Azimuthal Order Research Articles

Existence of small-scale Rossby waves points to low convective velocity amplitudes in the Sun

Inertial waves occur naturally in rotating fluids such as the Sun and the Earth's atmosphere. Rossby waves in the Sun have the potential to shed fresh light on interior turbulence and convection that prior seismic methods, reliant on sound waves, have been unable to accomplish. Here, we utilize ∼13 years of observational products taken by the space-based helioseismic and magnetic imager, onboard the solar dynamics observatory, to characterize solar equatorial Rossby waves. By examining maps of motions at the surface using two different methods, we are able to identify Rossby modes up to azimuthal order m = 30, approximately up to twice the spatial wavenumber limit of previous studies. The dispersion relation of these modes departs significantly from the classical two-dimensional Rossby-Haurwitz description. A parameter study of the effect of superadiabaticity and viscous diffusion on these inertial modes indicates that each parameter plays a role in influencing both the frequencies and linewidths of high m modes. Using the Rhines-scale relation, we constrain the root mean square amplitude of turbulent convection more tightly to ∼2 m/s, adding more evidence to the paradigm of weakly convective amplitudes at large scales.

Perfect vortex Laguerre-Gauss beams as a carrier in the MMF/FSO communication system

This paper presents a novel, to the best of our knowledge, high-speed transmission system that integrates a new structured light beam, specifically the perfect vortex Laguerre-Gaussian (PVLG) beam, with an optical code division multiple access (OCDMA) system utilizing a premutation vector (PV) code. The PVLG beams are distinguished by their unique shape, which remains nearly invariant during propagation regardless of the azimuthal order of the orbital angular momentum (OAM), facilitating the multiplexing of multiple OAM beams within the same spatial area. Additionally, the system employs hybrid multimode fiber (MMF) and free space optics (FSO) channels, with consideration of foggy weather conditions in the FSO channel. A comparative analysis between the performance of PVLG beams and standard LG beams is conducted. Performance evaluation metrics include the Q-factor, bit error rate (BER), and eye diagrams, providing comprehensive insights into received signal quality. The results demonstrate that the system utilizing PVLG beams outperforms the one using standard LG beams. Specifically, the system achieves a maximum MMF length of 0.35 km with a BER of approximately 10−4 and a Q-factor of around three when the MMF cable channel is used only. For the FSO channel, the achievable ranges are 1.1 km, 0.7 km, and 0.35 km under low fog (LF), medium fog (MF), and high fog (HF) conditions, respectively, maintaining the same BER and Q-factor values. Moreover, the hybrid MMF/FSO channel extends the transmission range to 1.2 km under LF conditions and to 0.45 km under HF conditions, with consistent BER and Q-factor values. Each of the four PVLG beams carries 40 Gbps, resulting in a total transmission capacity of 160 Gbps. Thus, the proposed system is well positioned to meet the high-speed data transmission demands of next-generation 6G networks.

A simple method improving acoustic mode identification capability based on genetic algorithms

This letter develops a simple approach of duct mode identification and reconstruction based on genetic algorithms, which can extend the azimuthal mode order range compared to the conventional method based on the (spatial) discrete Fourier transform. The underlying principle is reconstructing the dominant mode from the modal identification forward model through optimization by exploiting the sparsity of the mode amplitude vector. The performance is experimentally demonstrated for detections of one and two azimuthal modes under noisy conditions with nondominant modes. Overall, the proposed genetic-algorithm-based framework for solving acoustic inverse problems is beneficial to duct acoustic testing, particularly design evaluations of fan blades and acoustic liners for aeroengines.

Angular momentum transfer to charged particles by interaction with Laguerre–Gauss pulses

Orbital angular momentum of light and the associated Laguerre–Gauss modes have garnered increasing interest due to the many applications they promise in the fields of telecommunications and quantum information, as well as charged particle acceleration. Here, we use the numerical simulation of the dynamics of a large number of identical, charged, relativistic, but classical particles, forming a statistical ensemble and seen as test-particles in a time-dependent external electromagnetic field, to get insight into the process of a head-on collision with a pulsed Laguerre–Gauss mode. We have identified two steady-states regimes (low a0 and large a0), where the distribution of the final angular momentum gained by the particles as a function of their initial coordinates is well-behaved and does not change its structure with variations of the reduced amplitude. For small reduced amplitudes a0 of the incoming electromagnetic field, we have also found an analytic approximation of the expression for the angular momentum transferred to the particles after the pulse has left their region. Using both numerical integration and the analytic approximation, we have investigated the effects of the field’s gradient, initial phase of the field, polarization type, and azimuthal order m.

Effects of self-avoidance on the packing of stiff rods on ellipsoids.

Using a statistical-mechanics approach, we study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. Within a mean-field approximation, we show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. We find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. We compute the critical surface describing the transition between azimuthal and polar ordering in the three-dimensional parameter space (persistence length, eccentricity, and self-avoidance) and show that the critical behavior of this system is in fact related to the butterfly catastrophe model. We calculate the pressure and shear stress applied by the filament on the surface, and the injection force needed to be applied on the filament in order to insert it into the volume. We compare these results to the pure mechanical study where self-avoidance is ignored, and discuss similarities and differences.

Probing Depth Variations of Solar Inertial Modes through Normal Mode Coupling

Recently discovered inertial waves, observed on the solar surface, likely extend to the deeper layers of the Sun. Utilizing helioseismic techniques, we explore these motions, allowing us to discern inertial mode eigenfunctions in both radial and latitudinal orientations. We analyze 8 yr of space-based observations (2010–2017) taken by the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory using normal mode coupling. Couplings between the same and different-degree acoustic modes and different frequency bins are measured in order to capture the various length scales of the inertial modes. We detect inertial modes at high latitude with azimuthal order t = 1 and frequency ∼ −80 nHz, measured in a corotating frame with a rotation frequency of 453.1 nHz. This mode is present in the entire convection zone. The presence of Rossby modes may be seen down to a depth of ∼0.83R ⊙, and the Rossby signal is indistinguishable from noise below that depth for high azimuthal order. We find that the amplitudes of these modes increase with depth down to around 0.92R ⊙ and decrease below that depth. We find that the latitudinal eigenfunctions of Rossby modes deviate from sectoral spherical harmonics if we use a similar approach as adopted in earlier studies. We find that spatial leakage and even pure noise in the measurements of nonsectoral components can also explain the abovementioned characteristics of the latitudinal eigenfunctions. This realization underscores the necessity for careful interpretation when considering the latitudinal eigenfunctions of Rossby modes. Exploring the depth-dependent characteristics of these modes will enable us to capture interior dynamics distinctly, separate from p-mode seismology.

A Linear Model for Inertial Modes in a Differentially Rotating Sun

Inertial wave modes in the Sun are of interest owing to their potential to reveal new insight into the solar interior. These predominantly retrograde-propagating modes in the solar subsurface appear to deviate from the thin-shell Rossby–Haurwitz model at high azimuthal orders. We present new measurements of sectoral inertial modes at m > 15 where the modes appear to become progressively less retrograde compared to the canonical Rossby–Haurwitz dispersion relation in a corotating frame. We use a spectral eigenvalue solver to compute the spectrum of solar inertial modes in the presence of differential rotation. Focussing specifically on equatorial Rossby modes, we find that the numerically obtained mode frequencies lie along distinct ridges, one of which lies strikingly close to the observed mode frequencies in the Sun. We also find that the n = 0 ridge is deflected strongly in the retrograde direction. This suggests that the solar measurements may not correspond to the fundamental n = 0 Rossby–Haurwitz solutions as was initially suspected, but to those for a higher n. The numerically obtained eigenfunctions also appear to sit deep within the convection zone—unlike those for the n = 0 modes—which differs substantially from solar measurements and complicates inference.

Bridging the gap between annular and can-annular acoustic spectra.

In the literature on thermoacoustic instabilities in combustors, a distinction is typically made between annular and can-annular systems because these are the most common gas turbine architectures. In reality, however, annular combustors typically feature discretely symmetric elements, such as burner tubes, and can-annular combustors feature an azimuthally symmetric plenum at the turbine inlet. To better understand the general case in between the annular and can-annular extremes, we analyze the acoustic spectrum of an idealized can-annular combustion chamber with variable geometry, where the length of the axial gap distance beyond the ends of the cans-hence, the coupling strength-may be adjusted. For small gap sizes, the geometry approaches a set of isolated combustor cans, whereas for large gap sizes, it approaches that of pure annular systems. We present two theoretical models based on Bloch wave theory and validate them against finite-element simulations of the Helmholtz equation. We demonstrate that the azimuthal modes transform into the eigenmodes of an annular chamber as the gap is fully opened, and we show that below a certain frequency, all the modes in between the can-annular and annular limits can be classified by their axial and azimuthal mode orders.

Modeling Solar Oscillation Power Spectra. III. Spatiotemporal Spectra of Solar Granulation Velocity Field as Seen in HMI Velocity Measurements

We suggest a physically motivated model of the uncorrelated background, which can be used to improve the accuracy of helioseismic frequency measurements when the background contributes significantly to the formation of spectral lines of acoustic resonances. The basic assumption of our model is that the correlation length of the convective motions is small compared with the horizontal wavelength R ⊙/ℓ of the observations, where ℓ is the degree of the spherical harmonic Y ℓ m (θ, φ). When applied to solar power spectra at frequencies below acoustic resonances, the model reveals a distinct sensitivity to solar rotation: advection of the convective velocity pattern brings spatial correlations in the apparent stochastic velocity field (temporal correlations in the corotating frame induce spatial correlations in the inertial frame). The induced spatiotemporal correlations manifest themselves as an antisymmetric component in the dependence of the convective noise power on azimuthal order m, which allows us to address the solar differential rotation. With 360 days of data obtained by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we measure three components of the rotation rate as a function of latitude using only ℓ = 300. This result indicates that the model suggests a new way of measuring solar subsurface rotation. This approach can complement traditional measurements based on correlation tracking.

Spin-orbit coupling induced polarization transform in the autofocusing of ring Airy beams with hybrid polarizations.

Manipulating polarization is of significance for the application of light. Spin-orbit coupling provides a prominent pathway for manipulating the polarization of light field but generally requires tight focusing conditions or anisotropic media. In this paper, we construct ring Airy beams with hybrid polarizations and reveal the controllable polarization transforms in their autofocusing dynamics by manipulating concomitant spin-orbit coupling in free space. The numerical and experimental results show that the polarization transform is dependent on the azimuthal orders of amplitude and vortex phases of two spin constituents of ring Airy beams, that the focal spots present pure linear polarization whose orientation is determined by the initial phase when the vortex phase topological charge is equal to the amplitude angular factor, otherwise, the focal fields present cylindrical vector polarizations whose orders depend on the difference of amplitude angular orders and topological charges. Our work provides new insights for studying spin-orbit interactions and the depolarization of complex polarization.

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.

Loss-induced multiple modal coalescences in an acoustic ring cavity

Chiral exceptional points refer to a class of non-Hermitian degeneracies where two counter-propagating whispering-gallery-like eigenmodes coalesce into one travelling eigenmode, which have been utilized to create orbital angular momentum in various wave systems. However, most studies in this field have so far focused on the modal coalescence for a specific azimuthal order. In this work, we investigate the eigenmodes evolution of an acoustic ring cavity under complex spatial modulation of refractive index along the azimuthal direction. We show that a careful engineering of the complex modulation, possibly realized with acoustic metamaterials, can lead to multiple modal coalescences to produce a series of travelling eigenmodes with different orbital angular momentum orders. These coalesced eigenmodes can be directly excited by a simple source at their resonant frequencies. Our work provides a straightforward approach to the generation and manipulation of acoustic orbital angular momentum.

Solar Flare 1/f Fluctuations from Amplitude-Modulated Five-Minute Oscillation.

We first report that the solar flare time sequence exhibits a fluctuation characterized by its power spectral density being inversely proportional to the signal frequency. This is the 1/f fluctuation, or pink noise, observed ubiquitously in nature. Using GOES16 data, we found that low-energy flares (E≤Emean) display 1/f fluctuations, whereas high-energy flares (E>Emean) show a flat spectrum. Furthermore, we found that the timing sequence of the flares reveals clearer 1/f fluctuations. These observations suggest that the solar flare 1/f fluctuations are associated with low-energy phenomena. We investigated the origin of these 1/f fluctuations based on our recent hypothesis: 1/f fluctuations arise from amplitude modulation and demodulation. We propose that this amplitude modulation is encoded by the resonance with the solar five-minute oscillation (SFO) and demodulated by magnetic reconnections. We partially demonstrate this scenario by analyzing the SFO eigenmodes resolving the frequency degeneration in the azimuthal order number m using the solar rotation and resonance. Given the robust nature of 1/f fluctuations, we speculated that the solar flare 1/f fluctuations may be inherited by the various phenomena around the Sun, such as the sunspot numbers and cosmic rays. In addition, we draw parallels between solar flares and earthquakes, both exhibiting 1/f fluctuations. Interestingly, the analysis applied to solar flares can also be adapted to earthquakes if we read the SFO as Earth's free oscillation and magnetic reconnections as fault ruptures. Moreover, we point out the possibility that the same analysis also applies to the activity of a black hole/disk system if we read the SFO as the quasi-periodic oscillation of a black hole.

A Linear Operator Method to Compute the Normal Modes with Rotation of any Asymmetric 3D Planet with Pure Vector Spherical Harmonics

In order to compute the free core nutation of the terrestrial planets, such as Earth and Mars, the Moon and lower degree normal modes of the Jovian planets, we propose a linear operator method (LOM). Generalized surface spherical harmonics (GSSHs) are usually applied to the elliptical models with a stress tensor, which cannot be expressed in vector spherical harmonics explicitly. However, GSSHs involve complicated math. LOM is an alternative to GSSHs, whereas it only deals with the coupling fields of the same azimuthal order m, as is the case when a planet model is axially symmetric and rotates about that symmetry axis. We extend LOM to any asymmetric 3D model. The lower degree spheroidal modes of the Earth are computed to validate our method, and the results agree very well with what is observed. We also compute the normal modes of a two-layer Saturn model as a simple application.

Self-sustained azimuthal aeroacoustic modes. Part 2. Effect of a swirling mean flow on the modal dynamics

The whistling induced by a low-Mach turbulent flow through a deep axisymmetric cavity in a duct is investigated theoretically and experimentally. The experiments include acoustic measurements and stereoscopic particle image velocimetry (PIV). The paper focuses on the effect of a mean swirl on the dynamics of the azimuthal aeroacoustic modes. The mean swirl in the cavity has two origins: one component is imposed by a controlled tangential air injection upstream of the cavity, and the other component spontaneously arises under the action of the self-sustained azimuthal aeroacoustic mode, as explained in the companion paper, Part 1 (Faure-Beaulieu, Xiong, Pedergnana & Noiray, J. Fluid Mech., vol. 971, 2023, A21). Experiments show that the dynamics of the aeroacoustic wave is influenced by the imposed swirl. In particular, the spinning wave propagating against the swirl is promoted. To explain this, a linear perturbation analysis is performed around an incompressible mean swirling flow obtained from RANS simulations. It reveals that the dominant shear layer modes of azimuthal order 1 and −1 involved in the whistling phenomenon are helical modes winding respectively with and against the swirl, and spinning respectively in counterswirl and co-swirl directions. The counterswirl hydrodynamic mode is the least damped of the two, which is in agreement with the experimental observations. Finally, a low-order model based on the wave equation is derived. With only a few parameters, it fully reproduces the experimental observations for a wide range of imposed swirl intensity in the duct flow, and it allows us to disentangle the mechanisms responsible for this complex aeroacoustic instability.

Influence of Backbone Ladderization and Side Chain Variation on the Orientation of Diketopyrrolopyrrole-Based Donor-Acceptor Copolymers.

Ladder polymers with poly(diketopyrrolopyrrole) (DPP) moieties have recently attracted enormous interest for a large variety of opto-electronic applications. Since the rigidity of the backbone increases with ladderization, a strong influence on the self-organization of thin films is expected. We study the molecular orientation of DPP-based ladder polymers in about 50 nm thin films using polarization modulation-infrared reflection-absorption spectroscopy (PM-IRRAS). Exemplarily, for one polymer, the orientation in thicker films is qualitatively investigated by infrared spectroscopy in transmission. Further, this method allows us to rule out the effects of a possible azimuthal ordering, which would affect the analysis of the orientation by PM-IRRAS. For all polymers, the long axis of the polymer backbone is preferentially oriented parallel to the substrate surface, pointing to a high degree of ordering. It is suggested that the choice of the side chains might be a promising way to tune for face-on and edge-on orientations. The exemplarily performed investigation of interface properties on substrates with different work functions suggests that the choice of the side chains has a minor effect on the interfacial electronic interface structure.

Accurate mode purity measurement of ring core fibers with large mode numbers from the intensity distribution only

Mode purity measurement is crucial for various applications utilizing few-mode fibers and related devices. In this paper, we propose a simple and accurate method for measuring the mode purity of the output optical field in few-mode ring-core fibers (RCFs). Mode purity can be calculated solely from the outgoing intensity distribution with high precision. This method is theoretically capable of measuring the mode purity of RCFs that support orbital angular momentum modes with an infinite number of azimuthal orders and has strong applicability to various RCF types and image qualities simultaneously. We demonstrate our approach numerically and verify it experimentally in a few-mode RCF supporting four (five) mode groups at 1550 (1310) nm. A polarization test method is proposed to verify its accuracy. We believe that this straightforward and cost-effective characterization method for RCFs and RCF-based devices can promote the development of mode-division multiplexing technology and its applications.

Forcing of slow density waves in the C ring by Saturn's quasi-toroidal normal modes

We calculate Saturn's quasi-toroidal normal modes of azimuthal order three for several candidate models for the interior stratification. We propose that these oscillations are responsible for exciting a class of slowly propagating spiral density waves observed in the C ring, possessing the same azimuthal symmetry and pattern speeds, that cluster near the rotation rate of the planet. Both prograde and retrograde propagation relative to the planetary rotation are observed. We find that we can construct interior models for which the pattern speeds of the normal modes align with those of a majority of the slow density waves. Excitation of the retrograde density waves requires retrograde toroidal modes with matching pattern speeds. We find that in order to support such modes, the interior model must include a layer of positive static stability in the molecular hydrogen envelope. The model that performs best places the peak of the static stability at a fractional radius of 0.85, near the radius of the semi-conductive layer where Saturn's zonal jets are inferred to decay. The properties of the toroidal modes are less sensitive to the stratification in the deep interior, hence our results neither confirm nor contradict the presence of a dilute core. When differential rotation is included in the form of zonal winds based on analysis of Cassini gravity and magnetic field data, we find that several toroidal modes become inertially unstable, raising the possibility that this instability is the principal mechanism for their excitation. However, while we are able to construct interior models that align the pattern speeds of a few unstable retrograde modes with those of prominent density waves in the ring, the same models fail with respect to the unstable prograde modes. Consequently, the significance of the instability mechanism remains an open question. Our results suggest that the interaction of Saturn's quasi-toroidal modes with the C ring provides an important source of new, complementary constraints on the planet's internal stratification and that further study of these modes is warranted.

Unresolved Rossby and gravity modes in 214 A and F stars showing rotational modulation

ABSTRACT Here, we report an ensemble study of 214 A- and F-type stars observed by Kepler, exhibiting the so-called hump and spike periodic signal, explained by Rossby modes (r modes) – the hump – and magnetic stellar spots or overstable convective (OsC) modes – the spike, respectively. We determine the power confined in the non-resolved hump features and find additional gravity-mode (g-mode) humps always occurring at higher frequencies than the spike. Furthermore, we derive projected rotational velocities from FIES, SONG, and HERMES spectra for 28 stars and the stellar inclination angle for 89 stars. We find a strong correlation between the spike amplitude and the power in the r and g modes, which suggests that both types of oscillations are mechanically excited by either stellar spots or OsC modes. Our analysis suggests that stars with a higher power in m = 1 r-mode humps are more likely to also exhibit humps at higher azimuthal orders (m = 2, 3, or 4). Interestingly, all stars that show g-mode humps are hotter and more luminous than the observed red edge of the δ Scuti instability strip, suggesting that either magnetic fields or convection in the outer layers could play an important role.

Tip flow on rotating instability on an axial compressor with different tip clearances

Rotating instability (RI) as an unsteady phenomenon usually occurs at off-design conditions in compressors, featuring a broadband hump in the pressure spectra below the blade passing frequency (BPF). RI phenomenon could not only cause deterioration to the performance, but also lead to tip clearance noise or non-synchronous vibration to the compressor. In this paper a detailed experiment was carried out in a low-pressure single-rotor compressor. By replacing the casing the relative tip clearance size was changed and the time-resolved wall pressure with a distinct RI signature was thus measured under several different conditions through the Kulite pressure transducers both circumferentially and chordwise installed. The temporal-spatial distribution of RI signature evolution with the flow coefficient is interrogated, and its propagation characteristics are also investigated through the cross-correlation method. Moreover, the quasi-instantaneous contour measured by the chordwise transducers shows no distinct flow structure which could be connected to the RI signature, i.e., the prestall disturbance. Therefore, a quasi-SFT method is developed to identify different disturbance counts and the corresponding relationship between the disturbance count per revolution and the azimuthal mode order could thus be strictly established. The prestall disturbance is found to originate from the mid-chord positions as RI initiates and travel upstream as the reduction of flow coefficient, and eventually reaches the leading edge as rotating stall occurs. Furthermore, the location of prestall disturbances is proven to be independent on the blade position. These findings describe the tip flow field when the RI mode orders are relatively high, and provide new insights for the shear layer instability theory as RI mechanism.