Global axisymmetric Magnetorotational Instability with density gradients

We examine global incompressible axisymmetric perturbations of a differentially rotating MHD plasma with radial density gradients. It is shown that the standard magnetorotational instability, (MRI) criterion drawn from the local dispersion relation is often misleading. If the equilibrium magnetic field is either purely axial or purely toroidal, the problem reduces to finding the global radial eigenvalues of an effective potential. The standard Keplerian profile including the origin is mathematically ill-posed, and thus any solution will depend strongly on the inner boundary. We find a class of unstable modes localized by the form of the rotation and density profiles, with reduced dependence on boundary conditions.Comment: 22 pages, 5 figure

Walls Inhibit Chaotic Mixing

We report on experiments of chaotic mixing in a closed vessel, in which a highly viscous fluid is stirred by a moving rod. We analyze quantitatively how the concentration field of a low-diffusivity dye relaxes towards homogeneity, and we observe a slow algebraic decay of the inhomogeneity, at odds with the exponential decay predicted by most previous studies. Visual observations reveal the dominant role of the vessel wall, which strongly influences the concentration field in the entire domain and causes the anomalous scaling. A simplified 1D model supports our experimental results. Quantitative analysis of the concentration pattern leads to scalings for the distributions and the variance of the concentration field consistent with experimental and numerical results.Comment: 4 pages, 3 figure

Slow decay of concentration variance due to no-slip walls in chaotic mixing

Chaotic mixing in a closed vessel is studied experimentally and numerically in different 2-D flow configurations. For a purely hyperbolic phase space, it is well-known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincare section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1-D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.Comment: 17 pages, 12 figure

On the relevance of subcritical hydrodynamic turbulence to accretion disk transport

Hydrodynamic unstratified keplerian flows are known to be linearly stable at all Reynolds numbers, but may nevertheless become turbulent through nonlinear mechanisms. However, in the last ten years, conflicting points of view have appeared on this issue. We have revisited the problem through numerical simulations in the shearing sheet limit. It turns out that the effect of the Coriolis force in stabilizing the flow depends on whether the flow is cyclonic (cooperating shear and rotation vorticities) or anticyclonic (competing shear and rotation vorticities); keplerian flows are anticyclonic. We have obtained the following results: i/ The Coriolis force does not quench turbulence in subcritical flows; ii/ The resolution demand, when moving away from the marginal stability boundary, is much more severe for anticyclonic flows than for cyclonic ones. Presently available computer resources do not allow numerical codes to reach the keplerian regime. iii/ The efficiency of turbulent transport is directly correlated to the Reynolds number of transition to turbulence $Rg$, in such a way that the Shakura-Sunyaev parameter $\alpha\sim 1/Rg$. iv/ Even the most optimistic extrapolations of our numerical data show that subcritical turbulent transport would be too inefficient in keplerian flows by several orders of magnitude for astrophysical purposes. v/ Our results suggest that the data obtained for keplerian-like flows in a Taylor-Couette settings are largely affected by secondary flows, such as Ekman circulation.Comment: 21 pages, 17 figures, accepted in Astronomy and Astrophysic

Scaling laws and vortex profiles in 2D decaying turbulence

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, as predicted by Carnevale et al., and it is observed that viscous effects spoil this scaling regime. This scaling regime shows some trends toward that of the Kirchhoff model, for which a recent theory predicts a decay exponent $\xi=1$. In terms of scaled variables, the vortices have a similar profile close to a Fermi-Dirac distribution.Comment: 4 Latex pages and 4 figures. Submitted to Phys. Rev. Let

Dynamics and thermodynamics of axisymmetric flows: I. Theory

We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We derive relaxation equations which can be used as numerical algorithm to construct stable stationary solutions of axisymmetric flows. In a second part, we develop a thermodynamical approach to the equilibrium states at some fixed coarse-grained scale. We show that the resulting distribution can be divided in a universal part coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding non-ideal effects such as viscosity, small-scale forcing and dissipation (for forced systems). Finally, we derive a parameterization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale

Resolving Molecular Line Emission from Protoplanetary Disks: Observational Prospects for Disks Irradiated by Infalling Envelopes

Molecular line observations that could resolve protoplanetary disks of ~100 AU both spatially and kinematically would be a useful tool to unambiguously identify these disks and to determine their kinematical and physical characteristics. In this work we model the expected line emission from a protoplanetary disk irradiated by an infalling envelope, addressing the question of its detectability with subarcsecond resolution. We adopt a previously determined disk model structure that gives a continuum spectral energy distribution and a mm intensity spatial distribution that are consistent with observational constraints of HL Tau. An analysis of the capability of presently working and projected interferometers at mm and submm wavelengths shows that molecular transitions of moderate opacity at these wavelengths (e.g., C17O lines) are good candidates for detecting disk lines at subarcsecond resolution in the near future. We suggest that, in general, disks of typical Class I sources will be detectable.Comment: 41 pages, 16 figures. To be published in The Astrophysical Journa

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling

Stability of density-stratified viscous Taylor-Couette flows

The stability of density-stratified viscous Taylor-Couette flows is considered using the Boussinesq approximation but without any use of the short-wave approximation. The flows which are unstable after the Rayleigh criterion (\hat \mu<\hat \eta^2, with \hat \mu=\Omega_{out}/\Omega_{in} and \hat \eta= R_{in}/R_{out}) now develop overstable axisymmetric Taylor vortices. For the considered wide-gap container we find the nonaxisymmetric modes as the most unstable ones. The nonaxisymmetric modes are unstable also beyond the Rayleigh line. For such modes the instability condition seems simply to be \hat\mu<1 as stressed by Yavneh, McWilliams & Molemaker (2001). However, we never found unstable modes for too flat rotation laws fulfilling the condition \hat \mu >\hat \eta. The Reynolds numbers rapidly grow to very high values if this limit is approached (see Figs. 3 and 4). Also striking is that the marginal stability lines for the higher $m$ do less and less enter the region beyond the Rayleigh line so that we might have to consider the stratorotational instability as a 'low-$m$ instability'. The applicability of these results to the stability problem of accretion disks with their strong stratification and fast rotation is shortly discussed.Comment: 7 pages, 7 figures, Astron. Astrophys. (subm.

Deciphering the infectious process of Colletotrichum lupini in lupin through transcriptomic and proteomic analysis

The fungal phytopathogen Colletotrichum lupini is responsible for lupin anthracnose, resulting in significant yield losses worldwide. The molecular mechanisms underlying this infectious process are yet to be elucidated. This study proposes to evaluate C. lupini gene expression and protein synthesis during lupin infection, using, respectively, an RNAseq-based transcriptomic approach and a mass spectrometry-based proteomic approach. Patterns of differentially-expressed genes in planta were evaluated from 24 to 84 hours post-inoculation, and compared to in vitro cultures. A total of 897 differentially-expressed genes were identified from C. lupini during interaction with white lupin, of which 520 genes were predicted to have a putative function, including carbohydrate active enzyme, effector, protease or transporter-encoding genes, commonly described as pathogenicity factors for other Colletotrichum species during plant infection, and 377 hypothetical proteins. Simultaneously, a total of 304 proteins produced during the interaction were identified and quantified by mass spectrometry. Taken together, the results highlight that the dynamics of symptoms, gene expression and protein synthesis shared similarities to those of hemibiotrophic pathogens. In addition, a few genes with unknown or poorly-described functions were found to be specifically associated with the early or late stages of infection, suggesting that they may be of importance for pathogenicity. This study, conducted for the first time on a species belonging to the Colletotrichum acutatum species complex, presents an opportunity to deepen functional analyses of the genes involved in the pathogenicity of Colletotrichum spp. during the onset of plant infection