Observed Wave Amplitudes Research Articles

Nonlinear Damping and Field-aligned Flows of Propagating Shear Alfvén Waves with Braginskii Viscosity

Braginskii magnetohydrodynamics (MHD) provides a more accurate description of many plasma environments than classical MHD since it actively treats the stress tensor using a closure derived from physical principles. Stress tensor effects nonetheless remain relatively unexplored for solar MHD phenomena, especially in nonlinear regimes. This paper analytically examines nonlinear damping and longitudinal flows of propagating shear Alfvén waves. Most previous studies of MHD waves in Braginskii MHD have considered the strict linear limit of vanishing wave perturbations. We show that those former linear results only apply to Alfvén wave amplitudes in the corona that are so small as to be of little interest, typically a wave energy less than 10−11 times the energy of the background magnetic field. For observed wave amplitudes, the Braginskii viscous dissipation of coronal Alfvén waves is nonlinear and a factor around 109 stronger than predicted by the linear theory. Furthermore, the dominant damping occurs through the parallel viscosity coefficient η 0, rather than the perpendicular viscosity coefficient η 2 in the linearized solution. This paper develops the nonlinear theory, showing that the wave energy density decays with an envelope . The damping length L d exhibits an optimal damping solution, beyond which greater viscosity leads to lower dissipation as the viscous forces self-organize the longitudinal flow to suppress damping. Although the nonlinear damping greatly exceeds the linear damping, it remains negligible for many coronal applications.

Diffusive scattering of energetic electrons by intense whistler-mode waves in an inhomogeneous plasma

Electron resonant interactions with electromagnetic whistler-mode waves play an important role in electron flux dynamics in various space plasma systems: planetary radiation belts, bow shocks, solar wind and magnetic reconnection regions. Two key wave characteristics determining the regime of wave–particle interactions are the wave intensity and the wave coherency. The classical quasi-linear diffusion approach describes well electron diffusion by incoherent and low-amplitude waves, whereas the nonlinear resonant models describe electron phase bunching and trapping by highly coherent intense waves. This study is devoted to the investigation of the regime of electron resonant interactions with incoherent but intense waves. Although this regime is characterized by electron diffusion, we show that diffusion rates scale linearly with the wave amplitude,$D\propto B_w$, in contrast to the quasi-linear diffusion scaling$D_{QL}\propto B_w^2$. Using observed wave amplitude distributions, we demonstrate that the quasi-linear diffusion model significantly overestimates electron scattering by incoherent, but intense whistler-mode waves. We discuss the results obtained in the context of simulations of long-term electron flux dynamics in space plasma systems.

Multipoint Analysis of Source Regions of EMIC Waves and Rapid Growth of Subpackets

AbstractElectromagnetic Ion Cyclotron (EMIC) rising tone emissions are important in understanding the nonlinear wave evolution and interaction with the energetic particles. We present observations of rising tone emissions of EMIC waves by THEMIS A, D, and E spacecraft in the outer magnetosphere. These emissions with subpacket structures in the proton band were observed during the time interval 14:20 UT to 14:30 UT on September 9, 2010. The observed waves are left‐handed polarized with wave normal angles less than . THEMIS A was closest to the equator and was in a higher L‐shell than THEMIS E and D. The smallest radial separation is 2,000 km between THEMIS E and D spacecraft. This configuration of THEMIS allows us to investigate the subpackets of rising tone EMIC waves observed simultaneously at 14:23 UT by three spacecraft. Hilbert Huang Transformation (HHT) is applied to show the variations of the instantaneous frequency and the observed wave amplitude. The direction of energy flow is determined from the analysis of the Poynting flux. There is a rapid nonlinear growth of the EMIC subpackets within one wavelength. Subpackets are dynamic in nature as their structure changes within one wave period, which is further supported by the nonlinear wave growth theory. Optimum and threshold amplitudes for the EMIC wave growth are calculated beside the nonlinear transition time (). Observed ion energies and pitch angle spectra of the ion fluxes are consistent with the energy associated with the Landau and cyclotron resonance conditions.

Hybrid Simulations of Positively and Negatively Charged Pickup Ions and Cyclotron Wave Generation at Europa.

In the vicinity of Europa, Galileo observed bursty Alfvén‐cyclotron wave power at the gyrofrequencies of a number of species including K+, O 2+, Na+, and Cl+, indicating the localized pickup of these species. Additional evidence for the presence of chlorine was the occurrence of both left‐hand (LH) and right‐hand (RH) polarized transverse wave power near the Cl+ gyrofrequency, thought to be due to the pickup of both Cl+ and the easily formed chlorine anion, Cl−. To test this hypothesis, we use one‐dimensional hybrid (kinetic ion, massless fluid electron) simulations for both positive and negative pickup ions and self‐consistently reproduce the growth of both LH and RH Alfvén‐cyclotron waves in agreement with linear theory. We show how the simultaneous generation of LH and RH waves can result in nongyrotropic ion distributions and increased wave amplitudes, and how even trace quantities of negative pickup ions are able to generate an observable RH signal. Through comparing simulated and observed wave amplitudes, we are able to place the first constraints on the densities of Chlorine pickup ions in localized regions at Europa.

Detections and simulations of tropospheric water vapor fluctuations due to trapped lee waves by ALOS-2/PALSAR-2 ScanSAR interferometry

Detailed wave-like spatial patterns of atmospheric propagation delay signals associated with mountain lee waves were detected in Hokkaido and Tohoku by synthetic aperture radar (SAR) interferometry (InSAR) with the ScanSAR mode observation data of a Phased Array-type L-band Synthetic Aperture Radar 2 on board the Advanced Land Observing Satellite 2. Both cases occurred under stable atmosphere conditions. The InSAR-observed peak-to-trough line of sight changes in the mountain wave signals was 4 and 5 cm with the horizontal wavelengths of 9 and 15 km in Hokkaido and Tohoku, respectively. Locations of positive phase maxima in the mountain wave signals coincides with locations of cloud streets observed by visible satellite imagery, indicating that crests of mountain waves contain relatively much water vapor compared with wave troughs. Numerical weather simulations with the horizontal grid spacing of 1 km were performed to reproduce InSAR phase variations, and as a result those simulations could reasonably reproduce observed wave amplitudes and wavelengths in both cases. On the other hand, numerical simulations tended to overestimate wave attenuation rates: simulated mountain waves decreased as the wave propagated faster than those of observed signals. Because the simulated wave attenuation rate is sensitive to physics in the planetary boundary layer (PBL), we investigated the reproducibility of five PBL schemes implemented in the WRF model. As a result, all the PBL schemes showed little attenuation except for the Yonsei University scheme (YSU), while the wavelength in the YSU was most close to the observation. Our study demonstrated the uniqueness and usefulness of InSAR for meteorological application as the ability to map the detailed water vapor distribution regardless of cloud cover. In addition, the reasonable reproducibility of the water vapor delay signal due to lee waves by the numerical weather model encourages researchers who tackle the correction of the tropospheric propagation delay, increasing the accuracy in detecting surface deformations.Graphical abstract.

In situ observations of magnetosonic waves modulated by background plasma density

AbstractWe report in situ observations by the Van Allen Probe mission that magnetosonic (MS) waves are clearly relevant to the background plasma number density. As the satellite moved across dense and tenuous plasma alternatively, MS waves occurred only in lower density region. As the observed protons with “ring” distributions provide free energy, local linear growth rates are calculated and show that magnetosonic waves can be locally excited in tenuous plasma. With variations of the background plasma density, the temporal variations of local wave growth rates calculated with the observed proton ring distributions show a remarkable agreement with those of the observed wave amplitude. Therefore, the paper provides a direct proof that background plasma densities can modulate the amplitudes of magnetosonic waves through controlling the wave growth rates.

ON THE SOURCE OF PROPAGATING SLOW MAGNETOACOUSTIC WAVES IN SUNSPOTS

Recent high-resolution observations of sunspot oscillations using simultaneously operated ground- and space-based telescopes reveal the intrinsic connection between different layers of the solar atmosphere. However, it is not clear whether these oscillations are externally driven or generated in-situ. We address this question by using observations of propagating slow magneto-acoustic waves along a coronal fan loop system. In addition to the generally observed decreases in oscillation amplitudes with distance, the observed wave amplitudes are also found to be modulated with time, with similar variations observed throughout the propagation path of the wavetrain. Employing multi-wavelength and multi-instrument data we study the amplitude variations with time as the waves propagate through different layers of the solar atmosphere. By comparing the amplitude-modulation period in different layers, we find that slow magneto-acoustic waves observed in sunspots are externally driven by photospheric p-modes, which propagate upwards into the corona before becoming dissipated.

Marshall Islands Fringing Reef and Atoll Lagoon Observations of the Tohoku Tsunami

The magnitude 9.0 Tohoku earthquake on 11 March 2011 generated a tsunami which caused significant impacts throughout the Pacific Ocean. A description of the tsunami within the lagoons and on the surrounding fringing reefs of two mid-ocean atoll islands is presented using bottom pressure observations from the Majuro and Kwajalein atolls in the Marshall Islands, supplemented by tide gauge data in the lagoons and by numerical model simulations in the deep ocean. Although the initial wave arrival was not captured by the pressure sensors, subsequent oscillations on the reef face resemble the deep ocean tsunami signal simulated by two numerical models, suggesting that the tsunami amplitudes over the atoll outer reefs are similar to that in deep water. In contrast, tsunami oscillations in the lagoon are more energetic and long lasting than observed on the reefs or modelled in the deep ocean. The tsunami energy in the Majuro lagoon exhibits persistent peaks in the 30 and 60 min period bands that suggest the excitation of closed and open basin normal modes, while energy in the Kwajalein lagoon spans a broader range of frequencies with weaker, multiple peaks than observed at Majuro, which may be associated with the tsunami behavior within the more irregular geometry of the Kwajalein lagoon. The propagation of the tsunami across the reef flats is shown to be tidally dependent, with amplitudes increasing/decreasing shoreward at high/low tide. The impact of the tsunami on the Marshall Islands was reduced due to the coincidence of peak wave amplitudes with low tide; however, the observed wave amplitudes, particularly in the atoll lagoon, would have led to inundation at different tidal phases.

Pitch angle diffusion by whistler mode waves in the jovian magnetosphere and diffuse auroral precipitation

Bounce-averaged pitch angle diffusion rates of electrons due to whistler mode waves have been calculated in the Jupiter’s magnetosphere. Variations of electron density, magnetic field, wave intensity and upper cut-off frequency along the particle bounce trajectory have been taken into account. Field line tracing is performed to obtain the loss-cone size associated with the VIP 4 magnetic field model including the external field due to azimuthal current sheet. Numerical calculations have been carried out at L shells 10, 12, 15, 18, and 20. The longitudinal variations of electron energy precipitation into the atmosphere leading to diffuse aurora have been modelled. It is found that observed wave amplitudes at L⩽15 are insufficient to put electrons on strong pitch angle diffusion whereas at L=18 and 20 electrons of energies ⩽30keV can be put on strong diffusion. At L=10 electron energy precipitation supports auroral brightness of 25kR in the northern and 36kR in the southern hemisphere at west longitude ∼10–60°. At shells L=12 and 15 auroral brightness less than 10kR is obtained. This is in accord with Voyager observation of jovian UV aurora just beyond the Io torus (7–12RJ). At L=18 maximum auroral brightness 73kR in the northern hemisphere at west longitude of 163° and 30kR in the southern hemisphere for west longitudes ⩽50° are obtained. This is in agreement with the diffuse auroral brightness measured by Hubble Space Telescope (HST). Observations of longitudinal variation of diffuse auroral brightness are, however, required to ascertain the present findings.

Modeling Propagation of 2011 Honshu Tsunami

In this study, the Honshu tsunami on 11 March 2011 was simulated using the Regional Ocean Model System (ROMS) governed by two - dimensional nonlinear shallow - water equations and driven by three earthquake deformation fields as initial condition. The purpose of this study is to assess the model’s sensitivity to the tsunami source field, especially the case in which the horizontal deformation of earthquake was taken into account. The comparison between the model results and observed tsunami waves at 14 Deep-ocean Assessment and Reporting of Tsunami (DART) buoy stations showed that the average errors of modeled maximum wave amplitude were 23.2%, 26.9% and 37.4% for the three initial deformation fields, respectively. In the best performance case, when the observed wave amplitude was below 0.3 m, the average error of the modeled maximum wave amplitude was 0.034 m and relative error was 23.7%. On the other hand, the average errors of modeled arrival times of the first tsunami - wave peak at 13 DART stations were 2.82, 2.28 and 3.48 min earlier for the three cases of different initial fields, but the error is as big as ~3 hrs at Station 46412 located near the west coast of the USA. The model did not resolve the observed wave at Station 46412, which might be caused by the model’s coarse grid that cannot represent the bottom topography well, especially that near the shoreline. The two - dimensional (2D) model employing shallow - water equations could also be a limiting factor. In Case 4 based on the best performance case with horizontally generated wave, the average relative error of maximum wave amplitude was reduced from 23.2% to 20.6% and the root mean square error (RMSE) was reduced from 0.029 m to 0.014 m. The results suggest that the consideration of horizontal deformation of earthquake, which plays an important role in generating tsunami, can help to improve the performance of simulating tsunami wave.

Early Stage Soliton Observations in the Sulu Sea*

Abstract Observations of early stage, large-amplitude, nonlinear internal waves in the Sulu Sea are presented. Water column displacement and velocity profile time series show the passage of two solitary-like waves close to their generation site. Additional observations of the same waves are made as they propagate through the Sulu Sea basin. These waves of depression have an estimated maximum amplitude of 44 m. Observed wave amplitude and background stratification are used to estimate parameters for both a Korteweg–de Vries (K-dV) and a Joseph wave solution. These analytic model solutions are compared with a fully nonlinear model as well. Model wave half-widths bracket the observed wave, with the Joseph model narrower than the K-dV model. The modal structure of the waves change as they transit northward though the Sulu Sea, with higher mode features present in the southern Sulu Sea, which dissipate by the time the waves reach the north. Observed and modeled energies are roughly comparable, with observed potential energy estimated at 6.5 × 107 J m−1, whereas observed kinetic energy is between 4.6 × 107 J m−1 and 1.5 × 108 J m−1, depending on the integration limits. If this energy remains in the Sulu Sea, an average dissipation rate of 10−9 W kg−1 is required over its volume, helping to maintain elevated mixing rates.

Bone ultrasound transducer

Low-intensity pulsed ultrasound (LIPUS) is used on bone-healing. One expected healing mechanism of this technique is the contribution of piezoelectricity. Actually, the piezoelectricity in dry bone at low frequencies has been reported by many investigators. However, the ultrasonic investigation of the piezoelectricity in bone has still remained very few. We have then made original transducers with bovine cortical bone samples, which were fabricated into plates (diameter: 10 mm, thickness: 0.5~1.0 mm). Using a conventional ultrasonic pulse technique in MHz range, we confirmed the observation of ultrasonic wave by the transducer. Here, the bone transducer was set in water at the focal position of a PVDF transmitter, which was excited by a single sinusoidal pulse of 70 Vp-p in the MHz range. The maximum voltage of the received wave was about 200 μVp-p. It was almost 1/2000 of the homemade PVDF transducer, which was made by the same procedure. The observed wave amplitude changed due to the sound wave frequency and bone thickness. Considering the inhomogeneous bone microstructure and the thickness dependence of the bone transducer, the piezoelectricity of bone in the MHz range is discussed.

Detecting sound-wave-like surface brightness ripples in cluster cores

We investigate the observational requirements for the detection of sound-wave-like features in galaxy cluster cores. We calculate the effect of projection on the observed wave amplitude, and find that the projection factor depends only weakly on the underlying cluster properties but strongly on the wavelength of the sound waves, with the observed amplitude being reduced by a factor of ∼5 for 5 kpc waves but only by a factor of ∼2 for 25 kpc waves. We go on to estimate the time needed to detect ripples similar to those previously detected in the Perseus cluster in other clusters. We find that the detection time-scales most strongly with the flux of the cluster and the amplitude of the ripples. By connecting the ripple amplitude to the heating power in the system, we estimate detection times for a selection of local clusters and find that several may have ripples detected with ∼1-Ms Chandra time.

Modeling and experimental studies of large amplitude waves on vertically falling films

Experimental data on the amplitude of large waves on vertically falling films are presented over a wide range of fluid properties and flow rates. Attempts are made to correlate the amplitude of these naturally excited and saturated waves to the Weber ( We) and Kapitza numbers ( Ka), the two dimensionless groups characterizing the film. For viscous fluids (with 2 < Ka < 200 ), the wave amplitude increases with the reciprocal of the Weber number and saturates at values around 3 ( h max / h N ∼ 3 ) while the dependence on Ka is found to be weak. For less viscous fluids ( 200 < Ka < 3890 ), the waves are found to be much more dynamic with amplitudes saturating at much higher values of around 10. The film roughness, or more precisely, the standard deviation (r.m.s) of the film thickness is also found to be correlated with the reciprocal of the Weber number. Scaling arguments are used to explain the initial increase in wave amplitudes. A two-equation h– q model is used to study the spatio-temporal dynamics of waves on long domains with periodic inlet forcing. The model is used to examine the amplitude–celerity relation for three families of solitary waves: the slow moving γ 1 family, the fast moving γ 2 family and the very fast moving ‘tsunami ( Γ 2 ) family’ having Nusselt film as the substrate. It is found that the film profile at short distances depends on the forcing amplitude and frequency but once the wave amplitude exceeds a critical value, the amplitude–celerity relationship is linear for all solitary waves that exist on the film and is independent of the forcing frequency or amplitude. It is also found that for a fixed set of fluid properties and flow rate ( We and Ka), the Γ 2 wave has the largest amplitude and wavelength. Local bifurcation and computational results are used to explain the experimentally observed wave amplitudes on naturally excited films.

Internal gravity waves generated by a turbulent bottom Ekman layer

Internal gravity waves excited by the turbulent motions in a bottom Ekman layer are examined using large-eddy simulation. The outer flow is steady and uniformly stratified while the density gradient is set to zero at the flat lower wall. After initializing with a linear density profile, a mixed layer forms near the wall separated from the ambient stratification by a pycnocline. Two types of internal wave are observed. Waves with frequencies larger than the free-stream buoyancy frequency are seen in the pycnocline, and vertically propagating internal waves are observed in the outer layer with characteristic frequency and wavenumber spectra. Since a signature of the pycnocline waves is observed in the frequency spectrum of the mixed layer, these waves may affect the boundary-layer turbulence. The dominant outer-layer waves have a group velocity directed 35-60° from the vertical axis, which is consistent with previous laboratory studies. The energy flux associated with the radiated waves is small compared to the integrated dissipation in the boundary layer, but is of the same order as the integrated buoyancy flux. A linear model is proposed to estimate the decay in wave amplitude owing to viscous effects. Starting from the observed wave amplitudes at the bottom of the pycnocline, the model prediction for the spectral distribution of the outer layer wave amplitude compares favourably with the simulation results.

A Schumann-like resonance on Titan driven by Saturn's magnetosphere possibly revealed by the Huygens Probe

The low-frequency data collected with the antenna of the Permittivity, Wave and Altimetry experiment on board the Huygens Probe that landed on Titan on 14 January 2005 have been thoroughly analyzed considering different possible natural and artificial effects. Although a definite conclusion is still subject to the outcome of complementary inquiries, it results from our analysis that the observations can be explained, for the most part, in term of natural phenomena rather than being artifacts. Extremely-low frequency waves generated in the ionosphere of Titan, driven by the corotating Saturn's frozen plasma flow, are assumed to be the most likely source for the observation of the second eigenmode of a Schumann-like resonance at around 36 Hz in the moon-ionosphere cavity. This particular mode is thought to be enhanced with respect to other harmonics because of the particular location of the landing site with respect to that of the supposed sources. The power budget of the observed wave amplitude seems to be consistent with a rough model of the global current of the wake-ionosphere circuit. Broadband low-frequency noise events which are observed sporadically during the descent are probably due to shot noise on the antenna when the Probe is crossing aerosol clouds, an interpretation supported by post-flight ground tests. Contrary to the situation encountered on Earth, atmospheric lightning does not appear to be the source of a conventional Schumann resonance on Titan.

Short period fast waves in solar coronal loops

Short period fast magnetoacoustic waves propagating along solar coronal loops, perturbing the loop boundary along the line of sight (LOS), may be observed by imaging telescopes. The relationship between the difference in emission intensity, the angle between the LOS and the direction of propagation and the wave amplitude and wavelength, is explored for kink and sausage fast waves. It is shown that the compressibility of the plasma in the loop significantly affects the observability of the waves. For both wave types there is an optimal observation angle which is determined by the ratio of the wave length and the loop radius. The change of the observational conditions because of the loop curvature predicts a significant, up to an order of magnitude, change in the observed wave amplitude. This prediction is confirmed by the analysis of the evolution of the fast wave train amplitude, observed with the SECIS instrument. The wave train amplitude experiences a sharp increase and then a decrease along the loop. The observational results are in a good agreement with the theory.

Line-of-sight effects on observability of kink and sausage modes in coronal structures with imaging telescopes

Kink modes of solar coronal structures, perturbing the loop in the direction along the line-of-sight (LOS), can be observed as emission intensity disturbances propagating along the loop provided the angle between the LOS and the structure is not ninety degrees. The effect is based upon the change of the column depth of the loop (along the LOS) by the wave. The observed amplitude of the emission intensity variations can be larger than the actual amplitude of the wave by a factor of two and there is an optimal angle maximizing the observed amplitude. For other angles this effect can also attenuate the observed wave amplitude. The observed amplitude depends upon the ratio of the wave length of kink perturbations to the width of the structure and on the angle between the LOS and the axis of the structure. Sausage modes are always affected negatively from the observational point of view, as the observed amplitude is always less than the actual one. This effect should be taken into account in the interpretation of wave phenomena observed in the corona with space-borne and ground-based imaging telescopes.

Rapid acceleration of electrons in the magnetosphere by fast‐mode MHD waves

During major magnetic storms, enhanced fluxes of relativistic electrons in the inner magnetosphere have been observed to correlate with ULF waves. The enhancements can take place over a period of several hours. In order to account for such a rapid generation of relativistic electrons, we examine the mechanism of transit‐time acceleration of electrons by low‐frequency fast‐mode MHD waves, here the assumed form of ULF waves. Transit‐time damping refers to the resonant interaction of electrons with the compressive magnetic field component of the fast‐mode waves via the zero cyclotron harmonic. In terms of quasi‐linear theory, a kinetic equation for the electron distribution function is formulated incorporating a momentum diffusion coefficient representing transit‐time resonant interaction between electrons and a continuous broadband spectrum of oblique fast‐mode waves. Pitch angle scattering is assumed to be sufficiently rapid to maintain an isotropic electron distribution function. It is further assumed that there is a substorm‐produced population of electrons with energies of the order of 100 keV. Calculations of the acceleration timescales in the model show that fast‐mode waves in the Pc4 to Pc5 frequency range, with typically observed wave amplitudes (ΔB = 10–20 nT), can accelerate the seed electrons to energies of order MeV in a period of a few hours. It is therefore concluded that the mechanism examined in this paper, namely, transit‐time acceleration of electrons by fast‐mode MHD waves, may account for the rapid enhancements in relativistic electron fluxes in the inner magnetosphere that are associated with major storms.

Modeling tsunamis from earthquake sources near Gorringe Bank southwest of Portugal

The Azores‐Gibraltar fracture zone with the huge bathymetric reliefs in the area southwest of Portugal is believed to have been the source of large historic tsunami events. This report describes simulations of tsunami generation and propagation from sources near the Gorringe Bank. The well‐documented 1969 tsunami event is examined both with a ray‐tracing technique and with finite difference models based on various shallow water equations. Both methods show that the most likely source location is southeast of the Gorringe Bank near the epicenter location determined from seismic data. The tsunami source is calculated by formulas given by Okada [1985] for surface deformation of an elastic half‐space caused by faulting. Observed wave amplitude and travel time and values computed from an initial wave field according to Okada [1985] formulas show acceptable agreement for most stations along the coast of Portugal and Spain. However, in order to explain a large primary wave with downward displacement observed on the coast of Morocco, an alternative source model with a larger area of downward displacement has been introduced. This also leads to a better overall fit with observed travel time. Implications for disastrous events, as the one in 1755, are also discussed. Linear hydrostatic shallow water models are used for most of the simulations, but the importance of nonlinearity and dispersion is examined with the Boussinesq equations. The sensitivity of the solution to changes in the location and the strength of the source is discussed, and a series of grid refinement studies are performed in order to assess the accuracy of the simulations.