Phase Speed Of Waves Research Articles

The role of Lagrangian drift in the geometry, kinematics and dynamics of surface waves

The role of the Lagrangian mean flow, or drift, in modulating the geometry, kinematics and dynamics of rotational and irrotational deep-water surface gravity waves is examined. A general theory for permanent progressive waves on an arbitrary vertically sheared steady Lagrangian mean flow is derived in the Lagrangian reference frame and mapped to the Eulerian frame. A Lagrangian viewpoint offers tremendous flexibility due to the particle labelling freedom and allows us to reveal how key physical wave behaviour arises from a kinematic constraint on the vorticity of the fluid, inter alia the nonlinear correction to the phase speed of irrotational finite amplitude waves, the free surface geometry and velocity in the Eulerian frame, and the connection between the Lagrangian drift and the Benjamin–Feir instability. To complement and illustrate our theory, a small laboratory experiment demonstrates how a specially tailored sheared mean flow can almost completely attenuate the Benjamin–Feir instability, in qualitative agreement with the theory. The application of these results to problems in remote sensing and ocean wave modelling is discussed. We provide an answer to a long-standing question: remote sensing techniques based on observing current-induced shifts in the wave dispersion will measure the Lagrangian, not the Eulerian, mean current.

A Sea Surface–Based Drag Model for Large-Eddy Simulation of Wind–Wave Interaction

Abstract Monin–Obukhov similarity theory (MOST) is a well-tested approach for specifying the fluxes when the roughness surfaces are homogeneous. For flow over waves (inhomogeneous surfaces), phase-averaged roughness length scales are often prescribed through models based on the wave characteristics and the wind speed. However, such approaches lack generalizability over different wave ages and steepnesses due to the reliance on model coefficients tuned to specific datasets. In this paper, a sea surface–based hydrodynamic drag model applicable to moving surfaces is developed to model the pressure-based surface drag felt by the wind due to the waves. The model is based on the surface gradient approach of Anderson and Meneveau applicable to stationary obstacles and extended here to the wind–wave problem. The wave drag model proposed specifies the hydrodynamic force based on the incoming momentum flux, wave phase speed, and the surface frontal area. The drag coefficient associated with the wind–wave momentum exchange is determined based on the wave steepness. The wave drag model is used to simulate turbulent airflow above a monochromatic wave train with different wave ages and wave steepnesses. The mean velocity profiles and model form stresses are validated with available laboratory-scale experimental data and show good agreement across a wide range of wave steepnesses and wave ages. The drag force is correlated with the wave surface gradient and out-of-phase with the wave height distribution by a factor of π/2 for the sinusoidal wave train considered. These results demonstrate that the current approach is sufficiently general over a wide parameter space compared to wave phase-averaged models with a minimal increase in computational cost. Significance Statement Understanding the physics of wind waves plays an important role in the context of numerous geophysical and engineering applications. A drag-based model is developed that characterizes the effect of the sea surface waves on the wind above. The model is validated with existing experimental datasets and is shown to be effective in predicting the average wind velocity and stress over waves with varied steepnesses and phase speeds. The ease of implementation and low computational cost of the model make it useful for studying turbulent atmospheric-scale flows over the sea surface important in offshore wind energy research as well as for modeling air–sea fluxes of momentum, heat, and mass.

МОДЕЛИРОВАНИЕ ВОЗБУЖДЕНИЯ ПОВЕРХНОСТНЫХ ПЛАЗМОН-ПОЛЯРИТОНОВ В ПРЯМОУГОЛЬНОМ НАНОРЕЗОНАТОРЕ НА ОСНОВЕ ЗОЛОТА

This paper considers the modeling of surface plasmon polaritons excitation in a limited nanostructure on the basis of a two-dimensional area discrete model, the area interacts with the oscillator. The nanostructure is a rectangle defined on the metal surface at the interface of the gold–silicon oxide, the surface plasmon–polaritons are excited by an electromagnetic radiation point source located above the metal surface. The dynamics of radiation point source is described by a discrete version of the Van der Pol equation with a small nonlinearity of the source parameters. The parameters of the goldsilicon oxide structure (the wave phase speed, the radiation source frequency, the characteristic time in the system, etc.) will be received from the dispersion relation for surface plasmon–polaritons at a single metal–dielectric interface. The distributions of the wave field in the structure will be analyzed at different positions of the point oscillator and different coupling coefficients of the wave field with the oscillators. The resonant wave field mode composition at different positions of the point oscillator and different coupling coefficients will be found using the two-dimensional Fourier transform of the wave field, the time evolution of excited modes of the wave field amplitudes will be also analyzed. In conclusion, the paper gives applicability limits of the considered model for studying the surface plasmon polaritons excitation in a limited nanostructure.

Quasi-geostrophic monopoles in a sheared zonal flow: Influence of the beta-effect and variable shear

This work builds on and continues a suite of earlier studies of the interaction between a monopole and a sheared zonal flow in the framework of a 1.5-layer quasi-geostrophic model. In Reznik and Kravtsov [Phys. Fluids 33, 116606 (2021); hereafter RK21], this problem was considered under an f-plane approximation for the case in which the dependence of the zonal velocity U¯(y) on latitude y was linear. Here, the conclusions stemming from that work are generalized for the case of a beta-plane and a variable shear of the background flow. Namely, numerical experiments with singular vortices using the algorithm of Kravtsov and Reznik [“Numerical solutions of the singular vortex problem,” Phys. Fluids 31, 066602 (2019); hereafter KR19] confirm the existence of the trapping latitude ytr, which attracts (repels) prograde (retrograde) vortices and clarifies the underlying mechanisms. Unlike in the case of a linear shear on an f-plane, the latitude ytr here does not necessarily coincide with the latitude at which the effective beta-parameter β¯=β−∂yyU¯+Rd−2U¯ vanishes (here, β denotes the derivative of the Coriolis parameter with respect to latitude and Rd is the Rossby radius of deformation). Another important difference is that in the presence of nonzero β≠0, a trapped prograde vortex exhibits a near-zonal westward drift with the zonal velocity close to the phase speed of long Rossby waves −βRd2 and the meridional velocity at least two orders of magnitude smaller than that. On the other hand, the meridional velocity of a retrograde vortex appears to be unrestricted; such a vortex can rapidly move in any direction, including the direction across the zonal current.

On the interaction between Kelvin waves at different phase speeds and the background flow

AbstractKelvin waves have been theorized to be absorbed near the critical layer, where the phase speed matches the speed of the background flow. Nevertheless, it is not clear through observations how the structure of the Kelvin waves evolves near the critical layer or in response to vertical wind shear with or without a critical layer. A novel varying‐coefficient regression technique that has been used to study evolving relationships across the seasonal cycle is used to capture how the wavelet‐filtered waves with a specific phase speed appear in different background winds or vertical shear regimes or a combination of both. Results show a relaxation of the in‐phase relationship between the zonal wind and geopotential height anomalies at slower Doppler‐shifted speeds, followed by the appearance of the Gill pattern at further reduction of the Doppler‐shifted speed, demonstrating a lack of dominant Kelvin wave signals in those conditions. We define the “observed critical layer” as the layer where the signals consistent with Kelvin waves fade away irrespective of the value of the Doppler‐shifted speed, which reduces to zero at the “theoretical critical layer.” Results show that wave structures consistent with Kelvin waves are not present at the top of layer with westerly vertical shear of the zonal wind, yet they exist during the easterly vertical shear of the zonal wind. The second part of the paper presents the dispersion equation of the Kelvin wave under vertical wind shear. The phase speed of the Kelvin wave proportionally increases with the Richardson number (and hence proportionally decreases with the vertical wind shear). The Richardson number varies with the vertical resolution of the data used, adding uncertainty to the calculated phase speed of the wave in the presence of vertical wind shear.

A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming

A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming

Decadal variability and trends in extratropical Rossby wave packet amplitude, phase, and phase speed

Abstract. The ongoing global yet spatially inhomogeneous warming prompts the inspection of decadal variability in the extratropical upper-tropospheric circulation properties. This study provides observational evidence in this regard by utilizing reanalysis data to examine the past interannual-to-decadal variability and unveil trends in the probability distribution of Rossby wave packet (RWP) amplitude (E), phase (Φ), and phase speed (cp). First, a comparison between the NE Pacific and N Atlantic regions indicates that the 300 hPa E probability distribution exhibits a seasonally and regionally varying decadal variability. No apparent discrepancy arises between different reanalysis datasets, except from the JJA season where two historical reanalyses systematically underestimate E compared to three modern-era reanalyses. Further exploiting the local-in-space and local-in-time character of the employed diagnostics in ERA5 reveals that, while many areas experience pronounced RWP property variations at interannual and/or decadal timescales, patterns of statistically significant trends in the 1979–2019 period do emerge. Notably, the Northern Hemisphere E field exhibits positive trends in the N Pacific, the NE Atlantic, and S Asia in DJF, whereas negative trends are found in a substantial portion of the extratropics in JJA. In terms of cp, distinct patterns characterize MAM, with positive trends in parts of the N Atlantic and most of Europe and negative trends to the north of these regions and parts of the N Pacific. The Southern Hemisphere features a poleward shift in the band of climatologically maximum E values in DJF, widespread positive E trends in MAM, and positive cp trends in large parts of the extratropics in DJF and MAM. Assessing the decadal variability of RWP phase reveals zonally extended patterns of alternating trends in the trough–ridge occurrence ratio for MAM in the Northern Hemisphere and JJA in both hemispheres. Furthermore, no covariance is observed between area-averaged daily-mean E and cp at decadal timescales, as revealed by the bivariate probability distribution trends in the E–cp domains for the different regions and seasons. Finally, it is shown that many parts of the N Pacific and N America experience a shift to increasing occurrence of large-amplitude and/or quasi-stationary RWPs in DJF during 1999–2019, which is a manifestation of the pronounced interannual-to-decadal variability that characterizes the E and cp seasonal distributions in some areas and seasons. Overall, this study underscores that substantial seasonal and regional variations characterize the past decadal variability and trends that emerge in the seasonal probability distributions of key RWP properties.

Shear-imposed falling thin Newtonian film over a porous slippery surface

The stability of a Newtonian thin film flow over a porous slippery wall approximated by Darcy's law is investigated. The modified Orr–Sommerfeld system is derived for the frequency-dependent linear stability analysis and energy-budget analysis. Moreover, in the longwave regime, both linear and weakly nonlinear stability analyses are conducted for small aspect ratios. In addition, the multiple scale approach is performed directly in the nonlinear deformation equation of the free surface to predict the extraordinary behavior of the amplitude and speed of the nonlinear disturbance in the subcritical and supercritical regimes. The study finds that the larger slip-velocity and externally imposed shear on the thin film increase the total kinetic energy of the infinitesimal perturbations. In a longwave regime, the critical conditions of the primary instability are described as a function of imposed shear stress that destabilizes the film flow for low critical Reynolds number. Furthermore, in the supercritical stable zone, both the nonlinear wave amplitude and phase speed increase with an increase in induced shear in the flow direction and velocity slip, and a reverse trend is observed in applying the imposed shear in the opposite flow direction. On the other hand, the nonlinear wave amplitude in the subcritical unstable zone increases and decreases, corresponding to the larger values of imposed shear and slip parameters, respectively.

A Simple Model for an Internal Wave Spectrum Dominated by Non-Linear Interactions

Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay of Biscay showed that a finestructure of semidiurnal tidal and near-inertial higher harmonics fills the spectrum. Here, a simple model is presented of forced nondispersive motions with forward energy cascade. The model fits the spectral shape of higher harmonics well within statistical significance and shows that such interactions imply maximum wave steepness in a balance between forcing and turbulent mixing. The single fitting parameter takes a value of approximately one, at which the barotropic tidal flow speed equals the internal wave phase speed. We infer that the barotropic tide sets a non-linear limit to baroclinic current scales without generating non-linear higher harmonics directly.

Slowing down convective instabilities in corrugated Couette–Poiseuille flow

Couette–Poiseuille (CP) flow in the presence of longitudinal grooves is studied by means of numerical analysis. The flow is actuated by movement of the flat wall and pressure imposed in the opposite direction. The stationary wall features longitudinal grooves that modify the flow, change hydrodynamic drag on the driving wall and cause onset of hydrodynamic instability in the form of travelling waves with a consequent supercritical bifurcation, already at moderate ranges of the Reynolds number. We show that by manipulating this system it is possible to significantly decrease phase speed of the unstable wave and to effectively decouple time scales of wave propagation and amplification with a potential to significantly reduce the distance required for the onset of nonlinear effects. Current analysis begins with concise characterization of stationary, laminar CP flow and the effects of applying a selected corrugation pattern, followed by determination of conditions leading to the onset of instabilities. In the second part we illustrate selected nonlinear solutions obtained for low, supercritical values of the Reynolds numbers and due to the amplification of unstable travelling waves of possibly low phase velocities. This work is concluded with a short discussion of a linear evolution of a wave packet consisting of a superposition of a number of unstable waves and initiated by a localized pulse. This part illustrates that in addition to the reduction of the phase velocity of a single, unstable mode, imposition of the Couette component also reduces group velocity of a wave packet.

A New Approach to Kinetic Energy Flux at the Different Frequencies above the IRIS Bright Points* * Released on 2021 March 1

Various bright structures abound in the chromosphere playing an essential role in the dynamics and evolution therein. Tentatively identifying the wave characteristics in the outer solar atmosphere helps to understand this layer better. One of the most significant aspects of these characteristics is the wave phase speed (PS), which is a dominant contribution to solar coronal heating and energy distribution in the Sun’s atmosphere layers. To obtain energy flux (EF), it is necessary to calculate the filling factor (FF) and the PS. In this study, the FF was determined by tracking the size and intensity of the IRIS bright points (BPs). To estimate an accurate PS and EF, it is necessary to know the chromosphere and transition region (TR) thickness and the phase difference between the two desired levels. Chromosphere and TR thickness cannot be measured directly on the disk; this study is performed using spectral data and calibrated based on Doppler velocities. As a result, the PSs in active regions (ARs) and coronal holes (CHs), as well as the IRIS BPs, have been calculated using the cross-power wavelet transform of Doppler velocities. Consequently, about the CH, the PS mean values are from 40 to 180 km s−1 at the network and from 30 to 140 km s−1 at the internetwork; and about the AR, they are from 80 to 540 km s−1 at the network and 70 to 220 km s−1 at the internetwork. Finally, the EF for the IRIS BPs has been calculated in three different frequencies. The results indicate that the network BPs have an influential role in heating the higher layers, while in the internetwork BPs most of the energy returns to the lower layers.

Seasonal fluctuations in Baltic sea level determined from satellite altimetry

This study used gridded daily satellite altimetry observations to investigate the spatial variability in the Baltic seasonal sea-level cycle and to assess the main factors that affected its interannual changes during the 1993–2018 period. In addition to the widely studied annual (Sa) and semiannual (Ssa) harmonics, the characteristics of higher frequency oscillations (terannual (three times a year or Sta) and quarterannual (four times a year or Sqa)) were investigated. We demonstrated that the Sa, Ssa, and Sqa harmonics can be reliably identified from gridded daily satellite altimetry data for all regions of the Baltic Sea. The Sta harmonic was reliably identified in all regions except the southeast part of the Baltic Proper and Danish Straits. Low amplitudes and large uncertainties caused by noise in the SLA time series impeded the Sta evaluation in these two regions. In the Baltic Sea, annual oscillations of sea level propagate from the southwest to northeast at a speed of 0.15–0.36 m/s, which is close to the theoretical phase speed of the baroclinic Kelvin wave. The Ssa, Sta, and Sqa oscillations did not demonstrate a statistically reliable spatial variability in the phase. In many regions of the Baltic Sea for the 1993–2018 period, a statistically significant (at the 95% level) increase of +1.3– + 2.2 mm/yr was observed for the amplitudes of the Sa harmonic, while for the amplitudes of the Ssa harmonic, a statistically significant decrease was detected. No statistically significant changes were observed in the amplitudes of the Sta and Sqa harmonics. Wind, atmospheric pressure, and water exchange with the North Sea correlated well with interannual changes in the sea-level seasonal cycle. The air temperature correlated well only with the Sa component. Precipitation, evaporation, and river input were not correlated with seasonal or interannual changes in the sea-level cycle.

Evidence of the critical layer mechanism in growing wind waves

Highly resolved laboratory measurements of the airflow over wind-generated waves are examined using a novel wave growth diagnostic that quantifies the presence of Miles’ critical layer mechanism of wind-wave growth. The wave growth diagnostic is formulated based on a linear stability analysis, and results in growth rates that agree well with those found by a pressure reconstruction method as well as other, less direct, methods. This finding, combined with a close agreement between the airflow measurements and the predictions of linear stability (critical layer) theory, demonstrate that the Miles’ critical layer mechanism can cause significant wave growth in young (wave age $c/u_* = 6.3$ , where $c$ is the wave phase speed, and $u_*$ the friction velocity) wind-forced waves.

Ocean Surface Roughness from Satellite Observations and Spectrum Modeling of Wind Waves

Abstract Many wind wave spectrum models provide excellent wave height prediction given the input of wind speed and wave age. Their quantification of the surface roughness, on the other hand, varies considerably. The ocean surface roughness is generally represented by the mean square slope, and its direct measurement in open ocean remains a challenging task. Microwave remote sensing from space delivers ocean surface roughness information. Satellite platforms offer global coverage in a broad range of environmental conditions. This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling. The analysis presented in this paper shows that over two orders of magnitude of the wavenumber range (0.3–30 rad m−1), the spectral components follow a power function relating the dimensionless spectrum and the ratio between wind friction velocity and wave phase speed. The power function exponent is about 0.38, which is considerably smaller than unity as expected from the classical equilibrium spectrum function. It may suggest that wave breaking is not only an energy sink but also a source of roughness generation covering a wideband of wavelengths about 20 m and shorter. Significance Statement This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling that is critical to the investigation of air–sea interaction and ocean remote sensing. The analysis presented in this paper suggests that wave breaking is not only an energy sink but also a generation source of surface roughness covering a wide band of wavelengths about 20 m and shorter.

Global centroid moment tensor solutions in a heterogeneous earth: the CMT3D catalogue

SUMMARYFor over 40 yr, the global centroid-moment tensor (GCMT) project has determined location and source parameters for globally recorded earthquakes larger than magnitude 5.0. The GCMT database remains a trusted staple for the geophysical community. Its point-source moment-tensor solutions are the result of inversions that model long-period observed seismic waveforms via normal-mode summation for a 1-D reference earth model, augmented by path corrections to capture 3-D variations in surface wave phase speeds, and to account for crustal structure. While this methodology remains essentially unchanged for the ongoing GCMT catalogue, source inversions based on waveform modelling in low-resolution 3-D earth models have revealed small but persistent biases in the standard modelling approach. Keeping pace with the increased capacity and demands of global tomography requires a revised catalogue of centroid-moment tensors (CMT), automatically and reproducibly computed using Green's functions from a state-of-the-art 3-D earth model. In this paper, we modify the current procedure for the full-waveform inversion of seismic traces for the six moment-tensor parameters, centroid latitude, longitude, depth and centroid time of global earthquakes. We take the GCMT solutions as a point of departure but update them to account for the effects of a heterogeneous earth, using the global 3-D wave speed model GLAD-M25. We generate synthetic seismograms from Green's functions computed by the spectral-element method in the 3-D model, select observed seismic data and remove their instrument response, process synthetic and observed data, select segments of observed and synthetic data based on similarity, and invert for new model parameters of the earthquake’s centroid location, time and moment tensor. The events in our new, preliminary database containing 9382 global event solutions, called CMT3D for ‘3-D centroid-moment tensors’, are on average 4 km shallower, about 1 s earlier, about 5 per cent larger in scalar moment, and more double-couple in nature than in the GCMT catalogue. We discuss in detail the geographical and statistical distributions of the updated solutions, and place them in the context of earlier work. We plan to disseminate our CMT3D solutions via the online ShakeMovie platform.

Dynamics of fast and slow magnetoacoustic waves in plasma slabs with thermal misbalance

ABSTRACT The non-uniformity of the solar atmosphere along with the presence of non-adiabatic processes such as radiation cooling and unspecified heating can significantly affect the dynamics and properties of magnetoacoustic (MA) waves. To address the co-influence of these factors on the dispersion properties of MA waves, we considered a single magnetic slab composed of thermally active plasma. Using perturbation theory, we obtained a differential equation that determines the dynamics of the two-dimensional perturbations. Applying the assumption of strong magnetic structuring, we derived the dispersion relations for the sausage and kink MA modes. A numerical solution of the dispersion relations for coronal conditions was obtained to investigate the interplay between the non-uniformity and the thermal misbalance. For the heating scenario considered, it was found that the phase speed of both the sausage and the kink slow MA waves is strongly affected by the thermal misbalance in the long-wavelength limit. The obtained characteristic time-scales of the slow-wave dissipation coincide with the periods of waves observed in the corona. The phase speed of the fast waves, however, is not affected by the thermal misbalance. The geometry of the magnetic structure remains the main dispersion mechanism for the fast waves. Our analysis reveals that the dissipation of the fast waves is weaker than the dissipation of the slow waves under coronal conditions. The obtained results are of importance for the use of MA waves as a tool for estimating not only plasma parameters but also non-adiabatic processes.

Speed and Acceleration of Droplets Generated by Breaking Wind‐Forced Waves

AbstractLaboratory measurements of droplet size, velocity, and accelerations generated by mechanically and wind‐forced water breaking waves are reported. The wind free stream velocity is up to 12 m/s, leading to wave slopes from 0.15 to 0.35 at a fetch of 23 m. The ratio of wind free stream and wave phase speed ranges from 5.9 to 11.1, depending on the mechanical wave frequency. The droplet size distribution in all configurations can be represented by two power laws, N(d) ∝ d−1 for drops from 30 to 600 μm and N(d) ∝ d−4 above 600 μm. The horizontal and vertical droplet velocities appear correlated, with drops with slower horizontal speed more likely to move upward. The velocity and acceleration distributions are found to be asymmetric, with the velocity probability density functions (PDFs) being described by a normal‐inverse‐Gaussian distribution. The horizontal acceleration PDF are found to follow a shape close to the one predicted for small particles in homogeneous and isotropic turbulence, while the vertical distribution follows an asymmetric normal shape, showing that both acceleration components are controlled by different physical processes.

On the Energy Dispersion of Magnetic Rossby Waves

The energy dispersion of magnetic Rossby waves has been investigated by applying the two-dimensional incompressible magnetohydrodynamic (MHD) equations in both uniform basic flow and basic magnetic field. The dispersion relation suggests that the magnetic Rossby waves can be divided into fast- and slow-propagating modes, respectively. The fast-propagating mode propagates eastward and is similar to the fast Alfvén waves. The energy dispersion speed is faster than the phase speed, which means the perturbation energy can lead the perturbations themselves to arrive downstream. The slow-propagating waves with smaller (larger) horizontal scales are similar to those of the slow Alfvén waves (Rossby waves). The zonal group velocity is slower than the zonal phase speed for the slow-propagating magnetic Rossby waves. For the slow-propagating waves that propagate eastward, this means that the perturbation energy may trigger new perturbations that are located upstream of the perturbations themselves. The group velocity vector is basically same as (opposite of) the wavevector for the fast-propagating (slow-propagating) magnetic Rossby waves that propagate eastward. The endpoints of the group velocity vectors and the wavevector multiplying a factor are located on a cycle in the wavenumber space. Due to the uniform basic flow and the uniform basic magnetic field, the energy dispersion paths (called rays) are straight lines. Along the straight-line rays, the wave action, wave energy, and amplitude keep their initial values, and the wave neither develops nor decays.

Density and Velocity Fluctuations of Alpha Particles in Magnetic Switchbacks

Magnetic switchbacks, or sudden reversals in the magnetic field’s radial direction, are one of the more striking observations of the Parker Solar Probe (PSP) in its mission thus far. While their precise production mechanisms are still unknown, the two main theories are via interchange reconnection events and in situ generation. In this work, density and abundance variations of alpha particles are studied inside and outside individual switchbacks. We find no consistent compositional differences in the alpha particle abundance ratio, n α p , inside versus outside switchbacks, nor do we observe any signature when separating the switchbacks according to V α p /V pw , the ratio of the alpha–proton differential speed to the wave phase speed (the speed at which the switchback is traveling). We argue that these measurements cannot be used to rule in favor of one production mechanism over the other, due to the distance between PSP and the postulated interchange reconnection events. In addition, we examine the 3D velocity fluctuations of protons and alpha particles within individual switchbacks. While switchbacks are always associated with increases in proton velocity, alpha velocities may be enhanced, unchanged, or decrease. This is due to the interplay between V pw and V α p , with the Alfvénic motion of the alpha particles vanishing as the difference ∣V pw – V α p ∣ decreases. We show how the Alfvénic motion of both the alphas and the protons through switchbacks can be understood as an approximately rigid arm rotation about the location of the wave frame, and illustrate that the wave frame can therefore be estimated using particle measurements alone, via sphere fitting.

Rayleigh-like waves in multilayered elastic media containing voids: Use of the Haskell matrix method

Using the Haskell matrix method, the dispersion relation of Rayleigh-like surface waves propagating through a multilayered elastic solid half-space is derived. Each layer as well as the half-space is assumed to have voids (pores) distributed evenly throughout. This dispersion relation is then reduced for a 2-layered model (single layer over a half-space) to study the characteristics of phase speed of Rayleigh-like wave. For a particular model, the numerical computations are performed to observe the effect of voids on the fundamental mode of Rayleigh-like waves for n = 2 and 3. For the 2-layered model, it is also shown that the particle motion remains elliptical but influenced by the presence of voids. In the absence of voids from the model, the dispersion relation earlier obtained by Haskell (1953) for the case n = 2 is recovered successfully.