Normal-mode Wave Research Articles

Research on the Impact of a Fluid Field on an Acoustic Field in Herschel–Quincke Tube

A study concerning the influence of flow on the Herschel–Quincke duct is presented here, which includes the numerical model, the acoustic source and the absorption condition called the Perfectly Matched Layer. For the excitation of a sound field, a normal mode wave is placed at the inlet of the tube. The function of PML is to simulate the infinite tube and avoid the reflection of acoustic wave. To investigate the influence of flow field on sound field, a coupled calculation method combining the finite element method and computational fluid dynamics is used to solve the linearized Euler equation, named the Galbrun equation. Firstly, the influence of the cross-section of the tube on the acoustic field is considered. Secondly, the effects of flow on the acoustic field is also investigated. Lastly, a comparative analysis of the simulation results reveals the influence of flow and other parameters of the tube on sound propagation. Both the Mach number and the cross-section ratio have an influence on the acoustic resonance, and the resonance frequency decreases with the increase in the cross-section ratio.

Planetary-scale MLT waves diagnosed through multi-station methods: a review

Most experimental investigations on planetary-scale waves in the mesosphere and lower thermosphere (MLT) region are based on single-station or -satellite spectral analysis methods, which suffer from intrinsic spectral aliasing/ambiguity. To overcome the aliasing, the author has developed and utilized dual- and multi-station spectral methods in a series of recent works. These methods were implemented on meteor radar observations and surface magnetometer observations. In the implements, a variety of waves were discovered or investigated in terms of seasonal variations and responses to sudden stratospheric warming events, such as lunar and solar tides (migrating and non-migrating), Rossby wave normal modes, ultra-fast Kelvin waves, and secondary waves of wave–wave nonlinear interactions between the previous waves. The current paper illustrates these methods using synthetic data, comparatively reviews the methods and results in plain language, and proposes a new representation, termed the adjusted Feynman diagram, to summarize the nonlinear interactions and explain their implications.Graphical

Retracted] Analysis of VLF Wave Field Components and Characteristics Based on Finite Element Time‐Domain Method

Most traditional sound field calculation methods regard the seabed as the horizontal stratified liquid sea bottom and conduct simulation analysis based on the frequency domain. Hence, the generality of the above research methods is limited to varying degrees. To accurately clarify the propagation characteristics and mechanism of very low‐frequency (VLF, ≤100 Hz) sound waves in the shallow sea, a numerical calculation model is established using the finite element time‐domain method (FETD) based on the three‐dimensional cylindrical coordinate system. Using this model, the effects of sea‐bottom topographies and geoacoustic parameters on the composition and characteristics of VLF sound fields in the shallow sea and their corresponding mechanism are investigated through the comparative analysis of various numerical simulation examples. The simulation results demonstrate that the low‐frequency sound field in the full waveguide of the shallow sea is composed of normal mode waves in the seawater layer, Scholte waves at the liquid‐solid interface, and elastic waves at the sea bottom. Compared with the soft sea bottom, which has a more negligible elastic impedance, the hard sea bottom is more conducive to the long‐distance propagation of normal mode waves and the excitation of Scholte waves. The Scholte waves on the hard sea bottom are significantly stronger than those on the soft sea bottom. Compared with the horizontal sea bottom, the uphill topography enhances the sound energy leakage to the sea bottom. It is more favorable to receive Scholte waves at shallow depths, whereas the influence laws of downhill topography are the opposite.

Analysis on the seismic wave caused by low frequency sound source in shallow sea based on multi-transmitting formula artificial boundary

The elastic waves propagating in seabed caused by sailing ships are called ship seismic waves, which can be used to identify ship targets. The wave components and the influences of source frequency, source depth and depth of seawater to the seismic waves are important to the application of seismic wave to detect ship targets. Thus, a forward numerical simulation of seismic waves in shallow sea excited by low frequency sources in time domain was carried out with finite element method based on the Multi-Transmitting Formula artificial boundary. The numerical results show that the body waves and conical waves decay faster in space, but the interface wave decays relatively slow. Multi-transmitting Formula (MTF) artificial boundary has achieved good transmitting effect for longitudinal wave, upstream and downstream acoustic wave and transverse wave. When the source frequency is very low and the seawater layer is shallow, due to the effect of low-frequency cutoff, there is no normal mode wave which can propagate without attenuation in the seawater waveguide, and only the interface wave is propagating near the sea bottom surface. When the frequency of the source or the depth of the seawater layer increases, the effect of low frequency cutoff in the shallow water waveguide is weakened, and the normal mode waves propagating in seawater layer are gradually excited. The intensity of the interface wave caused by low-frequency point sound source mainly depends on the distance between the source and the seafloor.

Rossby wave second harmonic generation observed in the middle atmosphere

Second harmonic generation is the lowest-order wave-wave nonlinear interaction occurring in, e.g., optical, radio, and magnetohydrodynamic systems. As a prototype behavior of waves, second harmonic generation is used broadly, e.g., for doubling Laser frequency. Second harmonic generation of Rossby waves has long been believed to be a mechanism of high-frequency Rossby wave generation via cascade from low-frequency waves. Here, we report the observation of a Rossby wave second harmonic generation event in the atmosphere. We diagnose signatures of two transient waves at periods of 16 and 8 days in the terrestrial middle atmosphere, using meteor-radar wind observations over the European and Asian sectors during winter 2018–2019. Their temporal evolution, frequency and wavenumber relations, and phase couplings revealed by bicoherence and biphase analyses demonstrate that the 16-day signature is an atmospheric manifestation of a Rossby wave normal mode, and its second harmonic generation gives rise to the 8-day signature. Our finding confirms the theoretically-anticipated Rossby wave nonlinearity.

Numerical simulation of seismic wave triggered by low-frequency sound source with 3D staggered-grid difference method in shallow water

Ship seismic wave is often used for targeting ship location. This elastic wave that traveled in the seabed layer is triggered by low-frequency ship noise. At present, most of the theoretical studies of ship seismic wave were conducted in the frequency domain and the wave components such as P-wave, S-wave, and normal mode wave cannot be distinguished. In this study, the propagation characteristics were studied by numerical simulation in the time domain based on 3D staggered-grid finite difference method whose availability was firstly verified through a theoretical solution. The numerical simulation results show that seismic waves in the seabed layer were dominated by transmitted S-wave and interface wave in the near-field area, and transmitted P-wave is not obvious here, while seismic waves were dominated by normal mode and interface wave in the far-field area, and when the sound source is moved away from the seafloor, the amplitude of normal mode wave becomes larger, but the amplitude of interface wave becomes smaller.

Zonal Wave Number Diagnosis of Rossby Wave‐Like Oscillations Using Paired Ground‐Based Radars

AbstractFree traveling Rossby wave normal modes (RNMs) are often investigated through large‐scale space‐time spectral analyses, which therefore is subject to observational availability, especially in the mesosphere. Ground‐based mesospheric observations were broadly used to identify RNMs mostly according to the periods of RNMs without resolving their horizontal scales. The current study diagnoses zonal wave numbers of RNM‐like oscillations occurring in mesospheric winds observed by two meteor radars at about 79°N. We explore four winters comprising the major stratospheric sudden warming events (SSWs) 2009, 2010, and 2013. Diagnosed are predominant oscillations at the periods of 10 and 16 days lasting mostly for three to five whole cycles. All dominant oscillations are associated with westward zonal wave number m=1, excepting one 16‐day oscillation associated with m=2. We discuss the m=1 oscillations as transient RNMs and the m=2 oscillation as a secondary wave of nonlinear interaction between an RNM and a stationary Rossby wave. All the oscillations occur around onsets of the three SSWs, suggesting associations between RNMs and SSWs. For comparison, we also explore the wind collected by a similar network at 54°N during 2012–2016. Explored is a manifestation of 5‐day wave, namely, an oscillation at 5–7 days with m=1), around the onset of SSW 2013, supporting the associations between RNMs and SSWs.

Anderson localization of flexural waves in disordered elastic beams

We study, both experimentally and numerically, the Anderson localization phenomenon in flexural waves of a disordered elastic beam, which consists of a beam with randomly spaced notches. We found that the effect of the disorder on the system is stronger above a crossover frequency fc than below it. For a chosen value of disorder, we show that above fc the normal-mode wave functions are localized as occurs in disordered solids, while below fc the wave functions are partially and fully extended, but their dependence on the frequency is not governed by a monotonous relationship, as occurs in other classical and quantum systems. These findings were corroborated with the calculation of the participation ratio, the localization length and a level statistics. In particular, the nearest spacing distribution is obtained and analyzed with a suitable phenomenological expression, related to the level repulsion.

Vibrational spectroscopy of the double complex salt Pd(NH3)4(ReO4)2, a bimetallic catalyst precursor

Tetraamminepalladium(II) perrhenate, a double complex salt, has significant utility in PdRe catalyst preparation; however, the vibrational spectra of this readily prepared compound have not been described in the literature. Herein, we present the infrared (IR) and Raman spectra of tetraamminepalladium(II) perrhenate and several related compounds. The experimental spectra are complemented by an analysis of normal vibrational modes that compares the experimentally obtained spectra with spectra calculated using DFT (DMol3). The spectra are dominated by features due to the ammine groups and the ReO stretch in Td ReO4−; lattice vibrations due to the D4h Pd(NH3)42+ are also observed in the Raman spectrum. Generally, we observe good agreement between ab initio calculations and experimental spectra. The calculated IR spectrum closely matches experimental results for peak positions and their relative intensities. The methods for calculating resonance Raman intensities are implemented using the time correlator formalism using two methods to obtain the excited state displacements and electron-vibration coupling constants, which are the needed inputs in addition to the normal mode wave numbers. Calculated excited state energy surfaces of Raman-active modes correctly predict relative intensities of the peaks and Franck-Condon activity; however, the position of Raman bands are predicted at lower frequencies than observed. Factor group splitting of Raman peaks observed in spectra of pure compounds is not predicted by DFT.

In-plane vibrations of a rectangular plate: Plane wave expansion modelling and experiment

Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The theoretical calculations were obtained using the plane wave expansion method applied to the in-plane thin plate vibration theory. The agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from DC to 20kHz. Some measured normal-mode wave amplitudes were compared with the theoretical predictions; very good agreement was observed. The excellent agreement of the classical theory of in-plane vibrations confirms its reliability up to very high frequencies

Anisotropy of Earth's inner core intrinsic attenuation from seismic normal mode models

The Earth's inner core, the slowly growing sphere of solid iron alloy at the centre of our planet, is known to exhibit seismic anisotropy. Both normal mode and body wave studies have established that, when the global average is taken, compressional waves propagate faster in the North–South direction than in the equatorial plane. Recent body wave studies also indicate that this fast direction may be more attenuating, and interpret this anisotropic attenuation in terms of anisotropic scattering due to inner core texturing. Here we use the Earth's normal modes to study the attenuation anisotropy of both compressional and shear waves in the inner core. As normal modes have wavelengths several orders of magnitude longer than estimates of inner core grain size, any attenuation anisotropy quantified using normal modes must reflect the anisotropy of intrinsic (viscoelastic) attenuation of the crystalline inner core alloy. By inverting zonal anelastic and elastic normal mode splitting function coefficients of twenty inner core sensitive modes, we construct models of inner core intrinsic attenuation and velocity anisotropy. We find that, for compressional waves, the North–South direction is both fast and more strongly attenuating. The existence of intrinsic inner core attenuation anisotropy can be interpreted in terms of anisotropic Zener relaxation in the metallic alloy comprising the inner core. Such anisotropic Zener relaxation has only been observed in the presence of solute atoms, and is thus entirely consistent with the presence of a few atomic per cent of light elements in the Earth's inner core.

Numerical Calculation of Seafloor Synthetic Seismograms Caused by Low Frequency Point Sound Source

Abstract Elastic wave on seafloor caused by low frequency noise radiated from ship is called ship seismic wave which can be used to identify ship target. In order to analyze the wave components and the propagating properties of ship seismic wave, the numerical calculation of synthetic seismograms on seafloor aroused by a low frequency point sound source is carried out using a wave number integration technique combined with inverse Fourier transform. According to the numerical example of hard seafloor, the time series of seismic wave on seafloor are mostly composed of interface waves and normal mode waves. Each normal mode wave has a well-defined low cut-off frequency, while the interface wave doesn't have. The frequency dispersion of normal mode wave is obvious when frequency is lower than 100 Hz, while the interface wave is dispersive only in the infra-sound frequency range. The time series of seismic wave is dominated by the interface wave when the source frequency is less than the minimal cut-off frequency of normal mode wave.

Anderson localization in finite disordered vibrating rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length, measured using these wave amplitudes, decreases as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. From the spectrum, the nearest-neighbor spacing distribution can be obtained. This distribution can be described by a phenomenological expression that depends on a parameter α, related to the level repulsion, which is also a function of the frequency. Therefore, the localization length can be expressed in terms of the parameter α. There exists a range in which the localization length grows linearly with α. However, at low values of this parameter the linear dependence does not hold.

Interpretation of vector electric field measurements of bursty Langmuir waves in the cusp

An analysis of auroral Langmuir waves in the cusp observed by two high‐frequency electric field instruments on the TRICE high‐flyer sounding rocket shows many examples of Langmuir wave bursts modulated at approximately 10 kHz. Previous studies have explained these and similar observations as the result of beating between waves with very close frequencies near the Langmuir cutoff, resulting from either wave‐wave interactions or independent linear excitations. The unique three‐dimensional (3‐D) data set provided by the NASA Goddard Space Flight Center TAEFWD instrument shows that up to 25% of waveforms selected from the most intense bursts exhibit anisotropic modulations, i.e., the beat nulls and peaks are not aligned in time across the three perpendicular electric field components. Modulations of this type arise when superposed wave normal modes possess differing polarizations, and simulations using wave modes calculated with the J‐WHAMP numerical dispersion code show (1) that waves with differing polarizations can exist in conditions like those observed by TRICE‐High and (2) that superpositions of such waves can produce anisotropic modulation. Fourier analysis of the 3‐D waveform data suggests that both linear and elliptically polarized waves are present near the Langmuir cutoff at these times. These observations illustrate how 3‐D measurements can give valuable insight into the nature of wave interactions in the auroral plasma environment.

VSCF in internal coordinates and the calculation of anharmonic torsional mode transitions

The vibrational self-consistent field (VSCF) method assumes separability in normal modes in its usual version. However, the method fails in cases such as soft torsional modes which are better treated by angular variables. We develop VSCF equations based on the assumption of wave function separability in internal coordinates. To test the method, simple illustrative applications to small systems are provided: trans-HONO, cis-HONO, H 2S 2 , and H 2O 2 . The code directly uses points from ab initio calculations, and the method proves to be accurate for all types of transitions. For typical torsional transitions, the error in the computed frequency is smaller than that of VSCF in normal coordinates. The wave functions for the torsional mode are compared with the corresponding normal mode wave functions. The differences are substantial. The results are encouraging for extension of the model for large polyatomic systems. Work along these lines is in progress.

Measurement and implications of frequency dependence of attenuation

Constraining the frequency dependence of intrinsic seismic attenuation in the Earth is crucial for: 1. correcting for velocity dispersion due to attenuation; 2. constructing attenuation and velocity models of the interior using datasets with different frequency contents; and, 3. interpreting lateral variations of velocity and attenuation in terms of temperature and composition. Frequency dependence of attenuation q can be represented by a power law q ∝ q 0 ω – α . Despite its importance, efforts at determining α from surface wave and free oscillation data have been thwarted by the strong tradeoffs between the depth- and frequency dependence of attenuation. We develop and validate a new method that eliminates this tradeoff, allowing a direct estimation of effective frequency dependence of attenuation without having to construct a new depth-dependent model of attenuation. Using normal mode and surface wave attenuation measurements between 80 and 3000 s, we find that α varies with frequency within the absorption band. It is 0.3 at periods shorter than 200 s, it decreases to 0.1 between 300 and 800 s, and becomes negative at periods longer than 1000 s.

Inferring Propagation Direction of Nonlinear Internal Waves in a Vertically Sheared Background Flow

Abstract Internal waves heave the background flow through which they propagate. If the background flow is vertically sheared, the high-pass-filtered velocity field will thus contain signals of both the wave velocity and the heaved flow. Under conditions of large wave amplitude and large background shear—a common situation for nonlinear internal waves in coastal waters—the velocity fluctuations caused by wave heaving of the background flow can be comparable to the wave velocity itself. This complicates the inference of wave properties such as energy flux and propagation direction. The present study deals with methods to infer propagation direction in such situations. Attention is given to three methods that may be applied to acoustic Doppler current profiler measurements: a “filtering” method that estimates wave signals from high-pass-filtered time series, a “beamwise” method that infers wave direction from lagged correlations of echo intensity between the spatially separated acoustic beams of the profiler, and a “modal” method that separates background and wave signals by regressing the high-pass-filtered velocity field onto a normal-mode wave model. The methods are tested using synthetic datasets. The results suggest that the filtering method is biased by wave heaving of the background shear, while the beamwise and modal methods are resistant to heaving. The beamwise method provides accurate predictions of wave propagation angle for cases in which the measurements have high temporal resolution and the environment exhibits no depth-averaged background flow. The limitation on depth-averaged flow is relaxed for the modal method, but it requires the measurement of stratification. These issues are illustrated, and the applicability of these methods is explored with a series of sensitivity tests, and it is found that the different methods perform well under different circumstances.

Vibrational spectra and structure of isopropylbenzene

Infrared spectra (4000–400 cm −1) and Raman spectra (1700–40 cm −1) of the liquid and two crystalline solids of isopropylbenzene (cumene) and isopropylbenzene-d 12 have been recorded. The spectra indicate that in the liquid and crystalline solids isopropylbenzene exists in planar conformation only (C H bond is in the plane of the benzene ring). An assignment of the observed band wave numbers both isopropylbenzene and isopropylbenzene-d 12 is discussed by comparison with normal mode wave numbers and IR intensities calculated from ab initio 6-31G (d) force fields.

Radial anisotropy in seismic reference models of the mantle

Sambridge's Neighborhood Algorithm was applied to normal mode and surface wave phase velocity data to determine the likelihood of radial anisotropy in mantle reference models. This full model space search technique provides probability density functions for each model parameter and therefore reliable estimates of resolution and uncertainty, without having to introduce unnecessary regularization on the model space. Our results for shear wave anisotropy (described by parameter ξ) show a fast decrease with depth with no significant deviation from Preliminary Reference Earth Model (PREM) at any depth. The data do not require strong deviations from PREM for P wave anisotropy either, except between 220 and 400 km depth and in the D″ layer. The intermediate parameter η might depart from PREM between 220 and 670 km depth. This implies a likely deeper P wave anisotropy and η anisotropy than S wave anisotropy. The sign change in the anisotropic parameters across the 670‐km discontinuity found by other authors is not warranted by our data set, which is far more extensive than in previous studies. We found that density needs to be well resolved because we observe a high dependence of the results for P wave‐related parameters on the presence or absence of density in the parameterization. S wave anisotropy and η are less affected by density. A well‐resolved negative density anomaly was found in the uppermost mantle, and a density excess was observed in the transition zone and the lowermost mantle which might be a seismic signature of the recently identified postperovskite phase.

Dynamical Processes of Equatorial Atmospheric Angular Momentum

Abstract The dynamical processes that drive intraseasonal equatorial atmospheric angular momentum (EAAM) fluctuations are examined with the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data. The primary methodology involves the regression of relevant variables including the equatorial bulge, mountain, and friction torques, surface pressure, streamfunction, and outgoing longwave radiation, against the time derivative of the two components and the amplitude of the EAAM vector. The results indicate that the observed 10-day westward rotation of the EAAM vector corresponds to the propagation of a zonal wavenumber-1, antisymmetric, Rossby wave normal mode. Additional findings suggest that fluctuations in the amplitude of the EAAM vector are driven by poleward-propagating Rossby waves excited by the latent heating within equatorial mixed Rossby–gravity waves and also by wave–wave interaction among planetary waves. Both of these processes can induce surface pressure anomalies that amplify the EAAM vector via the equatorial bulge torque. The Antarctic and Greenland mountain torques were found to drive large fluctuations in the amplitude of the EAAM vector. Both the friction torque and wave–zonal-mean flow interaction were shown to dampen the EAAM amplitude fluctuations. A comparison of the EAAM dynamics in the atmosphere with that in an aquaplanet GCM suggests that the mountain torque also drives fluctuations in the phase speed of the atmospheric wave field associated with the EAAM vector, and it confines the wave–wave interaction to planetary scales.