Radial Wavelength Research Articles

Convective Overstability in Radially Global Protoplanetary Disks. I. Pure Gas Dynamics

Protoplanetary disks are prone to several hydrodynamic instabilities. One candidate, convective overstability (COS), can drive radial semiconvection that may influence dust dynamics and planetesimal formation. However, the COS has primarily been studied in local models. This paper investigates the COS near the midplane of radially global disk models. We first conduct a global linear stability analysis, which shows that linear COS modes exist only radially inward of their Lindblad resonance (LR). The fastest-growing modes have LRs near the inner radial domain boundary with effective radial wavelengths that can be a substantial fraction of the disk radius. We then perform axisymmetric global simulations and find that the COS’s nonlinear saturation is similar to previous incompressible shearing box simulations. In particular, we observe the onset of persistent zonal and elevator flows for sufficiently steep radial entropy gradients. In full 3D, nonaxisymmetric global simulations, we find the COS produces large-scale, long-lived vortices, which induce the outward radial transport of angular momentum via the excitation of spiral density waves. The corresponding α-viscosity values of order 10−3 agree well with those found in previous 3D compressible shearing box simulations. However, in global disks, significant modifications to their radial structure are found, including the formation of pressure bumps. Interestingly, the COS typically generates an outward radial mass transport, i.e., decretion. We briefly discuss the possible implications of our results for planetesimal formation and for interpreting dust rings and asymmetries observed in protoplanetary disks.

On corrugation mode radial wavelengths of the vertical shear instability

Abstract The vertical shear instability (VSI) is a promising mechanism to drive turbulence in protoplanetary disks. Numerical simulations in the literature demonstrate that the VSI non-linear saturation is predominated by the linear corrugation modes. These modes possess vertical wavelengths crucially longer than radial wavelengths. This paper aims to investigate the natural radial wavelength of corrugation modes upon VSI saturation, by a series of numerical simulations conducted in Athena++ at different grid resolutions, disk aspect ratios, and viscosity parameterized by ν. We find a sign of convergence emerges at 64 cells per gas scale height for fiducial simulations. Below it a continuous reduction of wavelengths with grid resolution is observed. Synthetic ALMA molecular line observations of $^{12}\rm CO(2-1)$ are performed to inspect the observability of the corrugation modes feature, which is significantly diminished with a resolution of 32 cells per scale height or above. Flared and viscous disks exhibiting longer saturation wavelengths may mitigate the observational difficulty.

On-demand flat-top wideband OAM mode converter based on a cladding-etched helical fiber grating.

A new method enabling to provide an on-demand flat-top wideband orbital angular momentum (OAM) mode converter is proposed and experimentally demonstrated, which is based on utilization of a cladding-etched helical long-period fiber grating (CEHLPG). By appropriately selecting the grating period and precisely controlling the diameter of the CEHLPG in-situ, both the radial order and central wavelength of the flat-top band for the generated OAM mode can be flexibly tailored according to specific requirements. As typical examples, the first azimuthal order OAM modes with a flat-top bandwidth of 95 nm at -20 dB, a central operating wavelength of ∼1500 nm, and the radial-orders of 9, 8, 5, and 2, respectively, have been demonstrated consecutively. The proposed method provides an excellent flexibility and robustness in controlling both the radial order and the central wavelength of the resulting flat-top wideband OAM mode conversion, which may support a variety of practical optical vortex applications.

Broadband Energization of Superthermal Electrons in Jupiter’s Inner Magnetosphere

AbstractThe Juno spacecraft in a polar orbit around Jupiter has observed broadband electron energization signatures at high latitudes (Mauk et al., 2017, https://doi.org/10.1038/nature23648). We investigate the origin of this energization by simulating the propagation of dispersive Alfvén waves from the Io plasma torus to high latitudes. These waves may be triggered by mechanisms such as the moon‐magnetosphere interaction or inflows from radial transport. We build on the initial hybrid gyrofluid‐kinetic electron simulation of Damiano et al. (2019, https://doi.org/10.1029/2018gl081219) to further quantify electron energization by Alfvénic waves, and investigate this process as a local source mechanism for observed broadband superthermal electron populations. We find that the magnitude of energization increases with the wave amplitude, while decreasing the radial wavelength reduces the high‐latitude wave and particle energy flux. Over the examined range of initial conditions we successfully generate broadband electron populations consistent with Juno observations (Mauk et al., 2017, http://doi.org/10.1038/nature23648; Szalay et al., 2018, https://doi.org/10.1029/2018je005752), that contribute to both precipitating populations and those that form trans‐hemispheric beams. Our energized electron distributions are consistent with observed superthermal populations critical for the torus energy budget (Bagenal & Delamere, 2011, https://doi.org/10.1029/2010ja016294) and Io‐related auroral emission.

The Representation of Spiral Gravity Waves in a Mesoscale Model With Increasing Horizontal and Vertical Resolution

AbstractRecent observational and numerical studies have investigated the dynamics of fine‐scale gravity waves radiating horizontally outward from tropical cyclones. The waves are wrapped into spirals by the tangential wind of the cyclone and are described as spiral gravity waves. This study addresses how well numerical simulations of these waves compare to observations as the horizontal grid spacing is decreased from 2.0 to 1.0 to 0.5 km, and the number of vertical levels changes from 25 to 50 to 100. Spectral filtering is applied to separate the fine‐scale waves in vertical velocity (w) and the larger‐scale waves in pressure (p) from moist updrafts and downdrafts in the eyewall and rainbands. As the grid spacing decreases, the radial wavelengths of the w waves decrease from 20 to 7 km, approaching observed values. For grid spacing 1.0 km, the p waves become well‐resolved with wavelength 70 km. The outward phase speeds range from 15 to 30 ms−1 for the w waves and 50 to 70 ms−1 for p waves. Analysis of the upper‐level outflow region finds that the spiral w waves propagate 5–10 ms−1 faster due to radial advection, but also finds what appear to be different classes of larger‐amplitude, slow‐moving spiral waves. Similar waves can be seen in satellite images, which appear to be caused by dynamical instability of the strongly vertically sheared radial and tangential winds in the TC outflow.

Three-dimensional inhomogeneity of electron-temperature-gradient turbulence in the edge of tokamak plasmas

Nonlinear multiscale gyrokinetic simulations of a Joint European Torus edge pedestal are used to show that electron-temperature-gradient (ETG) turbulence has a rich three-dimensional structure, varying strongly according to the local magnetic-field configuration. In the plane normal to the magnetic field, the steep pedestal electron temperature gradient gives rise to anisotropic turbulence with a radial (normal) wavelength much shorter than in the binormal direction. In the parallel direction, the location and parallel extent of the turbulence are determined by the variation in the magnetic drifts and finite-Larmor-radius (FLR) effects. The magnetic drift and FLR topographies have a perpendicular-wavelength dependence, which permits turbulence intensity maxima near the flux-surface top and bottom at longer binormal scales, but constrains turbulence to the outboard midplane at shorter electron-gyroradius binormal scales. Our simulations show that long-wavelength ETG turbulence does not transport heat efficiently, and significantly decreases overall ETG transport—in our case by ∼40%—through multiscale interactions.

Kronoseismology V: A panoply of waves in Saturn’s C ring driven by high-order internal planetary oscillations

Saturn’s rings act as a system of innumerable test particles that are remarkably sensitive to periodic disturbances in the planet’s gravitational field. We identify 15 additional density and bending waves in Saturn’s C ring driven by the planet’s internal normal mode oscillations. The collective response of the rings to Saturn’s oscillations results in a host of inward-propagating density waves at outer Lindblad resonances (OLRs) and outward propagating bending waves at outer vertical resonances (OVRs). In the emerging field of Kronoseismology, nearly two-dozen OLRs and OVRs have previously been identified in high-resolution radial profiles of the rings obtained from Voyager and Cassini occultation observations (see Hedman et al. (2019) and references cited therein for a recent summary). Here we apply similar wavelet techniques to extract and co-add phase-corrected waveforms from multiple Cassini VIMS stellar occultations. Taking advantage of a highly accurate absolute radius scale for the rings (French et al., 2017), we are able to detect weak, high-wavenumber (up to m=14) waves with km-scale radial wavelengths. From a systematic scan of the entire C ring, we report the discovery and identification of 11 new OLRs, two counterpart inner Lindblad resonances (ILRs), and two new OVRs. The close agreement of the observed resonance locations and wave rotation rates with the predictions of models of Saturn’s interior (Mankovich et al., 2019) suggests that all of the new waves are driven by Saturnian f-mode oscillations. As classified by their spherical harmonic shapes, the modes in question range in azimuthal wavenumber from m=8 to 14, with associated resonance orders ℓ−m ranging from 0 to 8, where ℓ is the overall angular wavenumber of the mode. Our suite of detections for ℓ−m=4 is now complete from m=8 near the inner edge of the C ring to m=14 near 81,300 km. Curiously, detections with ℓ−m=2 are less common. These newly-identified non-sectoral (ℓ>m) waves sample latitudinal as well as radial structure within the planet and may thus provide valuable constraints on Saturn’s differential rotation. Allowing for the fact that the two ILR-type waves appear to be due to the same normal modes as two of the OLR-type waves, the 13 additional modes identified here bring the number of distinct f-modes suitable for constraining interior models to 34.

An Investigation of Spiral Gravity Waves Radiating from Tropical Cyclones Using a Linear, Nonhydrostatic Model

AbstractA recent study showed observational and numerical evidence for small-scale gravity waves that radiate outward from tropical cyclones. These waves are wrapped into tight spirals by the radial and vertical shears of the tangential wind field. Reexamination of the previously studied tropical cyclone simulations suggests that the dominant source for these waves are convective asymmetries rotating along the eyewall, modulated in intensity by the preferred convection region on the left side of the environmental wind shear vector. A linearized, nonhydrostatic model for perturbations to a balanced vortex is used to study the waves. Forcing the linear model with rotating and pulsing asymmetric heat sources generates radiating gravity waves with multiple vertical and horizontal structures. The pulsation of the rotating heat source generates two types of waves: fast, deep waves with larger radial wavelengths, and slower, secondary waves with shorter radial and vertical wavelengths. The deeper waves produce surface pressure oscillations that have time scales consistent with surface observations, whereas the shorter waves have little surface indication but produce oscillations in vertical velocity with shorter radial wavelengths that are consistent with aircraft observations. Convective forcing that is either not pulsing or not rotating produces gravity waves but they are not as similar to the observed or simulated waves. The effects of varying the intensity of the cyclone, the asymmetry of the forcing, and the static stability of the surrounding atmosphere are explored.

The nearby spiral density-wave structure of the Galaxy: line-of-sight velocities of the Gaia DR2 main-sequence A, F, G, and K stars

ABSTRACT Distances and velocities of $\approx \!2400\, 000$ main-sequence A, F, G, and K stars are collected from the second data release of ESA's Gaia astrometric mission. This material is analysed to find evidence of radial and azimuthal systematic non-circular motions of stars in the solar neighbourhood on the assumption that the system is subject to spiral density waves (those produced by a spontaneous disturbance, a central bar, or an external companion), developing in the Galactic disc. Data analysis of line-of-sight velocities of $\approx \!1500\, 000$ stars selected within 2 kpc from the Sun and 500 pc from the Galactic mid-plane with distance accuracies of <10 per cent makes evident that a radial wavelength of the wave pattern is 1.1–1.6 kpc and a phase of the wave at the Sun’s location in the Galaxy is 55°–95°. Respectively, the Sun is situated at the inner edge of the nearest Orion spiral arm segment. Thus, the local Orion arm is a part of a predominant density-wave structure of the system. The spiral structure of the Galaxy has an oscillating nature corresponding to a concept of the Lin–Shu-type moderately growing in amplitude, tightly wound, and rigidly rotating density waves.

On MHD Oscillations of a Plasma Column of Finite Conductivity with a Jump of Parameters in the Near-Wall Region

In a straight-cylinder model in a strong longitudinal magnetic field, the MHD oscillations of a plasma of a finite conductivity are considered in a situation when there is no resonant surface in the plasma on which the component of the perturbation wave vector vanishes along the field. At high conductivity, there are large-scale oscillations with a radial wavelength on the order of the column radius, which in the entire volume differ little from those described by an ideal MHD. It is shown that with a jump in the density and electron temperature on a certain magnetic surface near the wall, another MHD mode may exist along with such oscillations due to the finite conductivity. In this mode, the perturbations are large-scale and almost ideal in most of the plasma volume, but small-scale in the radial coordinate and not ideal in the wall region.

Control of solitary-drift-wave formation by radial density gradient in laboratory magnetized cylindrical plasma

Solitary drift waves (SDWs) in magnetized plasmas were discovered and then first investigated by experiment and numerical simulation by the Kyushu University group [i.e., H. Arakawa et al., Plasma Phys. Controlled Fusion 52, 105009 (2010)]. However, the formation mechanisms of SDWs still await thorough examination. Our work experimentally identifies a clear transition from turbulent drift waves (DWs) to SDWs for varied radial gradients in background density, which is in agreement with the preceding numerical simulations [M. Sasaki et al., Phys. Plasmas 22, 032315 (2015)]. The formation of SDWs is accompanied by a significant growth in the total fluctuation level and three-wave phase coupling between the constitutive harmonic modes. A subsequent saturation in the total fluctuation level and intensity of three-wave coupling when further increasing the density gradient is witnessed for the first time. The transition from turbulent DWs to SDWs is also characterized by an increase in the radial wavelength of the DWs. The SDW is considered a meso- (or macro-) scale ordered structure nonlinearly generated by turbulent DWs. Our work on SDW generation indicates that this phenomenon in magnetized plasmas is a universal rather than a device-dependent phenomenon.

D-Shaped Fiber Bragg Grating Ultrasonic Hydrophone With Enhanced Sensitivity and Bandwidth

In this paper, we demonstrate a miniature flexible FBG-based underwater ultrasonic sensor with enhanced pressure sensitivity and bandwidth using a side-polished configuration of ∼54 μ m depth and ∼15 mm length. The opto-mechanical responses of the sensor to acoustic-induced strain in axial and radial receiving modes are investigated and characterize the gain sensitivity dependent on the wavelength/Bragg length ratio. Then, ultrasonic testing in a water tank exhibited a maximum radial acoustic pressure-induced wavelength shift of 91.29 nm/MPa and a noise equivalent acoustic signal level of ∼49.6 mPa/Hz1/2 in the range of 40–120 kHz, as well as a good gain flatness of less than 9.4 dB. This is significantly superior to FBG-based hydrophones previously ever reported to our knowledge. The proposed technique greatly simplifies the miniaturized integration of all-optical ultrasonic detectors and could, therefore, be further improved for ultra-high sensitive hydrophones in optoacoustic imaging.

Concentric ripples of lubrication film in electrowetting

When a water drop approaches a solid surface in an ambient oil environment, a thin oil film will be formed between the drop and the solid surface. The lubrication film presents more complex behaviors when the external electrical field varies discretely, and in this work, concentric ripples are found in the thin film under a series of voltage steps, which is obviously different from the film profile when the applied voltage is continuously increased. According to the time evolution of the thin film, each voltage step adds a new concentric ripple outside the existing lubrication film. The radial wavelength and the maximum height of each ripple are revealed to have a linear relationship with the amplitude of the corresponding voltage step. The ripples finally break into microscopic oil droplets, and the size and the number of the droplets can be predicted with the diameter and the radial wavelength of each ripple.

Coherent Turbulence in the Boundary Layer of Hurricane Rita (2005) during an Eyewall Replacement Cycle

Abstract The structure of coherent turbulence in an eyewall replacement cycle in Hurricane Rita (2005) is presented from novel airborne Doppler radar observations using the Imaging Wind and Rain Airborne Profiler (IWRAP). The IWRAP measurements and three-dimensional (3D) wind vector calculations at a grid spacing of 250 m in the horizontal and 30 m in the vertical reveal the ubiquitous presence of organized turbulent eddies in the lower levels of the storm. The data presented here, and the larger collection of IWRAP measurements, currently are the highest-resolution Doppler radar 3D wind vectors ever obtained in a hurricane over the open ocean. Coincident data from NOAA airborne radars, the Stepped Frequency Microwave Radiometer, and flight-level data help to place the IWRAP observations into context and provide independent validation. The typical characteristics of the turbulent eddies are the following: radial wavelengths of ~1–3 km (mean value is ~2 km), depths from the ocean surface up to flight level (~1.5 km), aspect ratio of ~1.3, and horizontal wind speed perturbations of 10–20 m s−1. The most intense eddy activity is located on the inner edge of the outer eyewall during the concentric eyewall stage with a shift to the inner eyewall during the merging stage. The evolving structure of the vertical wind shear is connected to this shift and together these characteristics have several similarities to boundary layer roll vortices. However, eddy momentum flux analysis reveals that high-momentum air is being transported upward, in contrast with roll vortices, with large positive values (~150 m2 s−2) found in the turbulent filaments. In the decaying inner eyewall, elevated tangential momentum is also being transported radially outward to the intensifying outer eyewall. These results indicate that the eddies may have connections to potential vorticity waves with possible modifications due to boundary layer shear instabilities.

Cassini-VIMS observations of Saturn’s main rings: II. A spectrophotometric study by means of Monte Carlo ray-tracing and Hapke’s theory

This work is the second in a series of manuscripts devoted to the investigation of the spectrophotometric properties of Saturn’s rings from Cassini-VIMS (Visible and Infrared Mapping Spectrometer) observations. The dataset used for this analysis is represented by ten radial spectrograms of the rings which have been derived in Filacchione et al. (2014) by radial mosaics produced by VIMS. Spectrograms report the measured radiance factor I/F of the main rings of Saturn as a function of both radial distance (from 73500 to 141375 km) and wavelength (0.35–5.1 µm) for different observation geometries (phase angle ranging in the 2°–132° interval). We take advantage of a Monte Carlo ray-tracing routine (Ciarniello et al., 2014) to characterize the photometric behavior of the rings at each wavelength and derive the spectral Bond albedo of ring particles. This quantity is used to infer the composition of the regolith covering ring particles by applying Hapke’s theory. Four different regions, characterized by different optical depths, and respectively located in the C ring, inner B ring, mid B ring and A ring, have been investigated. Results from photometric modeling indicate that, in the VIS-NIR spectral range, B ring particles are intrinsically brighter than A and C ring particles, with the latter having the lowest albedo, while the single particle phase function of the ring’s particles is compatible with an Europa-like or Callisto-like formulation, depending on the investigated region. Spectral modeling of the inferred Bond albedo indicates that ring spectrum can be reproduced by water ice grains with inclusion of organic materials (tholin) as a UV absorber intimately mixed with variable amounts of other compounds in pure form (carbon, silicates) or embedded in water ice grains (nanophase hydrated iron oxides, carbon, silicates, crystalline hematite, metallic iron, troilite). The abundance of tholin decreases with radial distance from C ring (0.2–0.6%) to A ring (0.06%) for the selected regions. Its distribution is compatible with an intrinsic origin and is possibly related to the different plasma environment of the different ring regions. The identification of the other absorber(s) and its absolute volumetric abundance is uncertain, depending on the adopted grain size and mixing modality (intraparticle or intimate). However, assuming a common composition of the other absorber in the ring plane, we find that its abundance anti-correlates with the optical depth of the investigated regions, being maximum in the thinnest C ring and minimum in the thickest mid B ring. In the case of the C ring, an additional population of low-albedo grains is required to match the positive spectral slope of the continuum in the 0.55–2.2 µm interval, represented by an intraparticle mixture of water ice and a spectrum similar to troilite or metallic iron. The distribution of the darkening compounds is interpreted as the result of a contamination by exogenous material, which is more effective in the less dense regions of the rings because of their lower surface mass density of pure water ice.

The Lin–Shu type density–wave structure of the Galaxy: Line-of-sight velocities of selected 37354 RAVE DR5 stars

We exploit information, including velocities from the fifth data release of the RAdial Velocity Experiment (RAVE), to find evidence of the Lin–Shu type tightly wound spiral density waves in the nearby Galactic disk. The Kunder et al. (2017) catalogue of 471117 stars with derived spectrophotometric distances and line-of-sight velocities are explored to find the geometry and parameters of the velocity field in the extended solar neighborhood. Possible existence of noncircular systematic motions of selected 37,354 disk objects within 2 kpc from the Sun and 500 pc from the Galactic mid-plane together with the ordinary differential rotation are assumed. Both the pitch angle of spiral arms and the spatial location of the Sun within the density–wave pattern and the deviations of the motion of objects from the circular motion are calculated by fitting the stellar line-of-sight velocities in RAVE DR5 with the simplest linear perturbation density–wave model. Two radial wavelengths of the wave pattern of about 0.5 kpc and 1.5 kpc in the solar vicinity are found. We argue that the spiral structure of the Galaxy has an oscillating nature corresponding to a concept of the fairly unstable, low amplitude, tightly wound, and rigidly rotating density waves.

Effect of pectoral fin kinematics on manta ray propulsion

Recent advancement of bio-inspired underwater vehicles has led to a growing interest in understanding the fluid mechanics of fish locomotion, which involves complex interaction between the deforming structure and its surrounding fluid. Unlike most natural swimmers that undulate their body and caudal fin, manta rays employ an oscillatory mode by flapping their large, flattened pectoral fins to swim forward. Such a lift-based mode can achieve a substantially high propulsive efficiency, which is beneficial to long-distance swimming. In this study, numerical simulations are carried out on a realistic manta ray model to investigate the effect of pectoral fin kinematics on the propulsive performance and flow structure. A traveling wave model, which relates a local deflection angle to radial and azimuthal wavelengths, is applied to generate the motion of the pectoral fins. Hydrodynamic forces and propulsive efficiency are reported for systematically varying kinematic parameters such as wave amplitude and wavelengths. Key flow features, including a leading edge vortex (LEV) that forms close to the tip of each pectoral fin, and a wake consisting of interconnected vortex rings, are identified. In addition, how different fin motions alter the LEV behavior and hence affect the thrust and efficiency is illustrated.

Electromagnetic banana kinetic equation and its applications in tokamaks

A banana kinetic equation in tokamaks that includes effects of the finite banana width is derived for the electromagnetic waves with frequencies lower than the gyro-frequency and the bounce frequency of the trapped particles. The radial wavelengths are assumed to be either comparable to or shorter than the banana width, but much wider than the gyro-radius. One of the consequences of the banana kinetics is that the parallel component of the vector potential is not annihilated by the orbit averaging process and appears in the banana kinetic equation. The equation is solved to calculate the neoclassical quasilinear transport fluxes in the superbanana plateau regime caused by electromagnetic waves. The transport fluxes can be used to model electromagnetic wave and the chaotic magnetic field induced thermal particle or energetic alpha particle losses in tokamaks. It is shown that the parallel component of the vector potential enhances losses when it is the sole transport mechanism. In particular, the fact that the drift resonance can cause significant transport losses in the chaotic magnetic field in the hitherto unknown low collisionality regimes is emphasized.

Electromagnetic characteristics of geodesic acoustic mode in the COMPASS tokamak

Axisymmetric geodesic acoustic mode (GAM) oscillations of the magnetic field, plasma potential and electron temperature have been identified on the COMPASS tokamak. This work brings an overview of their electromagnetic properties studied by multi-pin reciprocating probes and magnetic diagnostics. The n = 0 fluctuations form a continuous spectrum in limited plasmas but change to a single dominant peak in diverted configuration. At the edge of diverted plasmas the mode exhibits a non-local structure with a constant frequency over a radial extent of at least several centimeters. Nevertheless, the frequency still reacts on temporal changes of plasma temperature caused by an auxiliary NBI heating as well as those induced by periodic sawtooth crashes. Radial wavelength of the mode is found to be about 1–4 cm, with values larger for the plasma potential than for the electron temperature. The mode propagates radially outward and its radial structure induces oscillations of a poloidal E × B velocity, that can locally reach the level of the mean poloidal flow. Bicoherence analysis confirms a non-linear interaction of GAM with a broadband ambient turbulence. The mode exhibits strong axisymmetric magnetic oscillations that are studied both in the poloidal and radial components of the magnetic field. Their poloidal standing-wave structure was confirmed and described for the first time in diverted plasmas. In limited plasmas their amplitude scales with safety factor. Strong suppression of the magnetic GAM component, and possibly of GAM itself, is observed during co-current but not counter-current NBI.

Equilibrium potential well due to finite Larmor radius effects at the tokamak edge

We present a novel mechanism for producing an equilibrium potential well near the edge of a tokamak. Briefly, because of the difference in gyroradii between electrons and ions, an equilibrium electrostatic potential is generated in the presence of spatial inhomogeneity of the background plasma, which, in turn, produces a well associated with the radial electric field, Er, as observed at the edge of many tokamak experiments. We will show that this theoretically predicted Er field, which can be regarded as producing a long radial wavelength zonal flow, agrees well with recent experimental measurements. The relationship between the equilibrium configuration used in this study and that of the Woltjer-Taylor state will be discussed.