Helicity Spectrum Research Articles

Acoustic Radiation From Thick Laminated Cylindrical Shells With Sparse Cross Stiffeners

A general method for predicting acoustic radiation from multiple periodic structures is presented and a numerical solution is proposed to find the radial displacement of thick laminated cylindrical shells with sparse cross stiffeners in the wavenumber domain. Although this method aims at the sound radiation from a single stiffened cylindrical shell, it can be easily adapted to analyze the vibrational and sound characteristics of two concentric cylindrical shells or two parallel plates with complicated periodic stiffeners, such as submarine and ship hulls. The sparse cross stiffeners are composed of two sets of parallel rings and one set of longitudinal stringers. The acoustic power of large cylindrical shells above the ring frequency is derived in the wavenumber domain on the basis of the fact that sound power is focused on the acoustic ellipse. It transpires that a great many band gaps of wave propagation in the helical wave spectra of the radial displacement for stiffened cylindrical shells are generated by the rings and stringers. The acoustic power and input power of stiffened antisymmetric laminated cylindrical shells are computed and compared. The acoustic energy conversion efficiency of the cylindrical shells is less than 10%. The axial and circumferential point forces can also produce distinct acoustic power. The radial displacement patterns of the antisymmetric cylindrical shell with fluid loadings are illustrated in the space domain. This study would help to better understand the main mechanism of acoustic radiation from stiffened laminated composite shells, which has not been adequately addressed in its companion paper (Cao et al., 2012, “Acoustic Radiation From Shear Deformable Stiffened Laminated Cylindrical Shells,” J. Sound Vib., 331(3), pp. 651-670).

Acoustic Radiation From Stiffened Cylindrical Shells With Constrained Layer Damping

Acoustic radiation from cylindrical shells stiffened by two sets of rings, with constrained layer damping (CLD), is investigated theoretically. The governing equations of motion for the cylindrical shell with CLD are described on the basis of Sanders thin shell theory. Two sets of rings interact with the host cylindrical shell only through the normal line forces. The solutions are derived in the wavenumber domain and the stationary phase method is used to find an analytical expression of the far-field sound pressure. The effects of the viscoelastic material core, constrained layer and multiple loadings on sound pressure are illustrated. The helical wave spectra of sound pressure and the radial displacement clearly show the vibrational and acoustic characteristics of the stiffened cylindrical shell with CLD. It is shown that CLD can effectively suppress the radial vibration and reduce acoustic radiation.

Isotropization at small scales of rotating helically driven turbulence

AbstractWe present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami ($\mathit{ABC}$) forcing, creating helical flow. The Zeman scale ${\ell }_{\Omega } $ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $307{2}^{3} $ points, with Rossby and Reynolds numbers, respectively, equal to $0. 07$ and $2. 7\ensuremath{\times} 1{0}^{4} $. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond ${\ell }_{\Omega } $ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at ${\ell }_{\Omega } $, a clear sign of recovery of three-dimensionality in the small scales.

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.

Turbulence associated with corotating interaction regions at 1AU: Inertial range cross-helicity spectra

[1] We examine five corotating interaction regions and their surrounding slow and fast wind flows observed by the Advanced Composition Explorer spacecraft at 1 AU during solar minimum conditions in 2007 and 2008. We compute spectra of total power (magnetic + kinetic) and spectra of the cross helicity in an attempt to better understand turbulence generation within the shear flow. Consistent with previous work, we find that Sunward-propagation signatures exist at high levels compared with the surrounding flow and sometimes dominate over a broad range of spacecraft-frame frequencies. There is a suggestion that the Sunward-propagation signatures start at small scales and evolve toward larger scales, although this may simply reflect the need to inject larger amounts of energy at the large scales before significant Sunward propagation is observed. The power spectra are conspicuously lacking in any features that would normally be expected to show energy injection over a finite range of frequencies as is the often the case in kinetic instabilities.

High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000(3) grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfvén time increases with wave number, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow that is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity.

MAGNETIC HELICITY SPECTRUM OF SOLAR WIND FLUCTUATIONS AS A FUNCTION OF THE ANGLE WITH RESPECT TO THE LOCAL MEAN MAGNETIC FIELD

Magnetic field data acquired by the Ulysses spacecraft in high-speed streams over the poles of the Sun are used to investigate the normalized magnetic helicity spectrum σm as a function of the angle θ between the local mean magnetic field and the flow direction of the solar wind. This spectrum provides important information about the constituent modes at the transition to kinetic scales that occurs near the spectral break separating the inertial range from the dissipation range. The energetically dominant signal at scales near the thermal proton gyroradius k⊥ρi ∼ 1 often covers a wide band of propagation angles centered about the perpendicular direction, θ ≃ 90° ± 30°. This signal is consistent with a spectrum of obliquely propagating kinetic Alfvén waves with k⊥ ≫ k∥ in which there is more energy in waves propagating away from the Sun and along the direction of the local mean magnetic field than toward the Sun. Moreover, this signal is principally responsible for the reduced magnetic helicity spectrum measured using Fourier transform techniques. The observations also reveal a subdominant population of nearly parallel propagating electromagnetic waves near the proton inertial scale k∥c/ωpi ∼ 1 that often exhibit high magnetic helicity |σm| ≃ 1. These waves are believed to be caused by proton pressure anisotropy instabilities that regulate distribution functions in the collisionless solar wind. Because of the existence of a drift of alpha particles with respect to the protons, the proton temperature anisotropy instability that operates when Tp⊥/Tp∥ > 1 preferentially generates outward propagating ion-cyclotron waves and the fire-hose instability that operates when Tp⊥/Tp∥ < 1 preferentially generates inward propagating whistler waves. These kinetic processes provide a natural explanation for the magnetic field observations.

Imprints of magnetic power and helicity spectra on radio polarimetry statistics

Statistical properties of turbulent magnetic fields in radio-synchrotron sources should imprint on the statistics of polarimetric observables. In search of these imprints, we calculate correlation and cross-correlation functions from a set of observables containing the total intensity I, the polarized intensity P and the Faraday depth phi. The correlation functions are evaluated for all combinations of observables up to fourth order in the magnetic field B. We derive these as far as possible analytically and from first principles only using some basic assumptions such as Gaussian statistics of the underlying magnetic field in the observed region and statistical homogeneity. We further assume some simplifications to reduce the complexity of the calculations, as for a start we were interested in a proof of concept. Using this statistical approach, we show that it is in principle possible to gain information about the helical part of the magnetic power spectrum, namely via the correlation functions <P(k)phi(k')phi(k")> and <I(k)phi(k')phi(k")>. Using this insight, we construct an easy-to-use test for helicity, called LITMUS (Local Inference Test for Magnetic fields which Uncovers heliceS). For now, all calculations are given in a Faraday-free case, but set up in a way so that Faraday rotational effects could be included later on.

Magnetic Dynamo action at Low Magnetic Prandtl Numbers

Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid-metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.

Spectra of magnetic fields injected during baryogenesis

Helical magnetic fields are injected into the cosmic medium during cosmological baryogenesis and can potentially provide a useful probe of the early universe. We construct a model to study the injection process during a first order phase transition and to determine the power spectra of the injected magnetic field. By Monte Carlo simulations we evaluate the Fourier space symmetric and helical power spectra of the magnetic field at the time the phase transition completes. The spectra are peaked at the scale given by the inverse size of bubbles at percolation and with a comparable width. These injected magnetic fields set the initial conditions for further cosmological magneto-hydrodynamical evolution.

Lipid−Protein Nanodiscs as Reference Medium in Detergent Screening for High-Resolution NMR Studies of Integral Membrane Proteins

The choice of a suitable detergent-based membrane mimetic is of crucial importance for high-resolution NMR studies of membrane proteins. The present report describes a new approach of detergent screening. It is based on the comparison of 2D (1)H,(15)N-correlation spectra of a protein in a membrane-bilayer "reference" medium and in "trial" detergent-based environments. The proposed "reference" medium is the lipid-protein nanodisc (LPN) representing nanoscale phospholipid bilayers wrapped around by apolipoprotein A-1. The set of zwitterionic (DPC, DMPC/DHPC), anionic (SDS, LMPG, LPPG), and weakly cationic (LDAO) detergent-based media was screened for their ability to represent the native structure of the isolated voltage-sensing domain (VSD) of the archaeal potassium channel KvAP. The VSD/LPN complexes composed of saturated zwitterionic (DMPC), anionic (DMPG), or a mixture of unsaturated differently charged (POPC/DOPG, 3:1) lipids were used as reference. All assayed detergent media demonstrate similar CD spectra of the domain with a high level (approximately 60%) of overall helicity but different 2D NMR spectra. Using the reference spectrum of the VSD in LPN, we were able to choose the detergent composition in which the membrane-like structure of the VSD is preserved.

Rotating helical turbulence. I. Global evolution and spectral behavior

We present results from two 15363 direct numerical simulations of rotating turbulence where both energy and helicity are injected into the flow by an external forcing. The dual cascade of energy and helicity toward smaller scales observed in isotropic and homogeneous turbulence is broken in the presence of rotation, with the development of an inverse cascade of energy now coexisting with direct cascades of energy and helicity. In the direct cascade range, the flux of helicity dominates over that of energy at low Rossby number. These cascades have several consequences for the statistics of the flow. The evolution of global quantities and of the energy and helicity spectra is studied, and comparisons with simulations at different Reynolds and Rossby numbers at lower resolution are done to identify scaling laws.

Turbulent transport and dynamo in sheared magnetohydrodynamics turbulence with a nonuniform magnetic field

We investigate three-dimensional magnetohydrodynamics turbulence in the presence of velocity and magnetic shear (i.e., with both a large-scale shear flow and a nonuniform magnetic field). By assuming a turbulence driven by an external forcing with both helical and nonhelical spectra, we investigate the combined effect of these two shears on turbulence intensity and turbulent transport represented by turbulent diffusivities (turbulent viscosity, alpha and beta effect) in Reynolds-averaged equations. We show that turbulent transport (turbulent viscosity and diffusivity) is quenched by a strong flow shear and a strong magnetic field. For a weak flow shear, we further show that the magnetic shear increases the turbulence intensity while decreasing the turbulent transport. In the presence of a strong flow shear, the effect of the magnetic shear is found to oppose the effect of flow shear (which reduces turbulence due to shear stabilization) by enhancing turbulence and transport, thereby weakening the strong quenching by flow shear stabilization. In the case of a strong magnetic field (compared to flow shear), magnetic shear increases turbulence intensity and quenches turbulent transport.

LARGE-SCALE DYNAMOS AT LOW MAGNETIC PRANDTL NUMBERS

Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been determined for magnetic Prandtl numbers between 0.01 and 1, but only the case with the smallest magnetic Prandtl number shows large-scale magnetic fields. It is less organized than in the nonlinear stage. For small magnetic Prandtl numbers the growth rates are comparable to those calculated from an alpha squared mean-field dynamo. In the linear regime the magnetic helicity spectrum has a short inertial range compatible with a -5/3 power law, while in the nonlinear regime it is the current helicity whose spectrum may be compatible with such a law. In the saturated case, the spectral magnetic energy in the inertial range is in slight excess over the spectral kinetic energy, although for small magnetic Prandtl numbers the magnetic energy spectrum reaches its resistive cut off wavenumber more quickly. The viscous energy dissipation declines with the square root of the magnetic Prandtl number, which implies that most of the energy is dissipated via Joule heat.

Intermittency and scale-dependent statistics in fully developed turbulence

Fully developed homogeneous isotropic turbulent fields, computed by direct numerical simulation, are compared to divergence-free random fields having the same energy spectrum and either the same helicity spectrum as that of the turbulent data, or vanishing helicity. We show that the scale-dependent velocity flatness quantifies the spatial variability of the energy spectrum. The flatness exhibits a substantial increase at small scales for the turbulent field, but remains constant for the random fields. A diagnostic, the scale-dependent helicity, is proposed to quantify the geometrical statistics of the flow, which shows that only the turbulent flow is intermittent. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations confirm the inherently different dynamics of turbulent and random flows.

Helicity cascades in rotating turbulence

The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the dynamics of the flow. In particular, at small Rossby number, the energy cascades to large scales, as expected, but helicity then can dominate the cascade to small scales. A phenomenological interpretation in terms of a direct cascade of helicity slowed down by wave-eddy interactions leads to the prediction of non-Kolmogorovian inertial indices for the small-scale energy and helicity spectra.

Writhe in the stretch-twist-fold dynamo

This article looks at the influence of writhe in the stretch-twist-fold dynamo. We consider a thin flux tube distorted by simple stretch, twist, and fold motions and calculate the helicity and energy spectra. The writhe number assists in the calculations, as it tells us how much the internal twist changes as the tube is distorted. In addition it provides a valuable diagnostic for the degree of distortion. Non mirror-symmetric dynamos typically generate magnetic helicity of one sign on large-scales and the opposite sign on small scales. The calculations presented here confirm the hypothesis that the large-scale helicity corresponds to writhe and the small scale corresponds to twist. In addition, the writhe helicity spectrum exhibits an interesting oscillatory behavior. The technique of calculating Fourier spectra for the writhe helicity may be useful in other areas of research, for example, the study of highly coiled molecules.

Dissecting the N-terminal Helical Domain of Apolipoprotein B

High levels of low density lipoprotein (LDL, the bad cholesterol) are associated with cardiovascular disease, the leading cause of death in western countries. Very low density lipoprotein (VLDL, the precursor to LDL) secretion requires proper folding of the N-terminal domains of apolipoprotein B (ApoB). The N-terminal domain of ApoB is homologous to lipovitellin, whose structure is known. It is composed of a β-barrel, followed by a helical domain and two β-sheet domains. There is little direct structural information on any part of ApoB. Structural studies of the N-terminal domain of ApoB are complicated by aggregation in the absence of lipids. Our initial goal was to isolate an independent folding domain suitable for study by NMR. Two constructs encoding ApoB6.4-8 and ApoB6.4-9 were found to be cooperatively folded and show helical CD spectra. Single point mutations (e.g. L343V) within this region of ApoB have been shown to cause Familial Hypobetalipoproteinemia (FHBL). FHBL is characterized by low levels of plasma ApoB-containing lipoproteins. These mutations result in retention and degradation of ApoB in the ER. Despite the conservative mutation, our hypothesis is that the mutations cause a structural defect in this helical domain which disrupts efficient secretion of VLDL.

Acoustic Radiation From an Infinite Laminated Composite Cylindrical Shell With Doubly Periodic Rings

Abstract Acoustic radiation from a point-driven, infinite fluid-loaded, laminated composite shell, which is reinforced by doubly periodic rings, is investigated theoretically. The theory is based on the classical laminated composite shell theory, the Helmholtz equation, and the boundary conditions at the shell-fluid interface as well as at the junctions between the shell and the rings. The rings interact with the shell only through normal forces. The solution for the radial displacement in wave number domain is developed by using Mace’s method (1980, “Sound Radiation Form a Plate Reinforced by Two Sets of Parallel Stiffeners,” J. Sound Vib., 71(3), pp. 435–441) for an infinite flat plate. The stationary phase approximate is then employed to find the expression for the far-field pressure. Numerical results are presented for discussion of the effects of lamination schemes, Poisson’s ratios, ply angles, and damping on the far-field acoustic radiation, which may lend themselves to better understanding the characteristics of acoustic radiation from the laminated composite shells. In addition, the helical wave spectra of the stiffened cylinders are presented, in which the effects of wave number conversion due to the periodic rings are obviously identified as additional bright patterns.

Helicity of alpha(404-451) and beta(394-445) tubulin C-terminal recombinant peptides.

We have investigated the solution conformation of the functionally relevant C-terminal extremes of alpha- and beta-tubulin, employing the model recombinant peptides RL52alpha3 and RL33beta6, which correspond to the amino acid sequences 404-451(end) and 394-445(end) of the main vertebrate isotypes of alpha- and beta-tubulin, respectively, and synthetic peptides with the alpha-tubulin(430-443) and beta-tubulin(412-431) internal sequences. Alpha(404-451) and beta(394-445) are monomeric in neutral aqueous solution (as indicated by sedimentation equilibrium), and have circular dichroism (CD) spectra characteristic of nearly disordered conformation, consistent with low scores in peptide helicity prediction. Limited proteolysis of beta(394-445) with subtilisin, instead of giving extensive degradation, resulted in main cleavages at positions Thr409-Glu410 and Tyr422-Gln423-Gln424, defining the proteolysis resistant segment 410-422, which corresponds to the central part of the predicted beta-tubulin C-terminal helix. Both recombinant peptides inhibited microtubule assembly, probably due to sequestration of the microtubule stabilizing associated proteins. Trifluoroethanol (TFE)-induced markedly helical CD spectra in alpha(404-451) and beta(394-445). A substantial part of the helicity of beta(394-445) was found to be in the CD spectrum of the shorter peptide beta(412-431) with TFE. Two-dimensional 1H-NMR parameters (nonsequential nuclear Overhauser effects (NOE) and conformational C alphaH shifts) in 30% TFE permitted to conclude that about 25% of alpha(404-451) and 40% of beta(394-451) form well-defined helices encompassing residues 418-432 and 408-431, respectively, flanked by disordered N- and C-segments. The side chains of beta(394-451) residues Leu418, Val419, Ser420, Tyr422, Tyr425, and Gln426 are well defined in structure calculations from the NOE distance constraints. The apolar faces of the helix in both alpha and beta chains share a characteristic sequence of conserved residues Ala,Met(+4),Leu(+7),Tyr(+11). The helical segment of alpha(404-451) is the same as that described in the electron crystallographic model structure of alphabeta-tubulin, while in beta(394-451) it extends for nine residues more, supporting the possibility of a functional coil --> helix transition at the C-terminus of beta-tubulin. These peptides may be employed to construct model complexes with microtubule associated protein binding sites.