Azimuthal Number Research Articles

Subcritical transition of Taylor−Couette−Poiseuille flow at high radius ratio

We performed direct numerical simulations of Taylor–Couette–Poiseuille flows within an annular channel with a radius ratio of 0.883. A parametric study was conducted on subcritical transition processes of the wall-bounded combined shear flow with a torsional base-flow profile with three control parameters of F(P) representing the axial mean pressure gradient and two Reynolds numbers Rein and Reout, based on the inner cylinder and outer cylinder rotational velocities, respectively. In the set (Rein,Reout)=(400,−1000), the laminar flow becomes turbulent via finite-length and infinite-length turbulent bands, called one-way helical turbulence, as F(P) increases. Two-way helical turbulence appeared in the counterpart of the annular Poiseuille flow without cylindrical rotations, suggesting that the azimuthal Couette flow broke the symmetry of the helical turbulence of the axial Poiseuille flow. In the set of (Rein,Reout)=(800,−2000) and (1200,−3000), we found a ring-shaped localized turbulence at F(P) that provided an axial friction Reynolds number comparable to the azimuthal one. The flow states were mapped in parameter space spanned by the axial and azimuthal friction Reynolds numbers. Eight different flow regimes, including the laminar state, were identified based on turbulent statistics during these flow visualizations.

Control of the orbital angular momentum via radial numbers of structured Laguerre-Gaussian beams.

We found that the internal perturbations of the structured Laguerre-Gaussian beam in the form of two-parametric harmonic excitations of the Hermite-Gaussian (HG) modes in its composition mix up the radial and azimuthal numbers. The harmonic excitation is characterized by two parameters, one of them controls the amplitude of the HG modes, and the second parameter controls the phases of each HG mode. It was revealed that this mixing of the beam quantum numbers leads to the possibility of controlling the orbital angular momentum (OAM) by means of radial numbers. Non-zero radial numbers lead to rapid OAM oscillations as the phase parameter changes, while oscillations disappear if the radial number is zero. We have also shown that the variation of the phase parameter in a wide range of values does not change the modulus of the total topological charge of the structured beam, despite the fast OAM oscillations.

Creating a planar array of transversely polarized optical needles using a uniform line source antenna array

A method for generating a planar array of transversely polarized optical needles with prescribed characteristics is proposed firstly in this paper. The created needles are pure transversely polarized and located in the x–y plane, and perpendicular to the optical axis. In order to form the desired optical needle array, a virtual uniform line source antenna array, placed at the foci-pane of two high numerical aperture objectives, is employed to obtain the required illumination in the pupil plane by using the time-reversal holographic technique. Simulation results demonstrate that the focal field array of the identical transversely polarized optical needles constructed by the proposed method is located in the x–y plane. Parameters of the generated array can be readily controlled and customized according to practical requirements by adjusting the azimuthal direction, number, length, and spacing of needle elements. This particular array formed by transversely polarized optical fields has great potential applications in the area of parallel or synchronous operations, such as 2D simultaneous particle acceleration and manipulations and 2D parallel fabrication.

Towards Promising Platform by Using Annular Photonic Crystals to Simulate and Design Useful Mask

Human masks are considered the mainstay in air filtration and purification technologies and against the spreading of bacterial and viral infections. This paper introduces a novel design of a human mask to increase the ultraviolet germicidal irradiation effect on pathogens. The proposed design consists of a tube with an annular photonic crystal (APC) attached to the mask’s orifice, and a UV source is located in the tube’s center. The main role of this study is the enhancement of UV doses based on the reflectivity of the proposed APC. Therefore, increasing pathogens’ inactivation level in the incoming air to the mask’s orifice could be investigated. The numerical investigations demonstrated that the proposed APC could provide a complete photonic bandgap with a high reflectivity in the wavelength regime from 207 to 230 nm. In addition, we have considered the roles of the thickness of layers, inner core radius, and the azimuthal number. Meanwhile, the results showed the ability to use a wide range of core radius values without almost any variations in the optical properties of the proposed design. Such results could grant the advantage of using this design by the manufacturing of human masks with different sizes besides the inclusions in other ultraviolet germicidal irradiation applications.

Disc accretion shocks with alpha viscosity

ABSTRACT Shocks in rotating disc accretion flows under the vertically hydrostatic equilibrium are examined, taking into account the α viscosity. For the case that the stress tensor is proportional to the gas pressure, and neglects the effects of the mixture of gas and radiation pressure, we derive analytical expressions for jump conditions of disc accretion shocks with alpha viscosity; they would be useful for various disc accretion problems. As in the usual accretion disc, the alpha viscosity works as angular momentum transport and heat generation. When a steadily standing shock wave is generated in a disc, due to the viscous effect, the azimuthal velocity discontinuously decreases in the post-shock region inside the front. For sufficiently strong shocks, the post-shock azimuthal velocity vanishes; in other words, the rotating accretion flows turn to the radially accretion ones, after passing the shock front. This vanishing condition is roughly expressed as $\alpha {\cal M}_1/{\cal M}_{\varphi 1}$ 1, where α is the viscous alpha parameter, ${\cal M}_1$ the pre-shock radial Mach number, and ${\cal M}_{\varphi 1}$ the pre-shock azimuthal Mach number. Furthermore, due to the viscous heating, the disc height increases and the surface density decreases in the post-shock region, compared to the non-viscous case. This angular momentum transport via disc shocks would affect the accretion spin-up of the central objects and accretion problems in general.

Asymptotic Analysis of Nonlinear Resonance Interaction of Capillary Waves of Arbitrary Symmetry on Moving Charged Jet at Multimode Initial Deformation

The problem of research of a nonlinear resonance between capillary waves on a surface of the charged jet at multimode initial deformation moving regarding the material environment is considered. It is shown in analytical asymptotic calculations of the second order on the dimensionless amplitude of oscillations that on a surface of a jet an internal nonlinear resonant interaction of capillary waves of any symmetry, both degenerate and secondary combinational, takes place. Positions of resonances depend on physical parameters of the system: the values of the coefficient of a surface tension and of the radial electric field at a surface of a jet, the velocity of its movement regarding the material environment, the values of the wave and azimuthal numbers of the interacting waves, a range of the waves defining initial deformation.

Relating black hole shadow to quasinormal modes for rotating black holes

In this work, we explore the connection between the critical curves ("shadows") and the quasinormal mode frequencies (in the eikonal limit) of Kerr black holes. This mapping has been previously established for non-rotating black holes. We show that, the shadow seen by an distant observer at a given inclination angle, can be mapped to a family of quasinormal modes with $m/(\ell+1/2)$ bounded within certain range, where $m$ is is azimuthal node number and $\ell$ is the angular node number. We discuss the possibility of testing such relation with space-borne gravitational wave detectors and the next-generation Event Horizon Telescope.

Effect of an Azimuthal Mean Flow on the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model With Electroacoustic Feedback

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electro-acoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the azimuthal Mach number for two types of initial states and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing, or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, only spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation to an existing low-order model.

Robust higher-order optical vortices for information transmission in twisted anisotropic optical fibers

We study the propagation of light in twisted anisotropic fibers by obtaining the analytical expressions and propagation constants for higher-order modes with the azimuthal number . It is shown that for arbitrary fiber parameters, the modes are elliptically polarized optical vortices of well-defined orbital angular momentum. We reveal the phenomena of orbital birefringence and the optical Zeeman effect for the higher-order topologically charged fiber modes. Finally, circularly and linearly polarized optical vortices are demonstrated to be modes that are robust against small constant and spatially varying perturbations of both fiber material and form anisotropy; this robustness is due to the effects of the spin–orbit interaction and/or torsional-stress-induced orbital birefringence.

Stability of rotating scalar boson stars with nonlinear interactions

We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D, beginning with stationary boson star solutions. We show that the linear, non-axisymmetric instability found in mini boson stars with azimuthal number $m=1$ persists across the entire parameter space for these stars, though the timescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$ that is sufficiently far into the non-relativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar self-interactions. However, we do find regions of $m=1$ boson star parameter space where adding nonlinear interactions to the scalar potential quenches the non-axisymmetric instability, both on the non-relativistic, and the relativistic branches of solutions. We also consider select boson stars with $m=2$, finding instability in all cases. For the cases exhibiting instability, we follow the nonlinear development, finding a range of dynamics including fragmentation into multiple unbound non-rotating stars, and formation of binary black holes. Finally, we comment on the relationship between stability and criteria based on the rotating boson star's frequency in relation to that of a spherical boson star or the existence of a co-rotation point. The boson stars that we find not to exhibit instability when evolved for many dynamical times include rapidly rotating cases where the compactness is comparable to that of a black hole or neutron star.

Theory of three-magnon interaction in a vortex-state magnetic nanodot

We use vector Hamiltonian formalism (VHF) to study theoretically three-magnon parametric interaction (or three-wave splitting) in a magnetic disk existing in a magnetic vortex ground state. The three-wave splitting in a disk is found to obey two selection rules: (i) conservation of the total azimuthal number of the resultant spin-wave modes, and (ii) inequality for the radial numbers of interacting modes, if the mode directly excited by the driving field is radially symmetric (i.e. if the azimuthal number of the directly excited mode is $m = 0$). The selection rule (ii), however, is relaxed in the "small" magnetic disks, due to the influence of the vortex core. We also found, that the efficiency of the three-wave interaction of the directly excited mode strongly depends on the azimuthal and radial mode numbers of the resultant modes, that becomes determinative in the case when several splitting channels (several pairs of resultant modes) simultaneously approximately satisfy the resonance condition for the splitting. The good agreement of the VHF analytic calculations with the experiment and micromagnetic simulations proves the capability of the VHF formalism to predict the actual splitting channels and the magnitudes of the driving field thresholds for the three-wave splitting.

External Parameters Affecting on the Photoluminescence of InAs Spherical Layer Quantum Dot

Spherical layer quantum dots (SLQDs) attract a great deal of importance, and have various optoelectronics applications due to their outstanding optical and electrical properties. The photoluminescence (PL) and the electroluminescence (EL) spectra of InAs (SLQDs) were investigated theoretically under the presence of external parameters (pressure, temperature, electric field). Existing of both the temperature and the applied electric field lead to a significant decrease in photoluminescence peak energy (red-shift), while an increase existed in presence of applied hydrostatic pressure (blue-shift). Also with increasing the quantum azimuthal number the photoluminescence peak energy increase. In addition, we found no effect on the band shape of the luminescence as a result of existing such parameters. The study indicates the importance of such parameters as fitting parameters for photoluminescence spectra.

OV-bearing modes with ℓ = 2 of twisted anisotropic optical fibres

We investigated the high-order mode structure of a weakly guiding twisted anisotropic optical fibre. An analytical solution of the vector wave equation for this case is presented. We obtained analytical expressions for the higher-order modes with an azimuthal number ℓ = 2 and their propagation constants of such a fibre, considering the mutual effect of linear anisotropy of fibre’s material, twisting, including torsional mechanical stress, and spin-orbital interaction. We showed that optical vortex beams with topological charge ±2 are the modes of the fibres considered.

Digital sorting of Hermite-Gauss beams: mode spectra and topological charge of a perturbed Laguerre-Gauss beam

We developed and implemented an intensity moments technique for measuring amplitude and initial phase spectra, the topological charge (TC) and orbital angular momentum (OAM) of the Laguerre-Gauss (LG) beams decomposed into the basis of Hermite-Gaussian (HG) modes. A rigorous theoretical justification is given for measuring the TC of unperturbed LG beams with different values of radial and azimuthal numbers by means of an astigmatic transformation on a cylindrical lens. We have shown that the measured amplitude and phase spectra of the HG modes make it possible to find the orbital OAM and TC, as well as digitally sorting the HG modes and then restoring the initial singular beam.

Multi-Orthogonal High-Order Mode Converter Based on Acoustically Induced Fiber Gratings

We experimentally investigate the generation of high-order modes (HOMs) with flexible switchable output. Cascaded acoustically induced fiber gratings (AIFGs) act as mode converters. A periodic micro-bending in the AIFG is produced by travelling flexural acoustic wave, and two modes with adjacent azimuthal numbers can be coupled to each other. Different HOMs (LP21a/b and LP11a/b) could be obtained just by tuning the frequency of the radio frequency (RF) driving signal. The dependence of RF frequencies on the two acousto-optic (AO) coupling stages is theoretically analyzed and experimentally verified. Based on cascaded AIFGs mode converter, a multiple-level intensity modulator and an all-fiber Yb-doped laser with flexible mode switching output of HOMs (LP21a/b and LP11a/b) are demonstrated. Moreover, by optimizing the outer diameter of the second part of the AO coupling regions, the mode conversion between LP01 and LP21 can be realized by applying a single frequency on the piezoelectric transducer (PZT).

Whipping in gaseous flow focusing

We study both theoretically and experimentally the whipping instability in axisymmetric gaseous flow focusing realized in a converging-diverging nozzle. The lateral oscillation of both the tapering meniscus and emitted jet is explained in terms of the global linear instability of the lateral mode with the azimuthal number m=1. A comparison with previous experiments shows good agreement. The distance between the feeding capillary and the nozzle neck hardly affects the m=1 stability limit for the conditions considered in those experiments. We analyze the influence of the nozzle shape on the parameter conditions leading to whipping. As the nozzle convergence rate (the inverse of the length over which the diameter reduction takes place) increases, the flow becomes more stable under m=1 perturbations. The above results are in marked contrast with those of the axisymmetric mode m=0. For the axisymmetric mode, the minimum flow rate increases with the nozzle convergence rate, while the capillary-to-neck distance has considerable influence on the jetting-to-dripping transition. We also conduct experiments with different nozzles and capillary-to-neck distances to examine the effect of those factors on the stability of the jetting regime. The experiments allow us to distinguish between absolute whipping, in which both the tapering meniscus and the emitted jet oscillate, and convective whipping, in which the jet oscillates while the meniscus remains practically steady. Absolute whipping is observed for water and 1-cSt silicone oil focused with the nozzle with the smallest convergence rate and capillary-to-neck distance. The increase of the liquid viscosity stabilizes the liquid meniscus, producing the transition from absolute to convective whipping. In the high-viscosity case, the oscillation of the emitted jet far away from the discharge orifice is considerably affected by the shape of the nozzle in front of its neck. In fact, the increase of the convergence rate and capillary-to-neck distance eliminates the convective whipping as well. The reduction of surface tension enhances absolute whipping. We explain the appearance of the two types of whipping in terms of the flow pattern induced by the nozzle shape in front of the neck.

Tidal Asteroseismology: Possible Evidence of Nonlinear Mode Coupling in an Equilibrium State in Kepler Eclipsing Binary KIC 3230227

Abstract Previously, a series of tidally-excited oscillations were discovered in the eccentric eclipsing binary KIC 3230227. The pulsation amplitudes and phases suggest the observed oscillations are prograde quadruple modes. In this paper, we refine the analysis and extract more oscillation frequencies. We also study the temporal variations of amplitudes and phases and show that almost all modes have stable phases and amplitudes. We then focus on the non-orbital-harmonic oscillations. We consider two formation mechanisms: (1) nonlinear response of the surface convective layer, and (2) nonlinear three/multi-mode coupling. Although the former can explain some of the observed features, we find the latter mechanism is more probable. Assuming that these are coupled modes, the constant amplitude/phase over four years can be explained by either an equilibrium state in the mode coupling or modes undergoing limit cycles with very long periods. The observed frequency detuning and the calculated damping rates of the daughter modes favor the equilibrium-state interpretation. This is verified by integrating the amplitude equations of three-mode coupling. We find that the steady-state relation derived in Weinberg et al., which relates the observed frequency detuning, phase detuning, and mode damping rates, is approximately satisfied for one mode triplet. We also try to identify the azimuthal number of the modes based on the observed mode amplitude ratios and the selection rules in nonlinear three-mode coupling. We discuss further implications of these observations on nonlinear tidal asteroseismology.

Excitation of Negative Energy Surface Magnetohydrodynamic Waves in an Incompressible Cylindrical Plasma

Abstract Negative energy wave (NEW) phenomena may appear in shear flows in the presence of a wave decay mechanism and external energy supply. We study the appearance of negative energy surface waves in a plasma cylinder in the incompressible limit. The cylinder is surrounded by an axial magnetic field and by a plasma of different density. Considering flow inside and viscosity outside the flux tube, we derive dispersion relations and obtain analytical solutions for the phase speed and growth rate (increment) of the waves. It is found that the critical speed shear for the occurrence of the dissipative instability associated with NEWs and the threshold of Kelvin–Helmholtz instability (KHI) depend on the axial wavelength. The critical shear for the appearance of sausage NEW is lowest for the longest axial wavelengths, while for kink waves the minimum value of the critical shear is reached for the axial wavelength comparable to the diameter of the cylinder. The range between the critical speed of the dissipative instability and the KHI threshold is shown to depend on the difference of the Alfvén speeds inside and outside of the cylinder. For all axial wavenumbers, NEW appears for the shear flow speeds lower than the KHI threshold. It is easier to excite NEW in an underdense cylinder than in an overdense one. The negative energy surface waves can be effectively generated for an azimuthal number m = 0 with a large axial wavenumber and for higher modes (m > 0) with a small axial wavenumber.

Properties of Solar Rossby Waves from Normal Mode Coupling and Characterizing Its Systematics

Abstract Rossby waves play an important role in mediating the angular momentum of rotating spherical fluids, creating weather on Earth and tuning exoplanet orbits in distant stellar systems. Their recent discovery in the solar convection zone provides an exciting opportunity to appreciate the detailed astrophysics of Rossby waves. Large-scale Rossby waves create subtle drifts in acoustic oscillations in the convection zone, which we measure using helioseismology to image properties of Rossby waves in the interior. We analyze 20 yr of space-based observations, from 1999 to 2018, to measure Rossby-mode frequencies, line widths, and amplitudes. Spatial leakage affects the measurements of normal-mode eigenfunction coupling (which we refer to as “normal-mode coupling” in this paper) and complicates the analysis of separating out specific harmonic degree and azimuthal number of features on the Sun. Here we demonstrate a novel approach to overcome this difficulty and test it by performing synthetic tests. We find that the rms velocity of the modes is of the order of 0.5 m s−1 at the surface.

The flow regimes of the annular swirling turbulent jet

We perform Large-eddy simulations (LES) of an annular swirling turbulent jet. The swirl parameter is considered within the range S = 0.3−0.6. The Reynolds number based on the bulk velocity and outer pipe diameter is 8900 while the outer to inner diameter ratio is 2. We obtain different flow regimes without and with the vortex breakdown occurring for S = 0.4. Coherent vortical structures for each regime are indentified using the azimuthal Fourier decomposition and the Proper orthogonal decomposition (POD). The turbulent kinetic energy accumulates in the first POD modes with the azimuthal number m = 1.