Phase Speed Of Waves Research Articles

Dispersion of Slow Magnetoacoustic Waves in the Active Region Fan Loops Introduced by Thermal Misbalance

Slow magnetoacoustic waves observed in the solar corona are used as seismological probes of plasma parameters. It has been shown that the dispersion properties of such waves can vary significantly under the influence of the wave-induced thermal misbalance. In the current research, we study the effect of misbalance on waves inside the magnetic-flux tube under the second-order thin-flux-tube approximation. Using the parameters of active-region-fan coronal loops, we calculated wave properties such as the phase speed and decrement. It is shown that neglecting thermal misbalance may be the reason for the substantial divergence between seismological and spectrometric estimations of plasma parameters. We also show that the frequency dependence of the phase speed is affected by two features, namely the geometric dispersion and the dispersion caused by the thermal misbalance. In contrast to the phase speed, the wave decrement primarily is affected by the thermal misbalance only. The dependencies of the phase speed and decrement of the slow wave on the magnetic field and tube cross-section are also analysed.

The separation of ions and fluxes in nonlinear ion-acoustic waves

The multispecies plasma of natural or laboratory origin is often considered to host nonlinear ion-acoustic waves. We present calculations of ion fluxes induced by nonlinear ion-acoustic waves in a plasma consisting of multiple ion populations, electrons, and dust. The following plasma models are considered: an electron-ion plasma with cold ions, a bi-ion plasma with two types of warm positively charged ions, and a dusty bi-ion plasma. It is found that in the electron-ion plasma, the wave-induced ion flux is directed oppositely to the phase speed of the nonlinear ion-acoustic wave. In the bi-ion plasma, there are two modes of ion-acoustic waves which are fast and slow waves. In the nonlinear fast ion-acoustic wave, the fluxes of both types of ions are found to be codirected and drift against the wave. In a slow wave, the nonlinear fluxes of ions are directed in opposite directions. This result demonstrates the possibility to use these nonlinear wave-induced ion fluxes for effective separation of ions in the plasma. In a dusty bi-ion plasma, the ion separation process can be intensified by a supernonlinear regime of slow ion-acoustic waves.

Total Surface Current Vector and Shear From a Sequence of Satellite Images: Effect of Waves in Opposite Directions

AbstractThe total surface current velocity (TSCV)—the horizontal vector quantity that advects seawater—is an essential climate variable, with few observations available today. The TSCV can be derived from the phase speed of surface gravity waves, and the estimates of the phase speeds of different wavelengths could give a measure of the vertical shear. Here, we combine 10‐m resolution Level‐1C of the Sentinel‐2 Multispectral Instrument, acquired with time lags up to 1 s, and numerical simulation of these images. Retrieving the near‐surface shear requires a specific attention to waves in opposing directions when estimating a single‐phase speed from the phase difference in an image pair. Opposing waves lead to errors in phase speeds that are most frequent for shorter wavelengths. We propose an alternative method using a least squares fit of the current speed and amplitudes of waves in opposing directions to the observed complex amplitudes of a sequence of three images. When applied to Sentinel‐2, this method generally provides more noisy estimate of the current. A byproduct of this analysis is the “opposition spectrum” which is a key quantity in the sources of microseisms and microbaroms. For future possible sensors, the retrieval of TSCV and shear can benefit from increased time lags, resolution, and exposure time of acquisition. These findings should allow new investigations of near‐surface ocean processes including regions of freshwater influence or internal waves, using existing satellite missions such as Sentinel‐2, and provide a basis for the design of future optical instruments.

Planetary, inertia-gravity and Kelvin waves on the f-plane and -plane in the presence of a uniform zonal flow.

A linear wave theory of the Rotating Shallow‐Water Equations (RSWE) is developed in a channel on the midlatitude f‐plane or β‐plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. Here we show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f‐plane similar to the generation of these waves by PV sources such as the β‐effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting Rossby, Poincaré and “Kelvin‐like” waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean‐flow” phase speeds does not account for the difference in phase speeds, and the meridional structure is often trapped near one of the channel's boundaries and does not oscillate across the channel. A comparison between the phase speeds of Rossby waves of the present theory and those of the Quasi‐Geostrophic Shallow‐Water (QG‐SW) theory shows that the former can be 2.5 times faster than those of the QG‐SW theory. The phase speed of “Kelvin‐like” waves is modified by the presence of a mean flow compared to the classical gravity wave speed, and furthermore their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wave number, and the convexity of the dispersion curves also changes with the zonal wave number. These results have implications for the propagation of Rossby wave packets: QG theory overestimates the zonal group velocity.

Absorption of High-frequency Oscillations and Its Relation to Emissivity Reduction

Abstract Sunspots are known to be strong absorbers of solar oscillation modal power. The most convincing way to demonstrate this is done via Fourier–Hankel decomposition (FHD), where the local oscillation field is separated into in- and outgoing waves, showing the reduction in power. Due to the Helioseismic and Magnetic Imager’s high-cadence Doppler measurements, power absorption can be investigated at frequencies beyond the acoustic cutoff frequency. We perform an FHD on five sunspot regions and two quiet-Sun control regions and study the resulting absorption spectra α ℓ (ν), specifically at frequencies ν > 5.3 mHz. We observe an unreported high-frequency absorption feature, which only appears in the presence of a sunspot. This feature is confined to phase speeds of one-skip waves whose origins coincide with the sunspot’s center, with v ph = 85.7 km s−1 in this case. By employing a fit to the absorption spectra at a constant phase speed, we find that the peak absorption strength lies between 0.166 and 0.222 at a noise level of about 0.009 (5%). The well-known absorption along ridges at lower frequencies can reach up to . Thus our finding in the absorption spectrum is weaker, but nevertheless significant. From first considerations regarding the energy budget of high-frequency waves, this observation can likely be explained by the reduction of emissivity within the sunspot. We derive a simple relation between emissivity and absorption. We conclude that sunspots yield a wave power absorption signature (for certain phase speeds only), which may help in understanding the effect of strong magnetic fields on convection and source excitation and potentially in understanding the general sunspot subsurface structure.

Amphibious Shear Wave Structure Beneath the Alaska‐Aleutian Subduction Zone From Ambient Noise Tomography

AbstractI present a 3‐D isotropic shear wave velocity model of the crust and uppermost mantle beneath the Alaska‐Aleutian subduction zone offshore of the Alaska Peninsula, based on seismic data recorded by the Alaska Amphibious Community Seismic Experiment (AACSE) array and some other networks. The model derives from Rayleigh wave phase speed measurements extracted from ambient seismic noise. A new three‐station interferometry (Zhang et al., 2020) approach is applied to improve the data coverage of ambient noise surface waves. Based on the ambient noise Rayleigh wave dispersion data, a Bayesian Monte Carlo inversion is performed to produce the shear wave velocity model. There are several prominent structures captured by the model, including: (1) The major sedimentary basins across the study region are identified by model. (2) Crustal thickness estimates are related with the geological structures. (3) The imaged slab edge is consistent with both the Slab 2.0 model (Hayes et al., 2018) and earthquake locations. And lots of geological and tectonic features related to subduction zone are captured, including the serpentinized forearc and partial melting zone beneath the Aleutian arc volcanoes. (4) Near the Shumagin gap, reduction in Vs is observed at the uppermost part of the incoming Pacific plate, consistent with the active source study of Shillington et al. (2015). The Vs reduction reflects hydration of the oceanic plate which could be related to local seismicity variation.

A New Probabilistic Wave Breaking Model for Dominant Wind‐Sea Waves Based on the Gaussian Field Theory

AbstractThis study presents a novel method for obtaining the probability of wave breaking (Pb) of deep water, dominant wind‐sea waves (i.e., waves made of the energy within ±30% of the peak wave frequency) derived from Gaussian wave field theory. For a given input wave spectrum, we demonstrate how it is possible to derive a joint probability density function between wave phase speed (c) and horizontal orbital velocity at the wave crest (u) from which a model for Pb can be obtained. A nonlinear kinematic wave breaking criterion consistent with the Gaussian framework is further proposed. Our model would allow, therefore, the application of the classical wave breaking criterion (i.e., wave breaking occurs if u/c > 1) in spectral wave models which, to the authors' knowledge, has not been done to date. Our results show that the proposed theoretical model has errors in the same order of magnitude as six other historical models when assessed using three field data sets. With optimization of the proposed model's single free parameter, it can become the best performing model for specific data sets. Although our results are promising, additional, more complete wave breaking data sets collected in the field are needed to comprehensively assess the present model, especially in regards to the dependence on phenomena such as direct wind forcing, long wave modulation, and wave directionality.

High‐Resolution Crustal and Uppermost Mantle Structure Beneath Central Mongolia From Rayleigh Waves and Receiver Functions

AbstractIn this study, I present a high‐resolution 3‐D Vs model of the crust and uppermost mantle beneath central Mongolia, based on seismic data recorded at the Central Mongolia Seismic Experiment array and some other networks. The model is constructed by a Bayesian Monte Carlo inversion that jointly interprets Rayleigh wave phase speeds and receiver functions. The Rayleigh wave dispersion measurements are derived from both ambient noise and teleseismic earthquake data. To improve ambient noise data coverage, a recently developed three‐station interferometry (Zhang et al., 2020, https://doi.org/10.1093/gji/ggaa046) technique is applied to produce high‐quality three‐station interferograms that augment the ambient noise data base. There are several prominent geological and tectonic features captured by the model, including (1) the Khövsgöl rift system is imaged as a high‐speed anomaly in the upper crust, whose southern edge follows the Bulnay fault. (2) The estimated crustal thickness map identifies relatively thick crust beneath the Khövsgöl rift system, the Hangay Dome, and the Gobi‐Altai Mountains. (3) A crustal high‐velocity anomaly is imaged beneath the Taryatu‐Chulutu volcanic field, which is interpreted as a solidified intrusive magma body. (4) Dispersed low‐velocity anomalies in the mantle identify locations with possible partial melting. The melting zones could be related to small‐scale asthenospheric upwelling and convective removal of lithosphere, which produces uplift of the Hangay Dome.

Using Array‐Derived Rotational Motion to Obtain Local Wave Propagation Properties From Earthquakes Induced by the 2018 Geothermal Stimulation in Finland

AbstractWe estimate vertical rotation rates for 204 earthquakes that were induced by the 2018 stimulation of the Espoo/Helsinki geothermal reservoir from wavefield gradients across geophone arrays. The array‐derived rotation rates from seismograms recorded at 6–9 km hypocentral distances vary between 10−9 and 10−7 rad s−1, indicating a comparable sensitivity to portable rotational instruments. Using co‐located observations of translational and rotational motion, we estimate the local propagation direction and the apparent phase speed of SH waves, and compare these estimates with those obtained by S wave beamforming. Propagation directions generally align with the earthquake back azimuths, but both techniques show deviations indicative of heterogeneous seismic structure. The rotational method facilitates a station‐by‐station approach that resolves site specific variations that are controlled by the local geology. We measure apparent S wave speeds larger than 5 km s−1, consistent with steep incidence angles and high propagation velocities in the Fennoscandian Shield.

On the peristaltic pumping

Peristaltic pumping in a two-dimensional conduit using vibrations in the form of traveling waves has been investigated. Two qualitatively different responses producing vastly different flow rates have been identified, with a transition occurring at wavelengths of the order of the conduit opening. The flow rate is always proportional to the wave phase speed and the second power of the amplitude. Long waves produce sloshing which extends across the whole conduit producing a small, nearly wave-number-independent flow rate. The use of such in-phase waves on both walls nearly eliminates this flow while the use of out-of-phase waves maximizes it. Short waves affect the near-wall regions, which appear to the bulk of the fluid as moving walls. Such waves produce an order of magnitude larger flow rate, with its magnitude increasing proportionally to the second power of the wavenumber. Each vibrating wall produces its own wall boundary layer with an unmodulated core flow in the central zone of the conduit. The core flow looks like a Couette flow and reduces to a plug flow when both waves have identical amplitudes. The phase difference between such waves does not affect the flow rate. Wave tilting increases the flow rate similarly to the increase in distance between these waves. The use of waves characterized by a combination of wavenumbers increases the flow rate but only when the commensurability index is greater than one. The best performance is achieved by concentrating all wave energy in a single and largest achievable wavenumber.

Near real-time calculation of submarine fault properties using an inverse model of acoustic signals

A submarine earthquake that generates a tsunami sends a family of acoustic signals that carry information on the fault dynamics and geometry. These signals travel at the speed of sound in water, much greater than the phase speed of the gravity waves, and thus can act as early warning of tsunamis. To utilise this property in real-time, a semi-analytical inverse approach is employed assuming the fault is slender and the water depth is constant, allowing the calculation of some fault parameters analytically. However, the remaining parameters require a numerical evaluation, which increases the calculation time substantially. In order to overcome this difficulty, a probabilistic inverse model is proposed. The model analyses data at the envelope of a pressure signal, which reduces numerical complexities. More specifically, it selects multiple measurement points, in order to produce several sets of solutions within given ranges of the properties. The model is applied to real hydrophone recordings, where the fault geometry and dynamics are estimated near real-time on a standard PC. Some aspects of the model are general and can be used to estimate simplified geometry and dynamics of various signal sources from violent events in the ocean, such as impacting meteorites, submarine explosions, landslides and rogue waves.

High-phase-speed Dyakonov surface waves

The canonical boundary-value problem for Dyakonov-surface-wave propagation in a fixed direction guided by the planar interface of a uniaxial dielectric material and an isotropic nondissipative dielectric material was solved. Both partnering materials were taken to be homogeneous and the constitutive parameters for both to lie within the ranges of available materials. Solutions were found for which the phase speed of the Dyakonov surface wave is greater than the phase speed of a plane wave in the bulk isotropic partnering material.

A Stochastic Parameterization of Organized Tropical Convection Using Cellular Automata for Global Forecasts in NOAA's Unified Forecast System

AbstractIn the atmosphere, convection can organize from smaller scale updrafts into more coherent structures on various scales. In bulk‐plume cumulus convection parameterizations, this type of organization has to be represented in terms of how the resolved flow would “feel” convection if more coherent structures were present on the subgrid. This type of subgrid organization acts as building blocks for larger scale tropical convective organization known to modulate local and remote weather. In this work a parameterization for subgrid (and cross‐grid) organization in a bulk‐plume convection scheme is proposed using the stochastic, self‐organizing, properties of cellular automata (CA). We investigate the effects of using a CA which can interact with three different components of the bulk‐plume scheme that modulate convective activity: entrainment, triggering, and closure. The impacts of the revised schemes are studied in terms of the model's ability to organize convectively coupled equatorial waves (CCEWs). The differing impacts of adopting the stochastic CA scheme, as compared to the widely used Stochastically Perturbed Physics Tendency (SPPT) scheme, are also assessed. Results show that with the CA scheme, precipitation is more spatially and temporally organized, and there is a systematic shift in equatorial wave phase speed not seen with SPPT. Previous studies have noted a linear relationship between Gross Moist Stability (GMS) and Kelvin wave phase speed. Analysis of GMS in this study shows an increase in Kelvin wave phase speed and an increase in GMS with the CA scheme, which is tied to a shift from large‐scale precipitation to convective precipitation.

Phase Shift of Planetary Waves and Wave–Jet Resonance on Tidally Locked Planets

Abstract Recent studies found that atmospheric superrotation (i.e., west-to-east winds over the equator) on tidally locked planets can modify the phase of planetary waves. But a clear relationship between the superrotation and the magnitude of the phase shift was not examined. In this study, we re-investigate this problem using a 2D linear shallow-water model with a specified uniform zonal flow. We find that the degree of the phase shift is a monotonic but nonlinear function of the strength of the mean flow and the phase shift has two limits of -π and +π. The existence of these limits can be explained using the energy balance of the whole system. We further show that a resonance between the Rossby wave and the mean flow occurs when the speed of an eastward jet approaches to the westward phase speed of the Rossby wave, or a resonance between the Kelvin wave and the mean flow happens when the speed of a westward jet approaches to the eastward phase speed of the Kelvin wave. The resonance mechanism is the same as that found in the previous studies on Earth and hot Jupiters. Moreover, in the spin-up period of a 3D global atmospheric general circulation simulation for tidally locked rocky planet, we also find these two phenomena: phase shift and wave–jet resonance. This study improves the understanding of wave–mean-flow interactions on tidally locked planets.

Shear surface wave propagation in stratified media with slip interfaces

The surface shear wave propagation is studied in elastic semi-spaces separated by elastic layer with an imperfectly bonded interface between layer and semi-spaces. The dispersion equations are obtained analytically describing the surface wave phase speed. Based on the dispersion equation analysis it is shown that the interface imperfectness sufficiently decreases the phase speed and can increase the number of shear wave modes too.

Using Desmos to Understand the Difference Between Phase and Group Velocity

An individual harmonic wave (i.e., having a single frequency and wavelength over all time and space) traveling in a loss-free medium has a single constant speed, which is equal to the magnitude of the phase velocity of the wave. However, when a set of different harmonic waves are traveling in the same direction, they interfere to form wave packets. In general, the peak of a wave packet travels at a speed equal to the magnitude of the group velocity that can be vastly different than the phase speeds of the component harmonic waves, even if the entire set of harmonic waves only differ among themselves slightly in frequency and wavelength. It is difficult for students to understand the origin of this difference from verbal descriptions and static graphs of wave functions at successive instants in times, such as are typically presented in textbooks. However, considerable insight is possible using the free online software Desmos.

Nonplanar ion-acoustic subsonic shock waves in dissipative electron-ion-pcd plasmas

The dissipative electron-ion-pcd (positively charged dust) plasma, which is observed in both space and laboratory plasmas, is considered. The basic features of nonplanar cylindrical and spherical ion-acoustic subsonic shock waves in such a medium are investigated by deriving a modified Burgers equation using the reductive perturbation method. It is found that the stationary pcd species reduces the phase speed of the ion-acoustic waves and, consequently, supports the subsonic shock waves due to the kinematic viscosity (acting as a source of dissipation) of the ion species. It is observed that the cylindrical and spherical subsonic shock waves evolve with time very significantly and that the time evolution of the spherical shock structures is faster than that of the cylindrical ones. The implications of the results of this work to space and laboratory plasmas are discussed.

Azimuthal Anisotropy of the Crust and Uppermost Mantle Beneath Alaska

AbstractThis study presents an azimuthally anisotropic shear wave velocity model of the crust and uppermost mantle beneath Alaska, based on Rayleigh wave phase speed observations from 10 to 80 s period recorded at more than 500 broadband stations. We test the hypothesis that a model composed of two homogeneous layers of anisotropy can explain these measurements. This “Two‐Layer Model” confines azimuthal anisotropy to the brittle upper crust along with the uppermost mantle from the Moho to 200 km depth. This model passes the hypothesis test for most of the region of study, from which we draw two conclusions. (a) The data are consistent with crustal azimuthal anisotropy being dominantly controlled by deformationally aligned cracks and fractures in the upper crust undergoing brittle deformation. (b) The data are also consistent with the uppermost mantle beneath Alaska and surroundings experiencing vertically coherent deformation. The model resolves several prominent features. (1) In the upper crust, fast directions are principally aligned with the orientation of major faults. (2) In the upper mantle, fast directions are aligned with the compressional direction in compressional tectonic domains and with the tensional direction in tensional domains. (3) The mantle fast directions located near the Alaska‐Aleutian subduction zone and the surrounding back‐arc area form a toroidal pattern that is consistent with mantle flow directions predicted by recent geodynamical models. Finally, the mantle anisotropy is remarkably consistent with SKS fast directions, but to fit SKS split times, anisotropy must extend below 200 km depth across most of the study region.

Generation of highly nonlinear irregular waves in a wave flume experiment: Spurious harmonics and their effect on the wave spectrum

Spurious harmonics generation can occur in wave basins when strongly nonlinear waves are generated with linear wave maker theory. For regular long crested waves, the phenomena is known to cause a beating pattern for the amplitude of the higher harmonics, while for irregular waves the effect is often thought to average out. We here report on recent experimental results for spurious harmonic generation for highly nonlinear irregular waves. Long crested waves at two depths are considered. We find a systematic distortion of the spectral shape which is non-uniform in space. The effect occurs in the linear and super harmonic region of the spectrum and is strongest at the smaller depth. We analyze the phenomenon through re-computations in a fully nonlinear wave model and the further application of a four-phase harmonic separation. We next extend the analysis to allow separation of the third- and first-order content of the first-harmonic wave field, by computation at two different amplitudes. The numerical results resembles the measured spectrum closely and the harmonic separation shows that the spectral distortion in the super-harmonic region is to large extent a property of the second-harmonic wave field. Further, the match between the first-harmonic spectrum and the original target spectrum is shown to improve strongly by the removal of the extracted third-order contribution. The observed spectral distortion in the linear frequency region can thus be explained by this third-order field.Returning to the second-order wave field, we demonstrate that the extracted second-order wave field with associated spectral distortion can be reproduced by application of the Sharma and Dean theory with inclusion of the reconstructed spurious wave field from the linear wave generation. Finally, the effect of the spurious second-order harmonic generation on the measured forces is discussed and quantified. We find that the force peak exceedance probability is less influenced by the spurious waves than the spectral shape. We link this to the smaller phase speed of the spurious waves, that makes them arrive later than the main wave packet and thus leads to a limited enhancement of the local peaks.

On the Linkage Between Rossby Wave Phase Speed, Atmospheric Blocking, and Arctic Amplification

AbstractIt has been hypothesized that enhanced Arctic warming with respect to midlatitudes, known as Arctic amplification, had led to a deceleration of eastward propagating Rossby waves, more frequent atmospheric blocking, and extreme weather in recent decades. We employ a novel, daily climatology of Rossby wave phase speed between March 1979 and November 2018, based on upper‐level wind data, to test this hypothesis and describe phase speed variability. The diagnostic distinguishes between periods of enhanced or reduced eastward wave propagation and is related to the occurrence of blocking and extreme temperatures over midlatitudes. While remaining tied to the upper‐level geopotential gradient, decadal trends in phase speed did not accompany the observed reduction in the low‐level temperature gradient. These results confirm the link between low phase speeds and extreme temperature events, but indicate that Arctic amplification did not play a decisive role in modulating phase speed variability in recent decades.