Geometrical statistics and vortex structures in helical and nonhelical turbulences

In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and nonhelical turbulences generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the antisymmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe the following in both helical and nonhelical turbulences: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 with both the most contractive and the most extensive eigendirections of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3336012

A pandemic lesson for global lung diseases: exacerbations are preventable.

A dramatic global reduction in the incidence of common seasonal respiratory viral infections has resulted from measures to limit the transmission of SARS2-Cov-19 during the pandemic . This has been accompanied by falls reaching 50% internationally in the incidence of acute exacerbations of pre-existing chronic respiratory diseases that include asthma, Chronic Obstructive Pulmonary Disease (COPD) and Cystic Fibrosis (CF). At the same time, the incidence of acute bacterial pneumonia and sepsis has fallen steeply world-wide. Such findings demonstrate the profound impact of common respiratory viruses on the course of these global illnesses. Reduced transmission of common respiratory bacterial pathogens and their interactions with viruses appear also as central factors. This review summarises pandemic changes in exacerbation rates of asthma, COPD, Cystic Fibrosis (CF) and pneumonia. We draw attention to the substantial body of knowledge about respiratory virus infections in these conditions, and that it has not yet translated into clinical practice. Now the large-scale of benefits that could be gained by managing these pathogens is unmistakable, we suggest the field merits substantial academic and industrial investment. We consider how pandemic-inspired measures for prevention and treatment of common infections should become a cornerstone for managing respiratory diseases. This article is open access and distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives License 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Creation and evolution of magnetic helicity

Projecting a non-Abelian SU(2) vacuum gauge field - a pure gauge constructed from the group element U - onto a fixed (electromagnetic) direction in isospace gives rise to a nontrivial magnetic field, with nonvanishing magnetic helicity, which coincides with the winding number of U. Although the helicity is not conserved under Maxwell (vacuum) evolution, it retains one-half its initial value at infinite time.Comment: Clarifying remarks and references added; 12 pages, 1 figure using BoxedEPSF, REVTeX macros; submitted to Phys Rev D; email to [email protected]

Analytical theory of forced rotating sheared turbulence: The perpendicular case

Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear (ξ=νky2/A⪡1, where A is the shearing rate, ν is the molecular viscosity, and ky is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (Ω⪢A), they scale as A−1 and A−1|ln ξ|, respectively, while in the weak rotation limit (Ω⪡A), they scale as A−1 and A−2/3, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is, however, weaker by a factor of ξ1/3|ln ξ| (∝A−1/3|ln ξ|) in the rapid rotation limit (Ω⪢A) than that in the weak rotation limit (Ω⪡A) since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (Ω⪢A), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e., ∝Ω−1) while in the opposite case, it is reduced by shearing as A−1. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (Ω⪢A) while positive in the opposite limit of weak rotation (Ω⪡A). Even if the eddy viscosity is negative for strong rotation (Ω⪢A), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |νT|∝A−2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a nondiffusive flux of angular momentum (Λ effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

``Smoke Rings'' in Ferromagnets

It is shown that bulk ferromagnets support propagating non-linear modes that are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These are circular loops of {\it magnetic} vorticity which travel at constant velocity parallel to their axis of symmetry. The topological structure of the continuum theory has important consequences for the properties of these magnetic vortex rings. One finds that there exists a sequence of magnetic vortex rings that are distinguished by a topological invariant (the Hopf invariant). We present analytical and numerical results for the energies, velocities and structures of propagating magnetic vortex rings in ferromagnetic materials.Comment: 4 pages, 3 eps-figures, revtex with epsf.tex and multicol.sty. To appear in Physical Review Letters. (Postscript problem fixed.

On the three-dimensional temporal spectrum of stretched vortices

The three-dimensional stability problem of a stretched stationary vortex is addressed in this letter. More specifically, we prove that the discrete part of the temporal spectrum is only associated with two-dimensional perturbations.Comment: 4 pages, RevTeX, submitted to PR

Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations

We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibson, who observed that the vorticity vector {\boldmath\omega} aligns with the intermediate eigenvector of the strain matrix $S$, we study this problem in the context of both the three-dimensional Euler and Navier-Stokes equations using the variables \alpha = \hat{{\boldmath\xi}}\cdot S\hat{{\boldmath\xi}} and {\boldmath\chi} = \hat{{\boldmath\xi}}\times S\hat{{\boldmath\xi}} where \hat{{\boldmath\xi}} = {\boldmath\omega}/\omega. This introduces the dynamic angle $\phi (x,t) = \arctan(\frac{\chi}{\alpha})$, which lies between {\boldmath\omega} and S{\boldmath\omega}. For the Euler equations a closed set of differential equations for $\alpha$ and {\boldmath\chi} is derived in terms of the Hessian matrix of the pressure $P = \{p_{,ij}\}$. For the Navier-Stokes equations, the Burgers vortex and shear layer solutions turn out to be the Lagrangian fixed point solutions of the equivalent (\alpha,{\boldmath\chi}) equations with a corresponding angle $\phi = 0$. Under certain assumptions for more general flows it is shown that there is an attracting fixed point of the (\alpha,\bchi) equations which corresponds to positive vortex stretching and for which the cosine of the corresponding angle is close to unity. This indicates that near alignment is an attracting state of the system and is consistent with the formation of Burgers-like structures.Comment: To appear in Nonlinearity Nov. 199

Large Scale Structures a Gradient Lines: the case of the Trkal Flow

A specific asymptotic expansion at large Reynolds numbers (R)for the long wavelength perturbation of a non stationary anisotropic helical solution of the force less Navier-Stokes equations (Trkal solutions) is effectively constructed of the Beltrami type terms through multi scaling analysis. The asymptotic procedure is proved to be valid for one specific value of the scaling parameter,namely for the square root of the Reynolds number (R).As a result large scale structures arise as gradient lines of the energy determined by the initial conditions for two anisotropic Beltrami flows of the same helicity.The same intitial conditions determine the boundaries of the vortex-velocity tubes, containing both streamlines and vortex linesComment: 27 pages, 2 figure

Resolving singular forces in cavity flow: Multiscale modeling from atoms to millimeters

A multiscale approach for fluid flow is developed that retains an atomistic description in key regions. The method is applied to a classic problem where all scales contribute: The force on a moving wall bounding a fluid-filled cavity. Continuum equations predict an infinite force due to stress singularities. Following the stress over more than six decades in length in systems with characteristic scales of millimeters and milliseconds allows us to resolve the singularities and determine the force for the first time. The speedup over pure atomistic calculations is more than fourteen orders of magnitude. We find a universal dependence on the macroscopic Reynolds number, and large atomistic effects that depend on wall velocity and interactions.Comment: 4 pages,3 figure