Algebraic stability modes in rotational shear flow

We investigate the two-dimensional (2D) stability of rotational shear flows in an unbounded domain. The eigenvalue problem is formulated by using a novel algebraic mode decomposition distinct from the normal modes with temporal evolution $\exp(\omega t)$. Based on the work of \citeasnoun{NoldOberlack2013}, we show how these new modes can be constructed from the symmetries of the linearized stability equation. For the azimuthal base flow velocity $V(r)=r^{-1}$ an additional symmetry exists, such that a mode with algebraic temporal evolution $t^s$ is found. $s$ refers to an eigenvalue for the algebraic growth or decay of the kinetic energy of the perturbations. An eigenvalue problem for the viscous and inviscid stability using algebraic modes is formulated on an infinite domain with $r \to \infty$. An asymptotic analysis of the eigenfunctions shows that the flow is linearly stable under 2D perturbations. We find stable modes with the algebraic mode ansatz, which can not be obtained by a normal mode analysis. The stability results are in line with Rayleigh's inflection point theorem.

Solar wind speed and rotational shear at coronal hole boundaries, impacts on magnetic field inversions

<p>The solar wind is frequently perturbed by transient structures such as magnetic folds, jets, waves and flux-ropes that propagate rapidly away from the Sun over a large range of heliocentric distances. Parker Solar Probe has revealed that rotations of the magnetic field vector occur repeatedly at small heliocentric distances, on regions that also display surprisingly large solar wind rotation rates. Sun-to-spacecraft connectivity analysis shows that a large fraction of the solar wind flows probed so far by Parker Solar Probe were formed and accelerated in the vicinity of coronal hole boundaries.<br>We show by means of of global MHD simulations that coronal rotation is highly structured in proximity to those boundary regions (in agreement with preceding SoHO/UVCS observations), and that enhanced poloidal and toroidal flow shear and magnetic field gradients also develop there. We identified regions of the solar corona for which solar wind speed and rotational shear are significant, that can be associated with field-aligned and/or transverse vorticity, and that can be favourable to the development of magnetic deflections. Some of these wind flow shears are driven through large radial extensions, being noticeable tens of solar radii away from the surface, and therefore have a potential impact on the propagation of such magnetic perturbations across extended heights in the solar wind. We conclude that these regions of persistent shears are undoubtedly sources of complex solar wind structures, and suggest that they can trigger instabilities capable of creating magnetic field reversals detected in-situ in the heliosphere.<br>Our simulations furthermore indicate that the spatial structure of the solar wind shear will become more complex as the solar cycle progresses, with strong and extended shears appearing at heliographic latitudes that will be probed by Solar Orbiter in the near future.</p>

ANALYSIS OF LOCAL FIELDS OF ELASTIC STRESS GENERATED BY ROTATIONAL-SHEAR MESODEFECTS NEAR THE JUNCTIONS OF GRAINS

The work is devoted to the study of the structure of the elastic stress field in the area of junctions of grain boundaries containing strain-induced rotational-shear mesodefects. The jumps in plastic distortion of grains when passing through grain boundaries create additional misorientations on them, the mismatch of which at the junctions of grains leads to the appearance of linear mesodefects of the rotational type – junction disclinations. Planar mesodefects of the shear type appear on the flat sections of the boundaries, which are plastic shears uniformly distributed along the boundaries. These mesodefects create spatially inhomogeneous elastic stress fields near the junctions and ledges of the grains. They increase during plastic deformation and, at sufficiently large value of strain, initiate the formation of a fragmented material structure. Rotational-shear mesodefects are also the cause of the nucleation and accumulation of microcracks at the stage of viscous fracture of polycrystalline solids. In this work, asymptotic formulas are obtained that make it possible to analyze the distribution and anisotropy of the internal stress field in the vicinity of the grain junction from rotational-shear mesodefects. It was found that the components of the stress field weakly depend (logarithmically) on the length of the grain boundaries formatting junction of the grains. It is shown that the screening disclination of the dipole leads to the appearance of an angular dependence of the diagonal components of the elastic stress tensor in the vicinity of the junctions and its contribution to the elastic field of the disclinations dipole is about 10–15%. The obtained asymptotic expressions can be used to study the kinetics of a dislocation ensemble and to analyze the conditions for the nucleation of microcracks in the vicinity of joints and ledges of grains.