Increasing Wave Number Research Articles

Comparision of approximation methods for weakly damped waves Discussion paper

A number of applications involving wave propagation are asymptotically stable, but the decay rate of the mode does not increase with increasing wave number. Applications include electrical transmission, acoustic waves and water waves. There are many different approximation methods for these systems that are fine for simulation. But the qualitative behaviour of the approximated eigenvalues can be quite different. Controller and estimator design with different approximations can yield different results. A number of partial differential equations (PDEs) are derived using Hamilton’s principle. This provides information about the energy of the system that can be a guideline in establishing well-posedness on an appropriate state space. Recent work on a port-Hamiltonian approach to approximation shows promise in obtaining finite-dimensional approximations that are useful for control and estimation. A key feature of the port-Hamiltonian approach is careful attention to how the energy in the system is modelled and approximated. How does this approach compare to more traditional approaches to scientific computation? In particular, what are the similarities and what are the differences? These questions will be examined in the talk, and in discussion, through several relatively simple examples.

Vibration of thin cylindrical shells on an elastic foundation coupled with multiple discrete stiffnesses

Vibration properties of thin cylindrical shells on an elastic foundation coupled with multiple discrete stiffnesses were investigated. The discrete stiffnesses were modelled as external forces. Hamilton’s principle was applied to deduce the governing equations. To study the natural vibration properties, the wave-like solutions were applied. Then the governing equations were discretized in matrix form to obtain the eigenvalues. The properties of natural frequencies and vibration modes of thin cylindrical shells were studied. The results illustrate that each natural frequency of cylindrical shells is mainly dominated by one vibration mode, that is, flexural, longitudinal and shear modes. The natural frequency will get closer with the increase of circumferential wave numbers. The influences of several parameters to vibration properties of cylindrical shells were also investigated.

Lateral movements in Rayleigh-Taylor instabilities due to frontiers. Numerical analysis.

Numerical simulations were performed for Rayleigh-Taylor (RT) hydrodynamic instabilities when a frontier is present. The frontier formed by the interface between two fluids prevents the free movement of the fingers created by the instability. As a consequence, transversal movements at the rear of the fingers are observed in this area. These movements produce collapse of the fingers (two or more fingers join in one finger) or oscillations in the case that there is no collapse. The transversal velocity of the fingers, the amplitude of the oscillations, and the wave number of the RT instabilities as a function of the Rayleigh number (Ra) were studied near the frontier. We verified numerically that in classical RT instabilities, without a frontier, these lateral movements do not occur; only with a physical frontier, the transversal displacements of the fingers appear. The transverse displacement velocity and the initial wave number increase with Ra. This leads to the collapse of the fingers, diminishing the wave number of the instabilities at the interface. Instead, no significant changes in the amplitude of the oscillations are observed modifying Ra. The numerical results are independent of the type or origin of the frontier (gas-liquid, liquid-liquid, or solid-liquid). The numerical results are in good agreement with the experimental results reported by Binda et al. [Chaos 28, 013107 (2018)]. Based on these results, it was possible to determine the cause of the transverse displacements, which had not been explained until now.

Сегрегация частиц в магнитной жидкости при совместном действии магнитного и гравитационного полей

Transient problem of magnetic nanoparticles segregation under gravity and direct magnetic field action was solved by the method of control volumes. It was shown, that during the transition of the system from initial uniform state to the inhomogeneous stationary one, the long-live finger-like structures with a continuously increasing wave number are formed. To limit it, an additional Kahn-Hillard term was introduced into the magnetodiffusion equation. The appearance of finger-like structures is explained by the competition between gravitational and magnetostatic forces in a thin diffusion layer between regions with a low and high concentration of particles. The observed phenomenon is a diffusion analogue of the Rosenzweig instability of the free boundary of a magnetic fluid in a vertically directed magnetic field.

Thermocapillary Convection in a Binary Mixture with Moderate Prandtl Number in a Shallow Annular Pool

This paper presented a series of numerical simulations on thermocapillary convection for mixed toluene/hexane solution with mass fraction of $c_{0}= 26.27$ % in a shallow annular pool. The Prandtl number of the binary solution is 5.54. Results indicate that when the annular pool subjects to a radial temperature gradient, the solute shifts toward the inner wall under the Soret effect, which leads to a concentration gradient with the opposite direction to the temperature gradient. With the increase of surface heat dissipation, thermocapillary convection is enhanced and the flow is more prone to destabilization. Therefore, the critical thermocapillary Reynolds number of the flow destabilization and the corresponding critical oscillation frequency all decrease, but the critical wave number increases. After flow destabilization, the concentration fluctuation similar to the temperature fluctuation on the free surface appears. No matter the free surface is adiabatic or not, the flow always undergoes a transition from two-dimensional steady axisymmetric flow to the hydrothermal waves, and then to chaos with the increase of thermocapillary Reynolds number.

Detecting atmospheric normal modes with periods less than 6 h by barometric observations

The theory of atmospheric normal modes (ANMs) predicts the existence of relatively short-period gravity-inertia ANMs. Simultaneous observations of surface air-pressure variations by barometers at distant stations of the Global Geodynamics Project network during an interval of 6 months were used to detect individual gravity-inertia ANMs with periods of ∼2–5 h. Evidence was found for five ANMs with a lifetime of ∼10 days. The data of the stations, which are close in both latitude and longitude, were utilized for deriving the phases of the detected ANMs. The phases revealed wave propagation to the west and increase of zonal wavenumbers with frequency. As all the detected gravity-inertia ANMs are westward propagating, they are suggested to be generated due to the breakdown of migrating solar tides and/or large-scale Rossby waves. The existence of an ANM background will complicate the detection of the translational motions of the Earth's inner core.

Phonon stiffen and soften at zigzag- and armchair-dominated edges of exfoliated bilayer graphene ribbon presented by Raman spectra

The Raman spectra at the edge of the exfoliated bilayer graphene ribbon (GR) were investigated in detail. Results show that both G and 2D phonons stiffen (wave number increases) at zigzag-dominated edge, while they soften at armchair-dominated edge compared with those at the middle position in the GR. Furthermore, the full widths at half maximum intensity of both G and 2D Raman peaks narrow at the zigzag-dominated edge, while they broaden at the armchair-dominated edge. The stiffness and softness are attributed to the C–C bonds at the edge. For zigzag-dominated edge, the stiffness may originate in the increase of the force constant induced by the shrinking of C–C bond. For armchair-dominated edge, the softness may be due to the decrease of the force constant induced by the unsaturated hanging bonds at edge, which is different from Kohn anomaly and charge doping. The analysis is in agreement well with others calculation results about C–C bonds and the edge energy. These results may be useful to understand physical properties at the bilayer graphene edge and for applications in the device by taking advantage of the edge states in bilayer graphene.

Investigations of the micro surface shape for the gear-shaft/journal-bearing interface in water hydraulic internal gear pumps

This article presents an approach for improving the water film’s carrying capacity in the gear-shaft/journal-bearing interface in water hydraulic internal gear pumps by applying micro shapes to the gear shaft’s surface. The micro shapes are in the shape of sinusoidal waves that can be determined by three design parameters in terms of the wave number, the wave amplitude, and the convex ratio. An elasto-hydrodynamic model, which involves the evaluations of the film height, the film pressure, and the bearing deformation, is proposed to analyze the performance of the micro shapes, and the model is validated by comparison with the results from other research groups. By observing the performance of the micro shapes, it is seen that the convex shape has a positive effect while the concave shape has a negative effect on the film’s carrying capacity, and the carrying capacity decreases as the wave number increases. Additionally, further discussions are performed with respect to the design parameters of the convex shape under different operating conditions, suggesting that the wave amplitude should be maintained 0.8–0.9 times the maximum deformation of the bearing and the convex ratio should be 1/3.

Effect of enhanced dissipation by shear flows on transient relaxation and probability density function in two dimensions

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, streamers and zonal flows, and streamers combined), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in the turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale τe, previously taken to be a hybrid time scale τe∝τΩ2/3τη, is shown to depend on types of shear flow as well as the initial power spectrum. Here, τΩ and τη are shearing and molecular diffusion times, respectively. Furthermore, we present time-dependent Probability Density Functions (PDFs) and discuss the effect of enhanced dissipation on PDFs and a dynamical time scale τ(t), which represents the time scale over which a system passes through statistically different states.

Non-hydrodynamic transverse collective excitations in hard-sphere fluids.

Collective excitations in hard-sphere fluids were studied in a wide range of wave numbers and packing fractions η by means of molecular dynamics simulations. We report the observation of non-hydrodynamic transverse excitations for packing fractions η≥0.395 in the shape of transverse current spectral functions. Dispersion of longitudinal excitations in the whole range of packing fractions shows a negative deviation from the linear hydrodynamic law with increasing wave numbers even for dense hard-sphere fluids where the transverse excitations were observed. These results do not support a recent proposal within the "Frenkel line" approach that the positive sound dispersion in liquids is defined by transverse excitations. We report calculations of the cutoff "Frenkel frequencies" for transverse excitations in hard-sphere fluids and discuss their consistency with the estimated dispersions of shear waves.

Soliton interactions of a (2+1)-dimensional nonlinear Schrödinger equation in a nonlinear photonic quasicrystal or Kerr medium

Under investigation are the soliton interactions for a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which can describe the dynamics of a nonlinear photonic quasi-crystal or vortex Airy beam in a Kerr medium. With the symbolic computation and Hirota method, analytic bright N-soliton and dark two-soliton solutions are derived. Graphic description of the soliton properties and interactions in a nonlinear photonic quasicrystal or Kerr medium is done. Through the analysis on bright and dark one solitons, effects of the optical wavenumber/linear opposite wavenumber and nonlinear coefficient on the soliton amplitude and width are studied: when the absolute value of the optical wavenumber or linear opposite wavenumber increases, bright soliton amplitude and dark soliton width become smaller; nonlinear coefficient has the same influence on the bright soliton as that of the optical wavenumber or linear opposite wavenumber, but does not affect the dark soliton amplitude or width. Overtaking/periodic interactions between the bright two solitons and overtaking interactions between the dark two solitons are illustrated. Overtaking interactions show that the bright soliton with a larger amplitude moves faster and overtakes the smaller, while the dark soliton with a smaller amplitude moves faster and overtakes the larger. When the absolute value of the optical wavenumber or linear opposite wavenumber increases, the periodic-interaction period becomes longer. All the above interactions are elastic. Through the interactions, soliton amplitudes and shapes keep invariant except for some phase shifts.

Internal wave scattering in continental slope canyons, Part 2: A comparison of ray tracing and numerical simulations

When internal waves interact with topography, such as continental slopes, they can transfer wave energy to local dissipation and diapycnal mixing. Submarine canyons comprise approximately ten percent of global continental slopes, and can enhance the local dissipation of internal wave energy, yet parameterizations of canyon mixing processes are currently missing from large-scale ocean models. As a first step in the development of such parameterizations, we conduct a parameter space study of M2 tidal-frequency, low-mode internal waves interacting with idealized V-shaped canyon topographies. Specifically, we examine the effect of varying the canyon mouth width, shape and slope of the thalweg (line of lowest elevation) (i.e. flat bottom or near-critical slope). In Part 1 of this study (Nazarian and Legg, 2017a), we developed a ray tracing algorithm and used it to estimate how canyons can increase the wave Froude number, by increasing energy density and increasing vertical wavenumber. Here in Part 2 we examine the internal wave scattering in continental slope canyons using numerical simulations, and compare the results with the linear ray tracing predictions. We find that at intermediate canyon widths, a large fraction of incoming wave energy can be dissipated, which can be explained as a consequence of the increase in ray density and, for near-critical slope canyons, increase in vertical wave number, which leads to lower Richardson number followed by instability. Relative to a steep continental slope without a canyon, we find that V-shaped flat bottom canyons always dissipate more energy and are an effective geometry for wave trapping and subsequent energy loss. When both flat bottom canyons and near-critical slope canyons are made narrower, less wave energy enters the canyon, but a larger fraction of that energy is lost to dissipation due to subsequent reflections and wave trapping. There is agreement between the diagnostics calculated from the numerical model and the linear ray tracing, lending support for the use of linear theory to understand the fundamental dynamics of internal wave scattering in canyons.

Enhanced Raman and photoluminescence response in monolayer MoS2 due to laser healing of defects

Bound quasiparticles, negatively charged trions and neutral excitons are associated with the direct optical transitions at the K‐points of the Brillouin zone for monolayer MoS2. The change in the carrier concentration, surrounding dielectric constant, and defect concentration can modulate the photoluminescence and Raman spectra. Here, we show that exposing the monolayer MoS2 in air to a modest laser intensity for a brief period of time enhances simultaneously the photoluminescence intensity associated with both trions and excitons, together with ∼3 to 5 times increase of the Raman intensity of first‐order and second‐order modes. The simultaneous increase of photoluminescence from trions and excitons cannot be understood based only on known scenario of depletion of electron concentration in MoS2 by adsorption of O2 and H2O molecules. This is explained by laser‐induced healing of defect states resulting in reduction of nonradiative Auger processes. This laser healing is corroborated by an observed increase of intensity of both the first‐order and second‐order longitudinal acoustic Raman modes at the M‐point of Brillouin zone by a factor of ∼3 to 5. The A1g mode hardens by ∼1.4 cm−1, whereas the mode softens by ∼1 cm−1. The second‐order longitudinal acoustic Raman mode at the M‐point of Brillouin zone at ∼440 cm−1 shows an increase in wavenumber by ∼8 cm−1 with laser exposure. These changes are a combined effect of change in electron concentrations and oxygen‐induced lattice displacements. Copyright © 2017 John Wiley & Sons, Ltd.

Radial acceleration of geodesic acoustic modes in the presence of a temperature gradient

The global dynamics of geodesic acoustic modes (GAMs) is studied analytically and by means of gyrokinetic simulations for several equilibria with flat and nonuniform profiles. In particular, the effects of phase mixing via the continuum spectrum in the presence of a temperature gradient are investigated. We show that the frequency of GAM is not constant but can evolve in time because of the increase of the radial wavenumber. As a consequence, also the radial velocity of GAM increases in time. Thus, this study reduces the discrepancy between the linear theory and the experiments, in which strong velocities of GAM are generally observed. An estimate of phase and group velocity is given for simulations performed with experimental parameter values.

Linear Instability Analysis of Charged Jet in Liquid-liquid Systems

By discussing the perturbed pressure field and the perturbed electric field, the viscous dispersion equation of charged jet in water-biodiesel system was derived. Through numerical calculation, the temporal instability characteristics and the effects of parameters were discussed. The results show the effect of jet velocity and charged voltage of charged jet in liquid-liquid system on instability is same as that in liquid-gas system. with the increasing of jet velocity or charged voltage, the maximum of wave growth rate, the corresponding optimal wave number and the maximum of wave number turn bigger, and water droplet size gets smaller. Biodiesel viscosity promotes the jet breakup obviously, while water viscosity always hinders the jet breakup. The maximum growth rate and optimum wave number increase obviously with decreasing the water surface tension, while the biodiesel surface tension has the reverse effect on the maximum growth rate and optimum wave number. By comparison, the effect of water viscosity and biodiesel surface tension on instability is much less than that of biodiesel viscosity and water surface tension. Therefore, increasing jet velocity, charged voltage and biodiesel viscosity or decreasing water surface tension are good methods to obtain small water droplet in biodiesel.

Toward an optimal solver for time-spectral fluid-dynamic and aeroelastic solutions on unstructured meshes

The time-spectral method applied to the Euler and coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with time-spectral methods over traditional time-implicit methods hinges on the ability rapidly to solve the large non-linear system resulting from time-spectral discretizations which become larger and stiffer as more time instances are employed or the period of the flow becomes especially short (i.e. the maximum resolvable wave-number increases). In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances. The use of GMRES as the linear solver makes time-spectral methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods. In previous work, a wave-number independent preconditioner that mitigates the increased stiffness of the time-spectral method when applied to problems with large resolvable wave numbers has been developed. This preconditioner, however, directly inverts a large matrix whose size increases in proportion to the number of time instances. As a result, the computational time of this method scales as the cube of the number of time instances. In the present work, this preconditioner has been reworked to take advantage of an approximate-factorization approach that effectively decouples the spatial and temporal systems. Once decoupled, the time-spectral matrix can be inverted in frequency space, where it has entries only on the main diagonal and therefore can be inverted quite efficiently. This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.

Short‐crested waves in the surf zone

AbstractThis study investigates short‐crested waves in the surf zone by using the mesh‐free Smoothed Particle Hydrodynamics model, GPUSPH. The short‐crested waves are created by generating intersecting wave trains in a numerical wave basin with a beach. We first validate the numerical model for short‐crested waves by comparison with large‐scale laboratory measurements. Then short‐crested wave breaking over a planar beach is studied comprehensively. We observe rip currents as discussed in Dalrymple (1975) and undertow created by synchronous intersecting waves. The wave breaking of the short‐crested wavefield created by the nonlinear superposition of intersecting waves and wave‐current interaction result in the formation of isolated breakers at the ends of breaking wave crests. Wave amplitude diffraction at these isolated breakers gives rise to an increase in the alongshore wave number in the inner surf zone. Moreover, 3‐D vortices and multiple circulation cells with a rotation frequency much lower than the incident wave frequency are observed across the outer surf zone to the beach. Finally, we investigate vertical vorticity generation under short‐crested wave breaking and find that breaking of short‐crested waves generates vorticity as pointed out by Peregrine (1998). Vorticity generation is not only observed under short‐crested waves with a limited number of wave components but also under directional wave spectra.

Linear stability analysis of Rayleigh-Bénard convection of cold water near its density maximum in a vertically heated annular container

In order to understand the onset of Rayleigh-Benard convection of cold water near its density maximum in a vertical annular container heated from below and cooled from above, the instability of the static diffusive state was investigated by linear stability analysis. Two kinds of thermal boundary conditions, perfect insulating and conducting sidewalls, were used. The aspect ratio and radius ratio of the annular container varied from 0.5 to 4.5 and 0.1 to 0.8, respectively. Results indicate that the critical Rayleigh number and the critical wave number increase with the increase of density inversion parameter. There are some new flow modes with large azimuthal wave number near the convection onset for cold water with density maximum, which are not observed in Rayleigh-Benard convection of the Boussinesq fluids. The stratified flow phenomenon in cold water with density maximum is certified. The larger the density inversion parameter is, the more obvious the stratified flow phenomenon becomes. With the increase of the aspect ratio, the critical Rayleigh number decreases, but the critical wave number increases. However, with the increase of the radius ratio, both the critical Rayleigh number and the critical wave number increase continuously. Furthermore, the effect of thermal boundary conditions at the sidewalls on the convection stability is also validated.

Wave propagation in fluid-conveying viscoelastic carbon nanotubes under longitudinal magnetic field with thermal and surface effect via nonlocal strain gradient theory

Based on nonlocal strain gradient theory, wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes (SWCNTs) is studied in this paper. With consideration of thermal effect and surface effect, wave equation is derived for fluid-conveying viscoelastic SWCNTs under longitudinal magnetic field utilizing Euler–Bernoulli beam theory. The closed-form expressions are derived for the frequency and phase velocity of the wave motion. The influences of fluid flow velocity, structural damping coefficient, temperature change, magnetic flux and surface effect are discussed in detail. SWCNTs’ viscoelasticity reduces the wave frequency of the system and the influence gets remarkable with the increase of wave number. The fluid in SWCNTs decreases the frequency of wave propagation to a certain extent. The frequency (phase velocity) gets larger due to the existence of surface effect, especially when the diameters of SWCNTs and the wave number decrease. The wave frequency increases with the increase of the longitudinal magnetic field, while decreases with the increase of the temperature change. The results may be helpful for better understanding the potential applications of SWCNTs in nanotechnology.

Deformation of Topologically-Protected Supercooled Skyrmions in a Thin Plate of Chiral Magnet Co8Zn8Mn4.

Magnetic skyrmions in Co8Zn8Mn4 thin plates are observed to deform in a metastable state prepared in a magnetic-field-cooling process by way of the thermal-equilibrium skyrmion phase. In cooling, the disk-shape skyrmions change to bar- or L-shaped elongated form, whereas the skyrmion density is nearly conserved. The deformation of the skyrmions in the supercooled metastable phase is observed irrespective of the crystallographic orientation of the thin plate, whereas the elongation direction nearly aligns along the magnetic easy axis. It is proposed that the deformation should be induced by a large increase in magnetic modulation wavenumber when decreasing the temperature, whereas the topological protection of the skyrmions keeps the averaged skyrmion density constant.