Higher Azimuthal Modes Research Articles

Contained modes in mirrors with sheared rotation

In mirrors with E×B rotation, a fixed azimuthal perturbation in the laboratory frame can appear as a wave in the rotating frame. If the rotation frequency varies with radius, the plasma-frame wave frequency will also vary radially due to the Doppler shift. A wave that propagates in the high rotation plasma region might therefore be evanescent at the plasma edge. This can lead to radially localized Alfven eigenmodes with high azimuthal mode numbers. Contained Alfven modes are found both for peaked and nonpeaked rotation profiles. These modes might be useful for alpha channeling or ion heating, as the high azimuthal wave number allows the plasma wave frequency in the rotating frame to exceed the ion cyclotron frequency.

Comparison of Time-Domain Impedance Boundary Conditions for Lined Duct Flows

impedance of liners. This part of the model, however, is limited to single frequency sound source in its present form. The EHR is based on the z‐transformation of the corresponding impedance function for the Extended Helmholtz Resonator in the frequency‐domain. The implementations of the two models in the numerical simulation tool with the DRP scheme are discussed in details. The results from the both models in general agree notably well with each other. However, in one case, the results from the two models dier significantly due to the presence of strongly attenuated modes, which renders the approximations of the EFI invalid. The validation and verification of both models are carried out for the latest NASA impedance tube experiment and the generic aero‐engine frequency domain results of Rienstra and Eversman. In addition, an impedance eduction technique based on the EHR and the optimization process has been developed. This further extends applications of the time‐domain models. The simultaneous optimization of all frequencies considered in the NASA’s impedance tube experiments results in a physically reasonable set of parameters for the EHR. The fitted terminal impedances and the measured mean flow profiles are used for the impedance eduction. The numerical results of both models for the generic aero‐engine inlet test case with higher azimuthal modes also compare well if the same flow assumptions and eigenvalues are used as for the frequency domain methods. Overall both models give a similar physical behavior, but the EHR requires smaller time steps in the case of small face sheet reactances.

Active Control of a Mach 0.9 Jet for Noise Mitigation Using Plasma Actuators

longer time before decaying gradually. The saturation and decay of the seeded perturbations moved farther upstream as their Strouhal number was increased. Seeded perturbations with higher azimuthal modes exhibited faster decay. Particle image velocimetry results showed that when exciting the jet’s preferred-mode instability at lower azimuthal modes, the jet potential core was shortened and the turbulent kinetic energy was increased significantly. At higher Strouhal numbers and higher azimuthal modes, forcing had less of an impact on the mean velocity and turbulent kinetic energy. Far-field acoustic results showed a significant noise increase (2 to 4 dB) when thejetisexcitedaroundthejet’spreferred-modeinstabilityStrouhalnumber(StDF 0:2–0:5),inagreementwiththe results in the literature. Noise reduction of 0.5 to over 1.0 dB is observed over a large excitation Strouhal number range; this reduction seems to peak around StDF 1:5 to 2.0 at a 30-deg angle, but around StDF 3:0 to 3.5 at a 90deg angle. Although forcing the jet with higher azimuthal modes is advantageous for noise mitigation at a 30-deg angleandlowerStrouhalnumbers,theeffectisnotasclearathigherforcingStrouhalnumbersandata90-degangle.

A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow

A dynamical estimate of the axial component of a Mach 0.60 axisymmetric jet's turbulent velocity field is presented here using spectral linear stochastic estimation. The pressure field surrounding the exit of the jet is employed as the unconditional parameter in the estimation technique. A sub-grid interpolation method is used to improve the spatial resolution of the estimate. The model estimate is time-resolved and reconstructed using a purely experimental database. A decomposition of the model estimate using POD and Fourier-azimuthal techniques identifies the turbulent velocity modes that are responsible for driving the near-field pressure when compared with direct measurements of the jet's modal features. In effect, the signatures left in the near pressure field by the turbulence are a result of the low-order structure, the higher azimuthal modes being inefficient in driving the hydrodynamic pressure. A direct calculation of the source field using a Lighthill approach is performed, from which the low-dimensional features of the sound source mechanisms are illustrated.

Reduced-order representation of turbulent jet flow and its noise source

In the present study, subsonic turbulent jet noise is investigated employing reduced-order representations of the flow field and its noise source targeting 'least-order' approximations of the key processes. These representations utilize LES data for a compressible jet at Mach number 0.9 and Reynolds number 3600. The fluctuations of the velocity field and of the Lamb vector as noise source are investigated with three methods. Firstly, the streamwise development is characterised by a statistical analysis. Thus, the most active region of the flow field and the Lamb vector are observed at 11 and 8 jet diameters downstream, respectively. Secondly, an azimuthal mode decomposition is carried out. The first five azimuthal modes resolve most of the flow field and Lamb vector fluctuation. Thirdly, the dimension of the dynamics phase space is estimated by the proper orthogonal decomposition (POD). About 350 modes are necessary to resolve at least 50% of the fluctuation level of the hydrodynamics and even more modes are required for the noise source. As expected, the end of the potential core correlates with the location of a distinct peak in the noise source magnitude, thus indicating a highly active acoustical region. Intriguingly, the noise source efficiency per unit energy increases with higher azimuthal modes. The comparison of the compressible jet results with the incompressible LES at the same Reynolds number reveals a significant smaller energy concentration in the first azimuthal modes, i.e. the incompressible flow is dynamically more complex. The current results are part of an ongoing effort to predict far-field jet noise by reduced- order modelling of its hydrodynamic source.

Are galactic disks dynamically influenced by dust?

Dynamically cold components are well known to destabilize hotter, even much more massive components. E.g. stellar disks can become unstable by a small admixture of cold gas or proto-planetary disks might be destabilized by a small fraction of dust. In this paper we studied the dynamical influence of a cold dust component on the gaseous phase in the central regions of galactic disks. We performed two-dimensional hydrodynamical simulations for flat multi-component disks embedded in a combined static stellar and dark matter potential. The pressure-free dust component is coupled to the gas by a drag force depending on their velocity difference. It turned out that the most unstable regions are those with either a low or near to minimum Toomre parameter or with rigid rotation, i.e. the central area. In that regions the dust-free disks become most unstable for high azimuthal modes (m ∼ 8), whereas in dusty disks all modes have a similar amplitude resulting in a patchy appearance. The structures in the dust have a larger contrast between arm and inter-arm regions than those of the gas. The dust peaks are frequently correlated with peaks of the gas distribution, but they do not necessarily coincide with them. Therefore, a large scatter in the dust-to-gas ratios is expected. The appearance of the dust is more cellular (i.e. sometimes connecting different spiral features), whereas the gas is organized in a multi-armed spiral structure. We found that an admixture of 2% dust (relative to the mass of the gas) destabilizes gaseous disks substantially, whereas dust-to-gas ratios below 1% have no influence on the evolution of the gaseous disk. For a high dust-to-gas ratio of 10% the instabilities reach a saturation level already after 30 Myr. The stability of the gaseous disks also strongly depends on their Toomre parameter. But even in hot gaseous disks a destabilizing influence of the dust component has been found.

Microwave propagation in ferromagnetic semiconductors

Ferromagnetic semiconductors may exhibit gyroelectric and gyromagnetic behavior at the same time. In order to treat the Maxwell equations and the propagation in such semiconductors, the description of the two phenomena are unified in a general framework, concerning gyroelectromagnetic media. This allows one to describe the modes in waveguides with a gyroelectromagnetic core, so the high azimuthal index mode behavior may be predicted in ferromagnetic semiconductors, focusing on microwave frequency domain towards technological applications.

A study of Pc-5 ULF oscillations

Abstract. A study of Pc-5 magnetic pulsations using data from the Combined Release and Radiation Effects Satellite (CRRES) was carried out. Three-component dynamic magnetic field spectrograms have been used to survey ULF pulsation activity for the approximate fourteen month lifetime of CRRES. Two-hour panels of dynamic spectra were examined to find events which fall into two basic categories: 1) toroidal modes (fundamental and harmonic resonances) and 2) poloidal modes, which include compressional oscillations. The occurence rates were determined as a function of L value and local time. The main result is a comparable probability of occurence of toroidal mode oscillations on the dawn and dusk sides of the magnetosphere inside geosynchronous orbit, while poloidal mode oscillations occur predominantly along the dusk side, consistent with high azimuthal mode number excitation by ring current ions. Pc-5 pulsations following Storm Sudden Commencements (SSCs) were examined separately. The spatial distribution of modes for the SSC events was consistent with the statistical study for the lifetime of CRRES. The toroidal fundamental (and harmonic) resonances are the dominant mode seen on the dawn-side of the magnetosphere following SSCs. Power is mixed in all three components. In the 21 dusk side SSC events there were only a few examples of purely compressional (two) or radial (one) power in the CRRES study, a few more examples of purely toroidal modes (six), with all three components predominant in about half (ten) of the events. Key words. Magnetospheric physics (MHD waves and instabilities; magnetospheric configuration and dynamics) – Space plasma physics (waves and instabilities)

Can Dust Destabilise Galactic Disks?

AbstractWe studied the dynamic influence of a dust component on the gaseous phase in central regions of galactic disks. We performed two-dimensional hydrodynamic simulations for flat, multicomponent disks embedded in a stellar and dark matter potential. The pressure-free dust component is coupled to the gas by a drag force depending on their velocity difference. The most unstable regions are those with either a low or near-to-minimum Toomre parameter or with rigid rotation, i.e. the central area. In those regions the dust-free disks become most unstable for a small range of high azimuthal modes (m ∼ 8), whereas in dusty disks all modes have similar amplitudes resulting in a patchy appearance. The structures in the dust have a larger contrast between arm and interarm regions than those of the gas. The dust peaks are frequently correlated with peaks of the gas distribution, but they do not necessarily coincide with them. This leads to a large scatter in the dust to gas ratios. The appearance of the dust is more cellular (i.e. sometimes connecting different spiral features), whereas the gas is organised in a multi-armed spiral structure. We found that an admixture of 2% dust (relative to the mass of the gas) destabilises gaseous disks substantially, whereas dust to gas ratios below 1% have no influence on the evolution of the gaseous disk. For a high dust to gas ratio of 10% the instabilities reach the saturation level after 30 Myr.

Numerical simulation of the excitation and evolution of high-azimuthal-mode-number coherent vortices in hollow magnetized electron columns

A finite-element code is used to study the excitation of a perturbation with a range of azimuthal mode numbers in hollow magnetized plasma columns, and the subsequent nonlinear development and evolution of coherent vortices interacting to coalesce, while cascading to a lower azimuthal mode number. It is shown that, even for initially higher azimuthal mode numbers, the angular momentum remains a slowly varying ideal invariant, while the system cascades to lower azimuthal mode numbers. A detailed study of the evolution is presented for initially excited m = 3, m = 4, and m = 5 azimuthal modes, which underlines the physics of the inverse cascade of angular momentum.

Three-dimensional instability of a liquid layer flowing down a heated vertical cylinder

The three-dimensional thermocapillary instability of a fluid film coating the outside or the inside of a cylinder is investigated in the absence and in the presence of gravity. In the absence of gravity (pure thermocapillarity), it is found that it is possible to excite high azimuthal modes as the most unstable. In the presence of gravity the thermocapillary instability of a thin fluid film flowing down a vertical cylinder is investigated. It is shown that thermocapillarity also promotes the instability of high azimuthal modes, even higher than those found in the pure thermocapillary case. This is in contrast with the isothermal case where only the zeroth mode (the longitudinal one) is the most unstable and also with previous work on flow down a rotating cylinder where, in some conditions, rotation may promote the first azimuthal mode as the most unstable. Curves of criticality and those corresponding to the maximum growth rate are given for different values of the parameters.

Near- and far-field properties of annular CO_2 waveguide lasers

The theoretical and experimental investigation of field properties of annular waveguide lasers with a Fabry-Perot resonator is presented. Oscillation with high azimuthal mode order leads to an annular intensity distribution in the far field with almost linear dependence of the annular diameter on the mode order. Low-order fields form a distinct focal spot in the far field. A laser device with a discharge area of 6-cm diameter and 53-cm length yields an output power of 600 W.

The Evolution of Disturbed Neutral Point Equilibria

AbstractWe consider the linear and non-linear evolution of a perturbed X-type neutral point. A semi-analytic treatment is given for the case of small disturbances of the equilibrium field. This problem admits well defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that the longest lived modes are purely radial and decay of the timescale τ ≈ |ln η| where η defines the resistivity of the coronal plasma. Higher azimuthal modes decay much faster, generally on a fraction (O(m−1)) of the Alfvén timescale for the outer field.We go on to perform finite amplitude calculations that demonstrate the implosive current build-up that precedes the reconnective phase of the relaxation. In general both linear and non-linear studies support the idea of an initial implosive stage which rapidly releases the bulk of the energy associated with arbitrary field disturbances.

Evolution of vortical structures in flames

The detailed substructure of the large-scale coherent vortices in the mixing layer of an annular diffusion flame was studied using the Planar Laser Induced Fluorescence (PLIF) visualization technique. The formation, evolution and interaction of the coherent vortices and the various modes of azimuthal structures were visualized. These structures dominate the large- and fine-scale mixing processes in the flame and thus affect the combustion rate and stability characteristics. The concentration of the hydroxyl radical was used to visualize the reaction zones. The vortical structures were generated and stabilized by forcing the air jet at various instability frequencies. The vortex merging process, which is the main growth mechanism of the shear layer, was simulate and investigated as well. Phase-averaged measurements were used to get the global features of flow structures. Instantaneous planar measurements which were obtained on- and off- axis and in cross-sections perpendicular to the axis, revealed the details of the complex three-dimentional character of the flame. This three-dimensionality of an apparently axisymmetric flame is related to the amplification of high azimuthal modes of jet instability. The growth of these secondary structures is related to the transition of the coherent structures to small-scale turbulence.

Drift-Modified Tearing Instabilities Due to Trapped Electrons

It is shown that the collisional detrapping of magnetically trapped electrons in tokamaks can excite drift tearing modes with high azimuthal mode numbers. For normal temperature gradients ($\frac{d\mathrm{ln}{T}_{e}}{d\mathrm{ln}n}>0$), the modes are unstable in the collisional regime (${\ensuremath{\nu}}_{\mathrm{eff}}>{\ensuremath{\omega}}_{^{*}e}$), but stable in the collisionless regime (${\ensuremath{\nu}}_{\mathrm{eff}}<{\ensuremath{\omega}}_{^{*}e}$).