Turbulence model reduction by deep learning

A central problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce a new, data-driven method for parameterizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local \emph{gradient} of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.Comment: To be published in Phys. Rev. E Rap. Comm. 6 pages, 7 figure

Suppression of Cross-Field Transport of a Passive Scalar in Two-Dimensional Magnetohydrodynamic Turbulence

The theory of passive scalar transport in two dimensional turbulent fluids is generalized to the case of 2D MHD. Invariance of the cross correlation of scalar concentration and magnetic potential produces a novel contribution to the concentration flux. This pinch effect is proportional to the mean potential gradient, and is shown to drastically reduce transport of the passive scalar across the mean magnetic field when . Transport parallel to the mean magnetic field is unchanged. Implications for models of transport in turbulent magnetofluids are discussed. PAC NOS. 47.25.Jn, 47.65.+aComment: uuencoded compressed postscript fil

Dynamics of a 1-D model for the emergence of the plasma edge shear flow layer with momentum conserving Reynolds stress

A one-dimensional version of the second-order transition model based on the sheared flow amplification by Reynolds stress and turbulence supression by shearing is presented. The model discussed in this paper includes a form of the Reynolds stress which explicitly conserves momentum. A linear stability analysis of the critical point is performed. Then, it is shown that the dynamics of weakly unstable states is determined by a reduced equation for the shear flow. In the case in which the flow damping term is diffusive, the stationary solutions are those of the real Ginzburg-Landau equation.Comment: 21 pages, 8 figure

Modern theory of Fermi acceleration: a new challenge to plasma physics

One of the main features of astrophysical shocks is their ability to accelerate particles to extremely high energies. The leading acceleration mechanism, the diffusive shock acceleration is reviewed. It is demonstrated that its efficiency critically depends on the injection of thermal plasma into acceleration which takes place at the subshock of the collisionless shock structure that, in turn, can be significantly smoothed by energetic particles. Furthermore, their inhomogeneous distribution provides free energy for MHD turbulence regulating the subshock strength and injection rate. Moreover, the MHD turbulence confines particles to the shock front controlling their maximum energy and bootstrapping acceleration. Therefore, the study of the MHD turbulence in a compressive plasma flow near a shock is a key to understanding of the entire process. The calculation of the injection rate became part of the collisionless shock theory. It is argued that the further progress in diffusive shock acceleration theory is impossible without a significant advance in these two areas of plasma physics.Comment: 12 pages, 4 figures, invited talk at APS/ICPP, Quebec 2000, to appear in Phys. of Plasma

Critical self-organization of astrophysical shocks

There are two distinct regimes of the first order Fermi acceleration at shocks. The first is a linear (test particle) regime in which most of the shock energy goes into thermal and bulk motion of the plasma. The second is an efficient regime when it goes into accelerated particles. Although the transition region between them is narrow, we identify the factors that drive the system to a {\it self-organized critical state} between those two. Using an analytic solution, we determine this critical state and calculate the spectra and maximum energy of accelerated particles.Comment: To appear in ApJL, Sec.3 extensively rewritten, 4 pages, Latex, emulateapj.sty, eps

Hadronic Gamma Rays from Supernova Remnants

A gas cloud near a supernova remnant (SNR) provides a target for pp-collisions leading to subsequent gamma-ray emission through neutral pion decay. The assumption of a power-law ambient spectrum of accelerated particles with index near -2 is usually built into models predicting the spectra of very-high energy (VHE) gamma-ray emission from SNRs. However, if the gas cloud is located at some distance from the SNR shock, this assumption is not necessarily correct. In this case, the particles which interact with the cloud are those leaking from the shock and their spectrum is approximately monoenergetic with the injection energy gradually decreasing as the SNR ages. In the GLAST energy range the gamma-ray spectrum resulting from particle interactions with the gas cloud will be flatter than expected, with the cutoff defined by the pion momentum distribution in the laboratory frame. We evaluate the flux of particles escaping from a SNR shock and apply the results to the VHE diffuse emission detected by the HESS at the Galactic centre.Comment: 4 pages, 3 figures. Contribution to the 30th ICRC, Merida, Mexico, 2007 (final version

Polarization morphology of SiO masers in the circumstellar envelope of the AGB star R Cassiopeiae

Silicon monoxide maser emission has been detected in the circumstellar envelopes of many evolved stars in various vibrationally-excited rotational transitions. It is considered a good tracer of the wind dynamics close to the photosphere of the star. We have investigated the polarization morphology in the circumstellar envelope of an AGB star, R Cas. We mapped the linear and circular polarization of SiO masers in the v=1, J=1-0 transition. The linear polarization is typically a few tens of percent while the circular polarization is a few percent. The fractional polarization tends to be higher for emission of lower total intensity. We found that, in some isolated features the fractional linear polarization appears to exceed 100%. We found the Faraday rotation is not negligible but is ~15 deg., which could produce small scale structure in polarized emission whilst total intensity is smoother and partly resolved out. The polarization angles vary considerably from feature to feature but there is a tendency to favour the directions parallel or perpendicular to the radial direction with respect to the star. In some features, the polarization angle abruptly flips 90 deg. We found that our data are in the regime where the model of Goldreich et al (1973) can be applied and the polarization angle flip is caused when the magnetic field is at close to 55 deg. to the line of sight. The polarization angle configuration is consistent with a radial magnetic field although other configurations are not excluded.Comment: 14 pages, 15 figures. Accepted for publication in MNRA