Azimuthal Wave Research Articles

Смещение предела устойчивости течений при наличии случайных флуктуаций скорости вращения

Nonlinear stability of the isothermal three-dimensional flows of viscous incompressible fluid in the rotational spherical layer with the noise presence was studied numerically. Transition between stable non-stationary flow and unstable flow in the form of travelling azimuthal waves is under consideration. Small-amplitude noise inserted to the flow by random broadband disturbances of the inner sphere rotational rate about constant at time averaged value, outer sphere is fixed. An approach is proposed to simplify finding the critical Reynolds number, corresponding to the stability limit in the presence of noise. The results obtained by the proposed and well known methods are compared.

Shifting the flow stability limit in the presence of random fluctuation of the rotational velocity

Nonlinear stability of the isothermal three-dimensional flows of viscous incompressible fluid in the rotational spherical layer with the noise presence was studied numerically. Transition between stable non-stationary flow and unstable flow in the form of travelling azimuthal waves is under consideration. Small-amplitude noise inserted to the flow by random broadband disturbances of the inner sphere rotational rate about constant at time averaged value, outer sphere is fixed. An approach is proposed to simplify finding the critical Reynolds number, corresponding to the stability limit in the presence of noise. The results obtained by the proposed and well known methods are compared. Keywords: noise, rotational flows, spherical Couette flow, instability control.

The Magnetic Field as Trigger for Disturbances of a Flow of a Newtonian Fluid through a Cylindrical Pipe with a Horizontal Axis

A Fourrier Petrov Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables. It is written in FORTRAN. Systematic studies are presented on the dependence of eigenvalues and other quantities on the axial and azimuthal wave number; the reynolds’ number Re and a new none-dimensional number Ne. The flow will be considered stable if all the real parts of the eigenvalues are negative and unstable if only one of them is positive.

Подавление неустойчивости течений с вращением

Experimentally investigated the possibilities of controlling the instability that develops in the form of traveling azimuthal waves in the spherical Couette flow. It was found that the action on the traveling azimuthal waves of periodic modulation of the internal sphere rotation speed can lead to their suppression, when the modulation is switched-off, the instability in the form of traveling azimuthal waves is restored, including with a change in the wave number. It was found that it is possible to maintain a stable stationary flow for a long time after the end of modulation - at least 50 minutes, or 2000 revolutions of the inner sphere, which is four times longer than the transition time in the stationary flow.

Numerical investigation of atmospherelike flows in a spherical geometry.

Buoyancy-driven convection flows play a crucial role in global heat and momentum transport in atmosphere. Simplified planetary and stellar atmospheres can be described by a spherical gap geometry with special boundary conditions for the temperature. In the spherical gap, the dielectrophoretic effect is used to synthesize the radial gravity field. Lateral thermal boundary conditions are used to model solar radiation at the equator and at the poles. The temperature reaches a maximum value at the equator and becomes colder near the poles. In the case of a rotating gap, the influence of the Coriolis and centrifugal forces are taken into account. Different regimes of the two-dimensional steady basic flow are discussed in dependence on the Taylor number and Rayleigh number and for the radii ratio η=R_{in}/R_{out}, where R_{in},R_{out} are the radii of the inner and outer surfaces, respectively. Linear instability theory is used to study when the basic flow becomes unstable. The critical Rayleigh number at which the steady axisymmetric basic flow becomes time-dependently axisymmetric or three dimensional is found to be a function of the Taylor number. Furthermore, the critical azimuthal wave number m_{c}, which is responsible for the structure of the supercritical three-dimensional flow, and the critical frequency of the perturbation ω_{c} were found. The spatial location of the perturbation helps to understand the origin of the instability.

On the competition of anti-lift-up mechanism and Reynolds stress mechanism in Spiral Poiseuille flow

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in Spiral Poiseuille flow (SPF). The Poiseuille number [Formula: see text], representing the dimensionless axial pressure gradient, is varied from 0 to 20,000. The results show that for the axisymmetric case, with the increase of axial shear, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the inner cylinder, and a second peak appears near the outer cylinder for both velocity components. Viewing the time evolution of azimuthal shear contribution [Formula: see text] and axial shear contribution [Formula: see text] to the kinetic energy growth of the optimal perturbation, while [Formula: see text] is large enough ([Formula: see text], 20,000), the Reynolds stress mechanism in the meridional plane [Formula: see text] is dominant for the transient growth behavior in SPF relative to anti-lift-up mechanism, which is dominant in the absence of axial flow for co-rotating Taylor–Couette flow with wide gap. For the oblique mode with azimuthal wave number [Formula: see text], which becomes the optimal azimuthal mode over a wide range of azimuthal wave number ([Formula: see text]–10) when [Formula: see text] is large enough, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the outer cylinder, opposite to the axisymmetric case.

Multispacecraft Observation of the Presubstorm Long‐Lasting Poloidal ULF Wave

AbstractWe report global dayside observation of Pc4–5 wave at the late recovery phase of a magnetic storm from seven satellites. Oscillations lasted for 15 hr and revealed the wave appearance before the substorm onset. The continuous observation showed that substorm injections did not affect the wave behavior, and all the wave parameters change was caused by magnetospheric plasma recovery after a magnetic storm. The wave was identified as a second harmonic poloidal Alfvén wave propagating westward with a high azimuthal wave number (|m| ∼ 210) and coupled with 100 keV protons through the drift‐bounce resonance. A large radial gradient of phase space density was an energy source for the wave.

Symmetry and curvature effects on spin waves in vortex-state hexagonal nanotubes

Analytic and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from intrinsic Dzyaloshinskii-Moriya interaction or interface-induced anisotropies. In constrast, these chiral effects stem from isotropic exchange or dipole-dipole interaction, present in all magnetic materials, which acquire asymmetric contributions in case of curved geometry of the specimen. As a result, for example, the spin-wave dispersion in round magnetic nanotubes becomes asymmetric, namely spin waves of the same frequency propagating in opposite directions along the nanotube exhibit different wavelenghts. Here, using time-resolved scanning transmission X-ray microscopy experiments, standard micromagntic simulations and a dynamic-matrix approach, we show that the spin-wave spectrum undergoes additional drastic changes when transitioning from a continuous to a discrete rotational symmetry, i.e. from round to hexagonal nanotubes, which are much easier to fabricate. The polygonal shape introduces localization of the modes both to the sharp, highly curved corners and flat edges. Moreover, due to the discrete rotational symmetry, the degenerate nature of the modes with azimuthal wave vectors known from round tubes is partly lifted, resulting in singlet and duplet modes. For comparison with our experiments, we calculate the microwave absorption from the numerically obtained mode profiles which shows that a dedicated antenna design is paramount for magnonic applications in 3D nano-structures. To our knowledge these are the first experiments directly showing real space spin-wave propagation in 3D nano objects.

Alfvén Waves Generated Through the Drift‐Bounce Resonant Instability in the Ring Current: A THEMIS Multi‐Spacecraft Case Study

AbstractThe satellites THA, THD, THE of THEMIS mission (Time History of Events and Macroscale Interactions during Substorms) have consistently recorded quasi‐monochromatic poloidal oscillations of the Pc4‐5 range in the nighttime magnetosphere. Wave activity was recorded after a substorm in the ring current region, between L‐shells 6 and 7.3. According to the data of the THA satellite, the fundamental and second harmonics of Alfvén wave were simultaneously recorded at frequencies of about 7 and 18 mHz, respectively. The satellites THD and THE recorded only the second harmonic and oscillating modulations of proton fluxes with energies of about 50 keV at the harmonic frequency. For this second harmonic wave, the azimuthal wave number was estimated using the phase delays of the oscillations in the proton fluxes with different gyrophases. It is shown that the wave was in drift‐bounce resonance with 46 keV protons and was generated through resonant instability caused by non‐equilibrium distribution of ring current protons with the significant earthward spatial gradient at the resonance energy.

On the stability of parallel shear flows with embedded swirl

The temporal stability of inviscid parallel shear flows with embedded swirl is investigated. The base flow is divided into three regions: an inner irrotational jet flow, a thin swirl layer on the outer rim of the nozzle, and an external potential flow outside the nozzle. The swirl distribution in the thin shear layer is of solid-body rotation and of Rankine type outside the nozzle. The axial velocity profile in the jet base flow is assumed to be top-hat. The linear dispersion relation was derived and solved numerically. A parametric study on the effect of swirl parameter, S, and the swirl layer thickness fraction, d, on the amplification rates of the unstable modes is performed. A helical instability wave with azimuthal wave number, m = –3, is the most unstable mode with S = 0.8 and = 0.08. Our results indicate that the embedded thin layer swirl is capable of triggering the centrifugal instability waves to promote jet mixing. This powerful technique may be employed to mitigate jet noise without incurring significant thrust loss.

Rotational pumping revisited

This paper considers a pure electron plasma, with a small admixture of negative ions, confined in a Penning–Malmberg trap. When a diocotron mode is excited on the plasma, the end sheaths of the plasma are azimuthally distorted. During reflection at a distorted end sheath, an ion steps off of the surface characterizing the drift motion in the plasma interior, and this step produces transport. The diocotron mode transfers canonical angular momentum to the ions, and in response damps. These transport mechanism and associated damping are called rotational pumping. It is particularly strong when the axial bounce motion and the rotational drift motion, in the rotating frame of the mode, satisfy a resonance condition. This paper calculates the transport flux of ions and the associated damping rate of the mode in the resonant regime. Previous papers have discussed the theory and the experimental observation of rotational pumping for the special case of a diocotron mode with azimuthal wave number l = 1, and this paper extends the theory to modes with l≠1, which may sound like a trivial extension, but in fact is not.

Experimental Dispersion Relation of Surface Waves along a Torus of Fluid.

We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatiotemporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous, and sloshing modes. Standing azimuthal waves are also studied leading to polygonlike patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.

Instability of cumulation in converging cylindrical shock wave

The conditions of linear instability for a converging cylindrical shock wave in an arbitrary inviscid medium are obtained. The initial continuous cylindrical symmetry of the shock wave front is exchanged on a discrete symmetry that is determined by the most unstable small azimuthal dimensionless wave numbers 0<k<kth<1 of corrugation perturbations. Due to the long azimuthal wavelengths (λ=2πRs0/k, Rs0—the radius of the shock wave) of perturbations, the shape of the resulting shock wave front is not changed significantly, but the corresponding restriction of the internal energy cumulation can be caused by the intensification of the rotation of the medium behind the front. The instability and the restriction of cumulation are also possible in the case of the exponential rapid growth of the one-dimensional perturbations with k=0, when the shape of the shock front is not changed at all. The correspondence of present theory to the experimental and simulation data on underwater electrical explosion is considered.

Localized and extended patterns in the cubic-quintic Swift-Hohenberg equation on a disk.

Axisymmetric and nonaxisymmetric patterns in the cubic-quintic Swift-Hohenberg equation posed on a disk with Neumann boundary conditions are studied via numerical continuation and bifurcation analysis. Axisymmetric localized solutions in the form of spots and rings known from earlier studies persist and snake in the usual fashion until they begin to interact with the boundary. Depending on parameters, including the disk radius, these states may or may not connect to the branch of domain-filling target states. Secondary instabilities of localized axisymmetric states may create multiarm localized structures that grow and interact with the boundary before broadening into domain-filling states. High azimuthal wave number wall states referred to as daisy states are also found. Secondary bifurcations from these states include localized daisies, i.e., wall states localized in both radius and angle. Depending on parameters, these states may snake much as in the one-dimensional Swift-Hohenberg equation, or invade the interior of the domain, yielding states referred to as worms, or domain-filling stripes.

Nonreciprocity of spin waves in magnetic nanotubes with helical equilibrium magnetization

Spin waves (SWs) in magnetic nanotubes have shown interesting nonreciprocal properties in their dispersion relation, group velocity, frequency linewidth, and attenuation lengths. The reported chiral effects are similar to those induced by the Dzyaloshinskii–Moriya interaction but originating from the dipole–dipole interaction. Here, we show that the isotropic-exchange interaction can also induce chiral effects in the SW transport; the so-called Berry phase of SWs. We demonstrate that with the application of magnetic fields, the nonreciprocity of the different SW modes can be tuned between the fully dipolar governed and the fully exchange governed cases, as they are directly related to the underlying equilibrium state. In the helical state, due to the combined action of the two effects, every single sign combination of the azimuthal and axial wave vectors leads to different dispersions, allowing for a very sophisticated tuning of the SW transport. A disentanglement of the dipole–dipole and exchange contributions so far was not reported for the SW transport in nanotubes. Furthermore, we propose a device based on coplanar waveguides that would allow to selectively measure the exchange or dipole induced SW nonreciprocities. In the context of magnonic applications, our results might encourage further developments in the emerging field of 3D magnonic devices using curved magnetic membranes.

Prediction of velocity, gas content from neural network modeling and estimation of coal bed permeability from image log in coal bed methane reservoirs: Case study of South Karanpura Coalfield, India

P-wave velocity and gas content of major coal seams are predicted from three wells from the South Karanpura coalfield, India. Multilayered feed-forward neural network (MLFN) model is developed for prediction P-wave velocity from two wells using three input log parameters: gamma ray, resistivity and bulk density. The model is tested on coal seams: Sayal, Balkudra, Banasgarah and Argada of three wells namely; A, B and C with satisfactory goodness of fit (R2 = 0.77). The ratio of P-wave and S-wave velocities (Vp/Vs) ranges from 1.68 to 3.10 in the coal seams of this field. Cleat density using image log is obtained from four major coal seams namely; Balkudra, Kurse, Hathidari, Banasgarah varying from 1/m to 11/m. Ash content varies from 15 to 51% whereas gas content of major coal seams varies from 2.30 to 4.4 10−3 kg/m3. There is a good correlation between ash content and Vp/Vs of coal seams under the study area. MLFN model for prediction of gas content of the above-mentioned coal seams from two well is trained with input parameters such as: Vp/Vs, bulk density, cleat density and ash content. The model estimates gas content of other coal seams: Argada from well A, Hathidari from well B and Balkudra, Kurse, Banasgarah from well C with satisfactory R2 = 0.77. Maximum horizontal stress orientation is observed from azimuthal shear wave anisotropy from cross multipole array acoustic (XMAC) log for a well A. It varies from N110° to N115° in these coal seams. Permeability of coal seams are computed from X-tended Range Microresistivity Imager (XRMI) tool from a well C. Permeability of coal is varying from 0.5 md in Saunda seam to 17.29 md in Banasgarah seam. The estimated permeability matches well with the pre-fracture permeability of these seams. It is observed that increase in cleat density enhances coal seam fracture permeability in coal seam.

Numerical simulation of thermo-solutal Marangoni convection in a full floating zone with radiative heat transfer under zero gravity

A numerical simulation study of thermo-solutal Marangoni convection has been carried out in a full floating zone with radiative heat transfer under zero gravity. In this system, the thermal and solutal Marangoni flows develop in the same direction and/or opposite directions along the free surface depending on the location in the zone. In the model, the ambient temperature distribution along the zone is taken as a Gaussian profile, and the radiative heat transfer is considered dominant. The characteristics of the concentration pattern in the zone vary due to the varying thermal and solutal Marangoni numbers, as well as the characteristic azimuthal wave. The flow velocity field exhibits two or four main vortices along the free surface. These vortices get stronger at higher thermal Marangoni number values.

Blunt hub affecting the radar cross section of rotor based on dynamic scattering method

In order to study the radar characteristics of blunt-hub rotor, a dynamic scattering method (DSM) based on physical optics and physical theory of diffraction is presented. Important influencing factors are analyzed and discussed, including rotor disk inclination, azimuth, elevation angle, and radar wave frequency. The radar cross section (RCS) of the blunt-hub rotor is used for comparison with conventional-hub rotor and sharp-hub rotor. The RCS performance of the blunt-hub rotor at different radar wave frequencies is close to that of the sharp-hub rotor. At larger positive elevation angles, the RCS∼azimuth performance of the blunt-hub rotor is not as good as the other two rotors, while the RCS performance of the blunt-hub rotor has an advantage under the larger negative elevation angle and the inclination of the rotor disk. The presented DSM is feasible and effective for learning the electromagnetic scattering characteristics of the blunt-hub rotor.

Spin wave modes of skyrmioniums in the presence of Dzyaloshinskii-Moriya interaction

A skyrmionium or 2π skyrmion is an exotic magnetic configuration that can be stabilized in ferromagnetic nanostructures, e.g., nanodisks. Differently from the standard (or π) skyrmion, it can move without suffering deflections due to the skyrmion Hall effect (SkHE), a property that is desirable for potential applications in spintronics. In this work, using micromagnetic simulations, it is investigated the influence of the Dzyaloshinskii-Moriya interaction on the azimuthal and radial spin wave spectra of the skyrmionium. First, the ground state of the ferromagnetic disk is obtained for several values of Dzyaloshinskii-Moriya exchange constant Dint and a fixed value of perpendicular anisotropy constant Kz. The spin wave modes of the skyrmionium were obtained using in-plane and out-of-plane magnetic pulses. The results show that the values of the frequencies of the spin wave modes depend on the values of Dint. Additionally, it is shown that it is possible to create a skyrmionium using in-plane rotating magnetic fields, by tuning parameters such as the intensity of the applied perpendicular magnetic fields, and their duration.

Synopsis of Vogel–Escudier flow

The topology and the dynamics of Vogel–Escudier flow, which is the flow inside a circular cylinder with a top rotating lid, are presented in this paper. A three-dimensional direct numerical simulation of the Navier–Stokes equations in cylindrical coordinates is used to investigate the flow. Various combinations of Reynolds number and aspect ratio are studied and classified based on the flow topology. The flow is found to exhibit steady axisymmetric, unsteady axisymmetric, rotating azimuthal waves, and weak turbulence regimes. The perturbations found in the system are characteristically different for various flow regimes and are used for the classification of flow. The presence of several modes at high Reynolds number suggests a weak turbulence state, and a Taylor–Görtler type instability wave is found in the sidewall boundary layer.