Non-axisymmetric Waves Research Articles

Generation and propagation of elastic waves on a pipe by open-shell transducers

This paper deals with the generation and propagation of elastic waves on an empty pipe and on a water-filled pipe by open-shell transducers theoretically, numerically, and experimentally. The dispersion equations relating wave speed to frequency were derived by using the cylindrical shell theory. The theoretical analysis was verified by comparing the calculated dispersion curves with the frequencywavenumber spectrums obtained from the finite-element analysis and by comparing the calculated wave speeds with the results measured by using open-shell transducers as transmitters and receivers. The finite-element analysis revealed that the waves of only evennumbered wave modes were generated by the open-shell transducers symmetrically located along the circumference of the pipe and that the axisymmetric wave propagates faster than non-axisymmetric waves.

Guided wave propagation in single and double layer hollow cylinders embedded in infinite media

Millions of miles of pipes are being used for the transportation, distribution, and local use of petroleum products, gas, water, and chemicals. Most of the pipes are buried in soil, leading to the significance of the study on the subject of guided wave propagation in pipes with soil influence. Previous investigations of ultrasonic guided wave propagation in an elastic hollow cylinder and in an elastic hollow cylinder coated with a viscoelastic material have led to the development of inspection techniques for bare and coated pipes. However, the lack of investigation on guided wave propagation in hollow cylinders embedded in infinite media like soil has hindered the development of pipe inspection methods. Therefore the influence of infinite media on wave propagation is explored in this paper. Dispersion curves and wave structures of both axisymmetric and nonaxisymmetric wave modes are developed. Due to the importance of the convergence of numerical calculations, the requirements of thickness and element number of the finite soil layer between hollow cylinder and infinite element layer are discussed, and an optimal combination is obtained in this paper. Wave structures are used for the mode identification in the non-monotonic region caused by the viscoelastic properties of coating and infinite media.

Asymptotic analysis of nonlinear nonaxisymmetric waves on the surface of a neutral dielectric jet in a longitudinal electrostatic field

The problem of calculation of finite-amplitude waves on the cylindrical surface of an ideal incompressible dielectric liquid jet in a uniform electrostatic field collinear to the unperturbed jet axis is solved using a second-order asymptotic analytic procedure in ratio of the wave amplitude to the jet radius. Nonlinear corrections to the jet profile, velocity field potential, and electrostatic potentials inside and outside the jet are of resonant nature. The degenerate resonant interaction between the wave determining the initial strain and the waves excited due to nonlinearity of the hydrodynamic equations can take place for waves with different symmetries (different azimuth numbers).

Papaloizou-Pringle instability of magnetized accretion tori

Hot accretion tori around a compact object are known to be susceptible to a global hydrodynamical instability, the so-called Papaloizou-Pringle (PP) instability, arising from the interaction of non-axisymmetric waves across the corotation radius, where the wave pattern speed matches the fluid rotation rate. However, accretion tori produced in various astrophysical situations (e.g., collapsars and neutron star binary mergers) are likely to be highly magnetized. We study the effect of magnetic fields on the PP instability in incompressible tori with various magnetic strengths and structures. In general, toroidal magnetic fields have significant effects on the PP instability: For thin tori (with the fractional width relative to the outer torus radius much less than unity), the instability is suppressed at large field strengths with the corresponding toroidal Alfven speed $v_{A\phi}\go 0.2r\Omega$ (where $\Omega$ is the flow rotation rate). For thicker tori (with the fractional width of order 0.4 or larger), which are hydrodynamically stable, the instability sets in for sufficiently strong magnetic fields (with $v_{A\phi}\go 0.2 r\Omega$). Our results suggest that highly magnetized accretion tori may be subjected to global instability even when it is stable against the usual magneto-rotational instability.

Nonlinear propagating kink waves in thin magnetic tubes

The propagation of nonlinear nonaxisymmetric waves along a magnetic tube in an incompressible plasma embedded in a magnetic-free plasma is studied. The plasma and magnetic parameters in the tube core as well as plasma parameters in the external plasma are constant. Between the tube core and the magnetic-free plasma there is a thin annulus where the Alfvén speed monotonically decreases to zero. In this annulus there is a cylindrical surface where the phase speed of the global wave matches the local Alfvén speed. In the vicinity of this surface there is an efficient conversion of the global wave energy in the energy of local Alfvén waves. This results in the resonant absorption of the global wave and, as a consequence, in the global wave damping. The wave amplitude is assumed to be small and used as a small parameter in the singular perturbation method that is used to derive the nonlinear governing equation for nonaxisymmetric waves. This equation accounts both for nonlinearity and wave damping due to resonant absorption. A particular class of solutions of this equation in the form of helical waves is studied numerically. The main result obtained in this study is that nonlinearity accelerates the wave damping. It also distorts the shape of the tube boundary due to nonlinear generation of fluting modes.

Short Timescale Core Dynamics: Theory and Observations

Fluid motions in the Earth’s core produce changes in the geomagnetic field (secular variation) and are also an important ingredient in the planet’s rotational dynamics. In this article we review current understanding of core dynamics focusing on short timescales of years to centuries. We describe both theoretical models and what may be inferred from geomagnetic and geodetic observations. The kinematic concepts of frozen flux and magnetic diffusion are discussed along with relevant dynamical regimes of magnetostrophic balance, tangential geostrophy, and quasi-geostrophy. An introduction is given to free modes and waves that are expected to be present in Earth’s core including axisymmetric torsional oscillations and non-axisymmetric Magnetic-Coriolis waves. We focus on important recent developments and promising directions for future investigations.

Instability of the lateral surface of strongly charged jets in a collinear flow of material environment

On the basis of the analysis of the dispersion equation for nonaxisymmetric capillary waves with an azimuthal number equal to two on a surface of a charged cylindrical jet of an ideal incompressible conductive fluid, it is shown that the influence of the flow has a destabilizing character. The instability of the nonaxisymmetric waves with an azimuthal number equal to two has a threshold character based on both the speed and on size of the electrical charge per unit of length of the jet.

Progress in the analysis of non-axisymmetric wave propagation in a homogeneous solid circular cylinder of a piezoelectric transversely isotropic material

Non-axisymmetric waves in a free homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization are investigated on the basis of the linear theory of elasticity and linear electromechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained through the application of the mechanical and two types of electric boundary conditions at the surface of the cylinder. A convenient method of calculating dispersion curves and phase velocities is discussed, and resulting curves are presented for propagating and evanescent waves for the piezoelectric ceramic material PZT-4 for non-axisymmetric modes of circumferential wave number m=1. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the strength of the electromechanical coupling.

Formation of a single spiral arm from a central marking-admixture spot on a compound-vortex surface

Interest in studying the structure and dynamics ofvortices—the traditional objects of investigation in themechanics of fluids—has grown in recent years due tothe development of remote methods, which made itpossible to detect large groups of discrete vortex flowsin the atmosphere, ocean, and laboratory installations.The pronounced spiral structures with a transverse sizefrom several hundreds of meters to hundreds of kilometers are observed in the ocean [1, 2]. Vortices ofeven larger sizes are visualized by cloudy systems in theatmosphere [3]. The conditions and dynamics of theirformation remain insufficiently investigated.Under laboratory conditions, the dyespot transformation into spiral arms on the surface of a fluid in auniformly rotating pool of cylindrical or rectangularcross section was observed early in the last century [4].The dye penetrated deep into the fluid along thincylindrical surfaces figuratively called “the dye wall.”Individual observations [4] were repeated after30 years in several separate experiments [5], the interpretation of which was based on the analogy betweentwodimensional rotating and stratified flows. Such ananalogy for the twodimensional flows was justifiedlater in [6]. The spiral structures can be seen in individual horizontal cross sections within the thickness ofthe fluid rotating in the closed container in which nonaxisymmetric inertial waves [7] were artificiallyexcited.Although the illustrations from a previous study [4]were included in a number of monographs [8], thedyetransport mechanisms were not investigated,which is explained by the difficulty in carrying themout and in the interpretation of results of fine experiments in globally rotating fluids.A simpler flow allowing one to study the effect ofrotation on matter transport is the composite vortexformed by a rotating disk in an open cylindrical container. Here the free surface, the shape of whichreflects the pressure distribution, remains open andmakes it possible to introduce a marking admixture atan arbitrary distance from the rotation axis as in thecase of a globally rotating system [4, 5]. Previousexperiments showed that the dye spot introduced intoan arbitrary point of the compositevortex surface outside of the rotation axis is transformed into spiral armson the free surface and into dyed cylindrical surfaces inits body [9]. The pattern of the flow formed as a resultof introducing a marking admixture in the center ofthe composite vortex was not studied previously. Inthis study, we traced for the first time the transformation of a round spot of the marking admixture introduced into the center of the surface cavity in a singlespiral arm.The experiments were carried out in a cylindricalcontainer of radius

Ultrasonic field generated by a transducer non axially located at the end of a cylindrical waveguide surrounded by an elastic medium

The calculation of the ultrasonic field generated by a transducer non axially located at the end of a semi-infinite cylindrical waveguide surrounded by an elastic medium is performed. Numerical results representing power flow, waveforms and dispersion diagrams to highlight non-axisymmetric waves are discussed.

On electrostatic instability of a space-charged jet of dielectric liquid

On the basis of the dispersion equation for the nonaxisymmetric capillary waves at the surface of a strongly volumetrically charged cylindrical jet of an ideal incompressible dielectric liquid, it has been found that, for liquids with their dielectric permittivity changed in a wide range of values, there may occur electrostatic instability of the jet’s side surface.

Inertial waves near corotation in three-dimensional hydrodynamical discs

This paper concerns the interaction between non-axisymmetric inertial waves and their corotation resonances in a hydrodynamical disk. Inertial waves are of interest because they can localise in resonant cavities circumscribed by Lindblad radii, and as a consequence exhibit discrete oscillation frequencies that may be observed. It is often hypothesised that these trapped eigenmodes are affiliated with the poorly understood QPO phenomenon. We demonstrate that a large class of non-axisymmetric 3D inertial waves cannot manifest as trapped normal modes. This class includes any inertial wave whose resonant cavity contains a corotation singularity. Instead, these `singular' modes constitute a continuous spectrum and, as an ensemble, are convected with the flow, giving rise to shearing waves. Lastly, we present a simple demonstration of how the corotation singularity stabilizes three-dimensional perturbations in a slender torus.

The excitation of spiral density waves through turbulent fluctuations in accretion discs - II. Numerical simulations with MRI-driven turbulence

We present fully three-dimensional local MRI simulations with the object of studying the excitation of non-axisymmetric spiral density waves that are observed to always be present in such simulations. They are potentially important for affecting protoplanetary migration through the action of associated stochastic gravitational forces and producing residual transport in MHD inactive regions. The simulations we perform are with zero net flux and produce mean activity levels of alpha ~ 0.005. We reveal the nature of the mechanism responsible for the excitation of these waves by determining the time dependent evolution of the Fourier transforms of the participating state variables. The dominant waves are found to have no vertical structure and to be excited during periodically repeating swings in which they change from leading to trailing. The initial phase of the evolution of such a swing is found to be in excellent agreement with that expected from the WKBJ theory developed in a preceding paper by Heinemann & Papaloizou. We demonstrate that the important source terms causing excitation of the waves are related to a quantity that reduces to the potential vorticity for small perturbations from the background state with no vertical dependence. We find that the root mean square density fluctuations associated with the waves are positively correlated with both this quantity and the general level of hydromagnetic turbulence. The mean angular momentum transport associated with spiral density waves generated in our simulations is estimated to be a significant fraction of that associated with the turbulent Reynolds stress.

A NEW APPROACH FOR PROBING CIRCUMBINARY DISKS

Circumbinary disks are considered to exist in a wide variety of astrophysical objects, e.g., young binary stars, protoplanetary systems, and massive binary black hole systems in active galactic nuclei (AGNs). However, there is no definite evidence for the circumbinary disk except for some in a few young binary star systems. In this Letter, we study possible oscillation modes in circumbinary disks around eccentric and circular binaries. We find that prograde, nonaxisymmetric waves are induced in the inner part of the circumbinary disk by the tidal potential of the binary. Such waves would cause variabilities in emission line profiles from circumbinary disks. Because of prograde precession of the waves, the distance between each component of the binary and the inner edge of the circumbinary disk varies with the beat period between the precession period of the wave and the binary orbital period. As a result, light curves from the circumbinary disks are also expected to vary with the same period. The current study thus provides a new method to detect circumbinary disks in various astrophysical systems.

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.

Gravitational waves from 3D MHD core collapse simulations

We present the gravitational wave analyses from rotating (model s15g) and nearly non-rotating (model s15h) 3D MHD core collapse supernova simulations at bounce and during the first couple of ten milliseconds afterwards. The simulations are launched from 15 M� progenitor models stemming from stellar-evolution calculations. Gravity is implemented by a spherically symmetric effective general relativistic potential. The input physics uses the Lattimer-Swesty equation of state for hot, dense matter and a neutrino parametrisation scheme that is accurate until the first few ms after bounce. The 3D simulations allow us to study features already known from 2D simulations, as well as nonaxisymmetric effects. In agreement with recent results, we find only type I gravitational wave signals at core bounce. In the later stage of the simulations, one of our models (s15g) shows nonaxisymmetric gravitational wave emission caused by a low T/|W| dynamical instability, while the other model radiates gravitational waves due to a convective instability in the protoneutron star. The total energy released in gravitational waves within the considered time intervals is 1.52 × 10 −7 M� (s15g) and 4.72 × 10 −10 M� (s15h). Both core collapse simulations indicate that corresponding events in our Galaxy would be detectable either by the LIGO or Advanced LIGO detector.

On self-sustained dynamo cycles in accretion discs

Context. MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result that is not well understood. This type of turbulence is also related to the possibility of having a dynamo action in accretion discs, which may help to generate the large-scale magnetic field required by ejection processes. Aims. We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action. Methods. Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few orbits. The generation process of this field is investigated using the results of the simulations and an inhomogeneous linear approach. We show that quasilinear nonaxisymmetric waves may provide a positive back-reaction on the largescale field when a weak inhomogeneous azimuthal field is present, explaining the behaviour of the simulations. We finally reproduce the dynamo cycles using a simple closure model summarising our linear results. Results. The mechanism by which turbulence is sustained in zero-net-flux shearing boxes is shown to be related to the existence of a large-scale azimuthal field, surviving for several orbits. In particular, it is shown that MHD turbulence in shearing boxes can be seen as a dynamo process coupled to a magnetorotational-type instability.

Analysis of wave propagation in cylindrical pipes with local inhomogeneities

In this paper, we present a numerical approach to study the guided elastic wave propagation in cylindrical pipes with local inhomogeneities. A hybrid wave finite element (WFE) and finite element (FE) technique is introduced to investigate the dispersion and wave scattering in pipes by taking full advantage of the existing FE codes. Dynamic reduction technique is employed to improve the computational efficiency, which is particularly suitable for the pipes with standard local features. Numerical examples indicate that the proposed technique provides an effective way to calculate the dispersion relationship and the scattered field. Both the axisymmetric and non-axisymmetric wave scattering problems are considered.

Magnetic field tomography on two electrically conducting fluids

A cylindrical cell containing GaInSn alloy and aqueous solution of KOH, a highly simplified aluminium reduction cell, is constructed. A direct current is applied to the cylindrical cell to generate the magnetic field. In a range of amplitude and frequency of vertical vibration, a stable, non-axisymmetric wave pattern is produced, and the displacement of the oscillating interface is measured by a digital camcorder. The perturbation of the magnetic field caused by the non-axisymmetric interface is measured by fluxgate sensors and processed by fast Fourier transforms. The measurements are consistent with forward calculations, and have been exploited to reconstruct the deformed interface by solving an inverse problem so as to develop magnetic field tomography to reconstruct an unknown interface between two electrically conducting fluids.

Gravitationally unstable gaseous disks of flat galaxies

Context. The dynamics of a self-gravitating gaseous subsystem of a disk galaxy is considered analytically, using a local WKB approximation in the radial direction. The simplified model of a galaxy is used in which stars (and a dark matter, if it exists at all) do not participate in the disk collective oscillations and just form a background charge. Aims. For the first time in galactic dynamics, an equation is derived to describe the torque that results from the buildup of gravitational Jeans-type instability of nonaxisymmetric gravity perturbations (e.g., those produced by a spontaneous disturbance or, in rare cases, a satellite system). Methods. The torque serves to redistribute the angular momentum of the inhomogeneous disk by growing (that is, unstable) nonaxisymmetric density waves in such a way that a fraction of the mass (eventually residing in the central parts) retains only a minor fraction of the angular momentum, most of the latter being deposited in extended outer regions of the system. Results. The outward transfer of angular momentum (and the heating) bring the disk toward stability against all small perturbations, including the most unstable nonaxisymmetric ones.