Non-axisymmetric Modes Research Articles

Vertical Shear Instability with Partially Reflecting Boundary Conditions

Abstract The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary disks. Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disk surfaces. VSI depends critically on the boundary behaviors of waves at the disk surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disk surfaces naturally lead to non-symmetric modes relative to the disk midplane. The potential implications of our studies for further understanding planetary formation and evolution in protoplanetary disks (PPDs) are also briefly discussed.

In LIGO’s Sight? Vigorous Coherent Gravitational Waves from Cooled Collapsar Disks

We present the first numerical study of gravitational waves (GWs) from collapsar disks, using state-of-the-art 3D general relativistic magnetohydrodynamic simulations of collapsing stars. These simulations incorporate a fixed Kerr metric for the central black hole (BH) and employ simplified prescriptions for disk cooling. We find that cooled disks with an expected scale height ratio of H/R ≳ 0.1 at ∼10 gravitational radii induce Rossby instability in compact, high-density rings. The trapped Rossby vortices generate vigorous coherent emission regardless of disk magnetization and BH spin. For BH mass of ∼10 M ⊙, the GW spectrum peaks at ∼100 Hz, with some breadth due to various nonaxisymmetric modes. The spectrum shifts toward lower frequencies as the disk viscously spreads and the circularization radius of the infalling gas increases. Weaker-cooled disks with H/R ≳ 0.3 form a low-density extended structure of spiral arms, resulting in a broader, lower-amplitude spectrum. Assuming an optimistic detection threshold with a matched-filter signal-to-noise ratio of 20 and a rate similar to Type Ib/c supernovae, LIGO–Virgo–KAGRA (LVK) could detect ≲1 event annually, suggesting that GW events may already be hidden in observed data. Third-generation GW detectors could detect dozens to hundreds of collapsar disks annually, depending on the cooling strength and the disk formation rate. The GW amplitudes from collapsar disks are ≳100 times higher with a substantially greater event rate than those from core-collapse supernovae, making them potentially the most promising burst-type GW class for LVK and Cosmic Explorer. This highlights the importance of further exploration and modeling of disk-powered GWs, promising insights into collapsing star physics.

Effects of Halo Spin on the Formation and Evolution of Bars in Disk Galaxies

The spin of dark halos has been shown to significantly affect bar formation and evolution in disk galaxies. To understand the physical role of halo spin in bar formation, we run N-body simulations of isolated, Milky Way–sized galaxies by varying the halo spin parameter in the range −0.16 ≤ λ ≤ 0.16 and the bulge mass. We find that our adopted halo alone is subject to swing amplification of an m = 2 nonaxisymmetric mode rotating in the same sense as the halo, which assists or inhibits the bar formation in a disk depending on its sense of rotation. The m = 2 mode in the disk, growing via swing amplification, interacts constructively (destructively) with the m = 2 mode in the prograde (retrograde) halo, promoting (delaying) bar formation. A bar grows by losing its angular momentum primarily to a halo. Since the halo particles inside (outside) the corotation resonance with the bar can emit (absorb) angular momentum to (from) the bar, the bar pattern speed decays more slowly for larger λ > 0, while it decreases relatively fast almost independent of λ ≤ 0. Models with a strong bar develop a boxy peanut-shaped bulge. In models without a bulge, this occurs rapidly via buckling instability, while bars with a bulge thicken gradually without undergoing buckling instability. Among the models considered in the present work, the bar in the λ = 0.06 model with a bulge of 10% of the disk mass best describes the Milky Way in terms of its length and pattern speed.

An application of a beamforming technique, linear acoustic array and robot for pipe condition localization

Pipe inspection robots with sensors significantly enhance the maintenance of water systems by enabling early defect detection and reducing the risks of leaks and environmental damage. This paper introduces a sparse representation acoustic beamformer designed to locate artefacts within pipes using a short linear microphone array on a robot. The primary contributions include: (i) a new acoustic beamforming approach based on sparse representation that accurately predicts pipe conditions with a localization error within 3 % of the sensing distance; (ii) an enhanced beamforming algorithm combining plane wave and first non-axisymmetric mode, extending the frequency range from < 1300 Hz to < 2200 Hz in a 150 mm diameter pipe (an increase by 1.69 times), effectively managing unwanted acoustic reverberations and distinguishing blockages from lateral connections; and (iii) a novel robust algorithm predicting pipe length with an error margin within 2 %. This research advances acoustic sensing technologies for autonomous mobile robots inspecting buried pipes.

Magnetorotational dynamo can generate large-scale vertical magnetic fields in 3D GRMHD simulations of accreting black holes

ABSTRACT Jetted astrophysical phenomena with black hole engines, including binary mergers, jetted tidal disruption events, and X-ray binaries, require a large-scale vertical magnetic field for efficient jet formation. However, a dynamo mechanism that could generate these crucial large-scale magnetic fields has not been identified and characterized. We have employed three-dimensional global general relativistic magnetohydrodynamical simulations of accretion discs to quantify, for the first time, a dynamo mechanism that generates large-scale magnetic fields. This dynamo mechanism primarily arises from the non-linear evolution of the magnetorotational instability (MRI). In this mechanism, large non-axisymmetric MRI-amplified shearing wave modes, mediated by the axisymmetric azimuthal magnetic field, generate and sustain the large-scale vertical magnetic field through their non-linear interactions. We identify the advection of magnetic loops as a crucial feature, transporting the large-scale vertical magnetic field from the outer regions to the inner regions of the accretion disc. This leads to a larger characteristic size of the, now advected, magnetic field when compared to the local disc height. We characterize the complete dynamo mechanism with two time-scales: one for the local magnetic field generation, $t_{\rm gen}$, and one for the large-scale scale advection, $t_{\rm adv}$. Whereas the dynamo we describe is non-linear, we explore the potential of linear mean field models to replicate its core features. Our findings indicate that traditional $\alpha$-dynamo models, often computed in stratified shearing box simulations, are inadequate and that the effective large-scale dynamics is better described by the shear current effects or stochastic $\alpha$-dynamos.

Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Accretion disks are highly unstable to magnetic instabilities driven by shear flow, where classically, the axisymmetric, weak-field magnetorotational instability (MRI) has received much attention through local WKB approximations. In contrast, discrete nonaxisymmetric counterparts require a more involved analysis through a full global approach to deal with the influence of the nearby magnetohydrodynamic (MHD) continua. Recently, rigorous MHD spectroscopy identified a new type of ultralocalized, nonaxisymmetric instability in global disks with super-Alfvénic flow. These super-Alfvénic rotational instabilities (SARIs) fill vast unstable regions in the complex eigenfrequency plane with (near eigen)modes that corotate at the local Doppler velocity and are radially localized between Alfvénic resonances. Unlike discrete modes, they are utterly insensitive to the radial disk boundaries. In this work, we independently confirm the existence of these unprecedented modes using our novel spectral MHD code Legolas, reproducing and extending our earlier study with detailed eigenspectra and eigenfunctions. We calculate the growth rates of SARIs and MRI in a variety of disk equilibria, highlighting the impact of field strength and orientation, and find correspondence with analytical predictions for thin, weakly magnetized disks. We show that nonaxisymmetric modes can significantly extend instability regimes at high mode numbers, with maximal growth rates comparable to those of the MRI. Furthermore, we explicitly show a region filled with quasi-modes whose eigenfunctions are extremely localized in all directions. These modes must be ubiquitous in accretion disks, and play a role in local shearing box simulations. Finally, we revisit recent dispersion relations in the appendix, highlighting their relation to our global framework.

Damping Obliquities of Hot Jupiter Hosts by Resonance Locking

When orbiting hotter stars, hot Jupiters are often highly inclined relative to their host star equator planes. By contrast, hot Jupiters orbiting cooler stars are more aligned. Prior attempts to explain this correlation between stellar obliquity and effective temperature have proven problematic. We show how resonance locking—the coupling of the planet's orbit to a stellar gravity mode (g-mode)—can solve this mystery. Cooler stars with their radiative cores are more likely to be found with g-mode frequencies increased substantially by core hydrogen burning. Strong frequency evolution in resonance lock drives strong tidal evolution; locking to an axisymmetric g-mode damps semimajor axes, eccentricities, and, as we show for the first time, obliquities. Around cooler stars, hot Jupiters evolve into spin–orbit alignment and may avoid engulfment. Hotter stars lack radiative cores and therefore preserve congenital spin–orbit misalignments. We focus on resonance locks with axisymmetric modes, supplementing our technical results with simple physical interpretations, and show that nonaxisymmetric modes also damp obliquity. Outstanding issues regarding the dissipation of tidally excited modes and the disabling of resonance locks are discussed quantitatively.

Nonaxisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments: Linear and nonlinear dynamics

Nonaxisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments: Linear and nonlinear dynamics

The effect of 3D surface roughness on acoustic wave propagation in a cylindrical waveguide

This paper studies the acoustic wave scattering and attenuation in a cylindrical waveguide (pipe) with wall roughness varying along all three dimensions and roughness height smaller than the acoustic wavelength. Using the decomposition of the acoustic wave field into deterministic and random components, small perturbation method and Fourier transform the analytical solution of a 3-D averaged acoustic wave field is obtained. The correction term describing the mechanism of wave attenuation caused by roughness and determined by the modal cross-talk is also derived. The solution for the plane wave is validated in the frequency range extended well beyond the second cut-off frequency, where the crosstalk between the fundamental and non-axisymmetric modes are observed. The analytical solution is compared with the numerical results obtained with the Monte-Carlo method and Finite Element solver. The numerical study results have demonstrated a close agreement with the analytical solution for the averaged sound field, dispersion curves, and the wave attenuation effect expressed as the wavenumber correction term. A key novelty of this work is a comprehensive analysis of wave dispersion and cut-off frequency changes due to the presence of 3-D wall roughness in a pipe.

Role of the edge electric field in the resonant mode-particle interactions and the formation of transport barriers in toroidal plasmas

The impact of an edge radial electric field on the particle orbits and the orbital spectrum in an axisymmetric toroidal magnetic equilibrium is investigated using a guiding centre canonical formalism. Poloidal and bounce/transit-averaged toroidal precession frequencies are calculated, highlighting the role of the radial electric field. The radial electric field is shown to drastically modify the resonance conditions between particles with certain kinetic characteristics and specific perturbative non-axisymmetric modes, and to enable the formation of transport barriers. The locations of the resonances and the transport barriers that determine the particle, energy and momentum transport are shown to be accurately pinpointed in the phase space by employing the calculated orbital frequencies.

Solar Tachocline Confinement by the Nonaxisymmetric Modes of a Dynamo Magnetic Field

We recently presented the first 3D numerical simulation of the solar interior for which tachocline confinement was achieved by a dynamo-generated magnetic field. In this follow-up study, we analyze the degree of confinement as the magnetic field strength changes (controlled by varying the magnetic Prandtl number) in a coupled radiative zone (RZ) and convection zone (CZ) system. We broadly find three solution regimes, corresponding to weak, medium, and strong dynamo magnetic field strengths. In the weak-field regime, the large-scale magnetic field is mostly axisymmetric with regular, periodic polarity reversals (reminiscent of the observed solar cycle) but fails to create a confined tachocline. In the strong-field regime, the large-scale field is mostly nonaxisymmetric with irregular, quasi-periodic polarity reversals and creates a confined tachocline. In the medium-field regime, the large-scale field resembles a strong-field dynamo for extended intervals but intermittently weakens to allow temporary epochs of strong differential rotation. In all regimes, the amplitude of poloidal field strength in the RZ is very well explained by skin-depth arguments, wherein the oscillating field that gives rise to the skin depth (in the medium- and strong-field cases) is a nonaxisymmetric field structure at the base of the CZ that rotates with respect to the RZ. These simulations suggest a new picture of solar tachocline confinement by the dynamo, in which nonaxisymmetric, very long-lived (effectively permanent) field structures rotating with respect to the RZ play the primary role, instead of the regularly reversing axisymmetric field associated with the 22 yr cycle.

The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$ , where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$ . For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

Effect of inhaled air temperature on mucus dynamics in the proximal airways

The aim of the present study is to understand the role of steam/cold-air inhalation on the mucus layer dynamics in the proximal airways. We model these flows as a viscoelastic liquid (lining the inner side of a tube) sheared by a turbulent airflow and subjected to a radial heat flow. The linear stability analysis of the resulting flow is carried out using numerical and thin-film approaches. The air–mucus interface tension, coupled with the azimuthal curvature, leads to the previously predicted axisymmetric capillary mode responsible for airway closure in distal airways. The viscoelasticity of the mucus leads to axisymmetric and new non-axisymmetric elastic modes, with the former possessing a higher growth rate. The axisymmetric elastic and capillary modes merge to give rise to a new ‘elasto-capillary mode’ possessing a growth rate nearly equal to the combined growth rate of the elastic and capillary modes. The analysis predicts a strong stabilising effect of the thermocapillarity induced by steam inhalation on the elasto-capillary mode. Thus steam decreases airway resistance, which could explain the observed therapeutic effect of steam inhalation. The opposite is the case when the inhaled air is colder than the body temperature, in agreement with the observations. The theoretical predictions are corroborated by the physical mechanism explaining the suppression/amplification of the elasto-capillary mode due to thermocapillarity.

Microphone array analysis of the first non-axisymmetric mode for the detection of pipe conditions.

This paper reports on the use of a circular microphone array to analyze the reflections from a pipe defect with enhanced resolution. A Bayesian maximum a posteriori algorithm is combined with the mode decomposition approach to localize pipe defects with six or fewer microphones. Unlike all previous acoustic reflectometry techniques, which only estimate the location of a pipe defect along the pipe, the proposed method uses the phase information about the wave propagated in the form of the first non-axisymmetric mode to estimate its circumferential position as well as axial location. The method is validated against data obtained from a laboratory measurement in a 150 mm diameter polyvinyl chloride pipe with a 20% in-pipe blockage and 100 mm lateral connection. The accuracy of localization of the lateral connection and blockage attained in this measurement was better than 2% of the axial sensing distance and 9° error in terms of the circumferential position. The practical significance of this approach is that it can be implemented remotely on an autonomous inspection robot so that accurate axial location and circumferential position of lateral connections and small blockages can be estimated with a computationally efficient algorithm.

Influence of quality factor on operating mode of TM&lt;sub&gt;02&lt;/sub&gt; mode relativistic backwave oscillator

&lt;sec&gt;The mode competition in an overmoded relativistic backward wave oscillator is studied through theoretical analysis and three-dimensional particle-in-cell simulation in this work. Based on the quality factor and coupling impedance, the mode selection for a TM&lt;sub&gt;02&lt;/sub&gt; mode backward wave oscillator is achieved, and its output power and magnetic field strength are optimized in the simulation.&lt;/sec&gt;&lt;sec&gt;The quality factor is related to the group velocity and end reflection of each mode. The dispersion curves of some non-axisymmetric modes are very close, and the group velocities are basically equal. Therefore, the end reflection needs considering to distinguish between the quality factors of different modes. In frequency domain simulation, analyzing the quality factor of each mode by using the &lt;i&gt;S&lt;/i&gt;&lt;sub&gt;11&lt;/sub&gt; parameter curve can avoid calculating the end reflection.&lt;/sec&gt;&lt;sec&gt;The three-dimensional simulation results show that the coupling impedance and quality factor jointly affect the operating mode. When the coupling impedance advantage of the working mode is not obvious, changing the resonant frequency of the high-frequency structure can affect the beam-wave interaction process, thereby changing the excitation mode. When the advantage is obvious, the beam-wave interaction of the excitation mode will not be destroyed by the resonant mode, and other modes of microwave output mainly come from the conversion of the same frequency modes. Due to the constant dispersion curve, the effect of resonance on the mode is essentially the effect of the quality factor on the mode dominated by the end reflection.&lt;/sec&gt;&lt;sec&gt;The insensitive parameters and the electron beam radius obtained from the simulation are used as the optimal parameters, and the automatic optimization algorithm is used in combination with the two-dimensional simulation to perform multi-objective optimization design in the above device. The final output power of the backward wave oscillator reaches 534 MW, with an efficiency of 23.64%, an increase of 221.7% compared with the efficiency of the original device. The device operating mode remains stable, with a power ratio of TM&lt;sub&gt;02&lt;/sub&gt; mode reaching 94.95%.&lt;/sec&gt;

Non-axisymmetric modes in ultrathin annular liquid films coating a cylindrical fiber

This paper presents a detailed analysis of the three-dimensional stability properties of an annular liquid film coating a cylindrical fiber in the presence of van der Waals (vdW) interactions, whose influence depends on the wettability of the solid by the liquid. Under wetting conditions, vdW interactions can stabilize a uniform annular film when its thickness is smaller than a critical value that depends only on the fiber radius, the Hamaker constant, and the surface tension coefficient [Quéré et al., Science 249(4974), 1256–1260 (1990)]. In contrast, under non-wetting conditions, both surface tension and vdW forces contribute to destabilize the interface, and non-axisymmetric modes may become dominant depending on the thickness of the film and the relative strength of the surface tension and vdW forces. We perform temporal stability analyses of both the Stokes and lubrication equations of motion, allowing us to reveal the dominant azimuthal mode, as well as the optimal axial wavenumber and the corresponding temporal growth rate, as a function of the relevant governing parameters.

Dynamical Analysis of the Maclaurin Disk with Velocity Dispersion and Its Influence on the Formation of the Bar

We investigate the influence of Toomre’s Q parameter on the bar-forming dynamics of the Maclaurin disk using N-body simulations. According to Toomre’s criterion, the local velocity dispersion parametrized by Q ≥ 1 is required to suppress the local axisymmetric instability but, in turn, it deviates particle orbits from a nearly circular limit in which particle natural frequencies are calculated. We resolve this by including the effect of velocity dispersion, as the pressure potential, into the effective potential with the gravitational potential. With this formulation, a circular orbit approximation is retrieved. The effective potential hypothesis can describe the Q dependence of angular and epicyclic motions of the processes of the formation of a bar and the established bars reasonably well provided that Q ≥ 1. This indicates the influence of the initial Q imprinted on the entire disk dynamics and not only that Q serves as the indicator of stability. In addition, we perform a stability test for the disk-in-halo systems. With the presence of a halo, disks are more susceptible to the formation of a bar as seen by the elevated critical Q than that for the isolated disk. This is attributed to the differential rotation that builds the unstable non-axisymmetric spiral modes more efficiently, which are the ingredients of the bar instability.

A Spectral Method Algorithm for Modeling the Dispersion of Non-Axisymmetric Modes in Fluid-Filled Elastic Tubes

In order to design a low-noise water-filled pipeline system, it is necessary to obtain knowledge of the dispersion characteristics of axial propagation modes in different water-filled elastic tubes. In this work, an algorithm is developed based on the spectral method, which has previously been used to solve the dispersion of axisymmetric modes in cylindrical structures but has not yet been applied to non-axisymmetric modes. The algorithm can obtain the dispersion characteristics, modal displacement, and stress distribution of axial propagation modes in a fluid-filled elastic multi-layer tube. The algorithm behaves well both at low and ultrasonic frequencies, and it is suitable for any tube dimensions, wall thickness and layers. The results of a water-filled PMMA tube obtained using the spectral method algorithm were verified using a COMSOL simulation, while the dispersion curves of the same tube from the literature were found to be missing some low-order modes. In addition, the dispersion curves of a water-filled three-layer tube are given. The spectral method algorithm has the advantages of fast calculation speed, less computational resources consumed, accurate results, and no modal omission.

Walking droplets have been halted

The swinging motion of the eigenmodes of a free inviscid drop has been known for nearly a century. Yet, as the drop sits on a solid substrate, getting flattened by gravity, analytical solutions waver due to the non-spherical base state and the dynamics of the three-phase contact line. The recent paper by Zhang et al. (J. Fluid Mech., vol. 962, 2023, A10) investigated the effect of gravity on the harmonic modes of sessile droplets for free and pinned contact line conditions. An effective boundary element method has been used to solve both axisymmetric and non-axisymmetric modes for a variety of Bond numbers and static contact angles, also revising on the way a debated capillary instability.

Gravity waves in strong magnetic fields

ABSTRACT Strong magnetic fields in the cores of stars are expected to significantly modify the behaviour of gravity waves: this is likely the origin of suppressed dipole modes observed in many red giants. However, a detailed understanding of how such fields alter the spectrum and spatial structure of magnetogravity waves has been elusive. For a dipole field, we analytically characterize the horizontal eigenfunctions of magnetogravity modes, assuming that the wavevector is primarily radial. For axisymmetric modes (m = 0), the magnetogravity wave eigenfunctions become Hough functions, and they have a radial turning point for sufficiently strong magnetic fields. For non-axisymmetric modes (m ≠ 0), the interaction between the discrete g-mode spectrum and a continuum of Alfvén waves produces nearly discontinuous features in the fluid displacements at critical latitudes associated with a singularity in the fluid equations. We find that magnetogravity modes cannot propagate in regions with sufficiently strong magnetic fields, instead becoming evanescent. When encountering strong magnetic fields, ingoing gravity waves are likely refracted into outgoing slow magnetic waves. These outgoing waves approach infinite radial wavenumbers, which are likely to be damped efficiently. However, it may be possible for a small fraction of the wave power to escape the stellar core as pure Alfvén waves or magnetogravity waves confined to a very narrow equatorial band. The artificially sharp features in the Wentzel–Kramers–Brillouin-separated solutions suggest the need for global mode solutions which include small terms neglected in our analysis.