muddy coast of the Guianas, primarily fed by the Amazon. A coupled wave–current–sediment transport model is developed to analyze the sediment exchange in an environment with strong interactions between the waves and the fluid mud. Simulations explore how seasonal changes in waves, mud availability, and tides affect sediment fluxes. The main processes influencing suspended particulate matter (SPM) and sediment transport are well emulated, notwithstanding the complexity of the ambient muddy environment. The results show that during the rainy season, strong wave damping and wave refraction zones cause high SPM resuspension in shallow waters (<5 m). In contrast, during the dry season, wave influence shifts to the estuary mouth. Erosion and sedimentation patterns indicate that ebb currents associated with neap tides during the rainy season represent the most favourable conditions for the alongshore migration of mud banks. Neaptide ebb currents also contribute to sedimentation during the dry season but only in the estuary mouth and the nearby coastal area. The abundance of mud leads to an extension of the estuary’s intertidal area during the dry season.

Visco‐elastic damped wave models with time‐dependent coefficient

AbstractIn this paper, we study the following Cauchy problem for linear visco‐elastic damped wave models with a general time‐dependent coefficient : We are interested to study the influence of the damping term on qualitative properties of solutions to () as decay estimates for energies of higher order and the parabolic effect. The main tools are related to WKB‐analysis. We apply elliptic as well as hyperbolic WKB‐analysis in different parts of the extended phase space.

Convex integration solution of two-dimensional hyperbolic Navier–Stokes equations*

Abstract Hyperbolic Navier–Stokes equations replace the heat operator within the Navier–Stokes equations with a damped wave operator. Due to this second-order temporal derivative term, there exist no known bounded quantities for its solution; consequently, various standard results for the Navier–Stokes equations such as the global existence of a weak solution, that is typically constructed via Galerkin approximation, are absent in the literature. In this manuscript, we employ the technique of convex integration on the two-dimensional hyperbolic Navier–Stokes equations to construct a weak solution with prescribed energy and thereby prove its non-uniqueness. The main difficulty is the second-order temporal derivative term, which is too singular to be estimated as a linear error. One of our novel ideas is to use the time integral of the temporal corrector perturbation of the Navier–Stokes equations as the temporal corrector perturbation for the hyperbolic Navier–Stokes equations.

Analysis of the perceived intensity of vibratory stimuli driven by the Modal Overlap Factor

The vibro-tactile perception experiment reported in this paper aims to investigate correlations between the perceived vibratory intensity and the Modal Overlap Factor (MOF) of vibratory stimuli. The MOF is often used to physically characterise the vibratory behavior of a structure and can be estimated from the product of frequency, modal density and modal loss factor. In this experiment, stimuli are applied to the participant's hands by means of a steering wheel set in vibration by a shaker. The vibratory stimuli are synthesized from filtered white noise convolved with an impulse response defined as a sum of damped sine waves. The MOF can be controlled by selecting the number of sine waves, their frequency and damping ratio. A set of 100 stimuli, with MOF values ranging from 2 to 200%, in the 5-305Hz range, and equalized in acceleration, is used. Each of the 80 participants is asked to rate twice the perceived intensity of 10 stimuli, pseudo-randomly chosen among the 100 stimuli. Data are analyzed to establish trends between perceived vibratory intensity and the physical parameters of the stimuli.

Physical modelling study on wave damping induced by an idealized floating kelp farm

A physical modelling study was carried out to investigate random wave damping promoted by an idealized floating kelp farm. The experimental conditions spanned intermediate water depths and both linear and nonlinear water waves. Unlike previous studies of wave damping promoted by vegetation, the floating kelp farm was placed close to the water surface with a ratio between vegetation height and water depth close to 0.25. The wave transmission coefficient induced by the floating kelp farm ranged between 0.56 and 0.96. This coefficient decreased for longer floating kelp farms and it was a function of the ratio between kelp farm length and incident wavelength and of the relative wave depth. Spectral analysis showed that wave damping was not frequency-dependent for wave frequencies close to the peak frequency. The wave transmission coefficients of a floating kelp farm with about 100 culture lines and with an extension of approximately 200 m were similar to those of submerged detached breakwaters with a relative crest freeboard smaller than -0.4. Furthermore, the bulk drag coefficient of near-surface idealized floating kelp farms can be modelled as a function of the Keulegan-Carpenter number. This study highlights the potential viability of nature-based solutions such as floating kelp farms for coastal protection.

The Effects of Cooling on Boundary Layer Accretion

In many cases accretion proceeds from disks onto planets, stars, white dwarfs, and neutron stars via a boundary layer, a region of intense shear where gas transitions from a near-Keplerian speed to that of the surface. These regions are not susceptible to the common magnetorotational and Kelvin–Helmholtz instabilities, and instead global modes generated by supersonic shear instabilities are a leading candidate to govern transport in these regions. This work investigates the dynamics of these systems under a range of thermodynamic conditions, surveying both disk sound speeds and cooling rates. Very fast and very slow cooling have little effect on wave dynamics: In the fast-cooling limit, waves propagate in an effectively isothermal manner, and in the slow-cooling limit, wave propagation is effectively adiabatic. However, when the cooling timescale is comparable to the wave period, wave damping becomes extreme. In cases with intermediate cooling rates, mass and angular momentum transport can be suppressed by orders of magnitude compared to isothermal and uncooled cases. Cooling in accretion disks leads to a preference for wavenumbers near and below the Mach number of the disk; the corresponding lower frequencies can (in nonisothermal systems) couple to gravity modes within the star, potentially driving low-frequency variability such as dwarf nova and quasi-periodic oscillations in accreting systems.

Surface wave damping by a Robin boundary condition at a permeable seabed

We investigate the damping of inviscid surface gravity waves when they propagate over a permeable seabed. Traditionally, this problem is solved by considering the wave motion in the upper water layer interacting with the Darcy flow in the porous bottom layer through matching of the solutions at the permeable interface. The novel approach in this study is that we describe the interaction between the upper fluid layer and the permeable bottom layer by the application of a Robin boundary condition. By varying the magnitude of the Robin parameter R, we can model the bottom structure of the fluid layer from rigid to completely permeable. In the case when the bottom is a porous medium where Darcy’s law applies, or composed by densely packed vertical Hele-Shaw cells, R is small, and can by determined by comparison with analytical results for a two-layer structure. In this case the wave damping is small. For larger values of R, the damping increases, and for very large R, the wave is almost critically damped. For the nonlinear transport in spatially damped shallow-water waves, increasing bottom permeability (larger R), reduces the magnitude of the horizontal Stokes drift velocity, while the drift profile tends to become parabolic with height. The vertical Stokes drift in the limit of large permeability is linear with height, with a magnitude that is larger than the horizontal drift. It is suggested that the implementation of a permeable bottom bed in some cases could prevent shorelines from damaging erosion by incoming surface waves.

Energetic seed particles in self-consistent particle acceleration modeling at interplanetary shock waves

Aims. The study investigates the relevance of the seed particle population in the results of particle acceleration in interplanetary shock waves, when wave–particle interactions are treated self-consistently. Methods. We employed the SOLar Particle Acceleration in Coronal Shocks (SOLPACS) model, which is a proton acceleration simulation in shocks with self-consistent nonlinear wave–particle interactions. We compared a suprathermal monoenergetic injection with a two-component injection, including the suprathermal monoenergetic component and a broad-spectrum energetic component corresponding to the observed background particle spectrum. Energetic particles in the beginning of the simulation could increase the local wave intensities sufficiently to increase the rate of acceleration for injected particles and even reshape the resulting particle energy spectra and spatial distributions. The resulting particle energy spectra, particle spatial distributions, and wave intensity spectra are compared to observations made by Solar Orbiter’s instrument suite of the 2021 October 30 energetic storm particle (ESP) event to evaluate the relevance of the seed particle population in the acceleration model. Results. The energetic component of the seed particle population shortens the needed acceleration time for particles and enhances the tail of the spectrum to a level that matches the observations. The highest compared energies (> 1 MeV) match only when an energetic component is included in the seed particle population. The wave intensities and spatial distributions, on the other hand, showed no significant differences with the monoenergetic and two-component injection. While the simulated and observed wave intensities match within five minutes before the shock passing, the simulated wave field is too intense farther out from the shock, probably due to a lack of wave damping and/or decay processes in the simulation, leading to particles being slightly overly trapped to regions closer to the shock.

Determination of Submerged Breakwater Efficiency Using Computational Fluid Dynamics

Wind-induced waves can lead to the partial or complete wash-over of beaches, causing erosion that impacts both the landscape and tourist infrastructure. In some regions of the world, e.g., Croatia, this process, which usually occurs during a harsh winter, has a major impact on the environment and the economy, and preventing or reducing this process is highly desirable. One of the simplest methods to reduce or prevent beach erosion is the use of innovative underwater structures designed to decrease wave energy by reducing wave height. In this study, submerged breakwaters are numerically investigated using various topologies, positions, and angles relative to the free surface. Not only is the optimal topology determined, but the most efficient arrangement of multiple breakwaters is also determined. The advantage of newly developed submerged breakwaters over traditional ones (rock-fixed piers) is that they do not require complex construction, massive foundations, or high investment costs. Instead, they comprise simple floating bodies connected to the seabed by mooring lines. This design makes them not only cheap, adaptable, and easy to install but also environmentally friendly, as they have little impact on the seabed and the environment. To evaluate wave damping effectiveness, the incompressible computational fluid dynamics (ICFD) method is used, which enables the use of a turbulence model and the possibility of accurate wave modelling.

Investigating the impact of shear and bulk viscosity on the damping of confined acoustic modes in phononic crystal sensors

Phononic crystal (PnC) sensors are recognized for their capability to control acoustic wave propagation through periodic structures, presenting considerable potential across various applications. Despite advancements, the effects of fluid viscosity on PnC performance remain intricate and inadequately understood. This study theoretically investigates the influence of shear (dynamic) and bulk viscosity on acoustic wave damping in defective one-dimensional phononic crystal (1D PnC) sensors designed for detecting liquid analytes. Acetic acid with varying viscosities is considered to fill a cavity layer intermediated by a multilayer stack of lead and epoxy. The effects of dynamic and bulk viscosity on the resonance characteristics of the defective mode were analyzed. Numerical results reveal that increased dynamic viscosity leads to substantial broadening and decreased intensity of resonance peaks, accompanied by a shift to higher frequencies due to enhanced elastic wave attenuation and damping. At low dynamic viscosity (η = 0.2 ηd), numerous resonance peaks with varying intensities are observed. However, at higher viscosities (η = 2.0 ηd to η = 10.0 ηd), only one prominent peak appears in the spectrum. The intensity of this resonant peak starts at 98% for η = 2 ηd and decreases to 58.8% as the dynamic viscosity increases to η = 10 ηd. Additionally, the combined effect of dynamic and bulk viscosity introduces further damping, causing a strong shift of the resonance peak to higher frequencies, along with an increase in the full width at half maximum (FWHM) and a decrease in the quality factor (QF). These findings emphasize the necessity of incorporating both shear and bulk viscosity in the design of PnC sensors to enhance their sensitivity and accuracy in practical applications. This theoretical framework provides critical insights for optimizing sensor performance and bridging gaps between theoretical predictions and experimental observations, especially in 1D PnCs, offering potential solutions to challenges in real-world PnC sensor applications.