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Register a new userMHD Turbulent Mixing Layers: Equilibrium Cooling Models
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We present models of turbulent mixing at the boundaries between hot (T~10^{6-7} K) and warm material (T~10^4 K) in the interstellar medium, using a three-dimensional magnetohydrodynamical code, with radiative cooling. The source of turbulence in our simulations is a Kelvin-Helmholtz instability, produced by shear between the two media. We found, that because the growth rate of the large scale modes in the instability is rather slow, it takes a significant amount of time (~1 Myr) for turbulence to produce effective mixing. We find that the total column densities of the highly ionized species (C IV, N V, and O VI) per interface (assuming ionization equilibrium) are similar to previous steady-state non-equilibrium ionization models, but grow slowly from log N ~10^{11} to a few 10^{12} cm^{-2} as the interface evolves. However, the column density ratios can differ significantly from previous estimates, with an order of magnitude variation in N(C IV)/N(O VI) as the mixing develops.
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Radiative turbulent mixing layers should be ubiquitous in multi-phase gas with shear flow. They are a potentially attractive explanation for the high ions such as OVI seen in high velocity clouds and the circumgalactic medium (CGM) of galaxies. We perform 3D MHD simulations with non-equilibrium (NEI) and photoionization modeling, with an eye towards testing simple analytic models. Even purely hydrodynamic collisional ionization equilibrium (CIE) calculations have column densities much lower than observations. Characteristic inflow and turbulent velocities are much less than the shear velocity, and the layer width $h propto t_mathrm{cool}^{1/2}$ rather than $h propto t_mathrm{cool}$. Column densities are not independent of density or metallicity as analytic scalings predict, and show surprisingly weak dependence on shear velocity and density contrast. Radiative cooling, rather than Kelvin-Helmholtz instability, appears paramount in determining the saturated state. Low pressure due to fast cooling both seeds turbulence and sets the entrainment rate of hot gas, whose enthalpy flux, along with turbulent dissipation, energizes the layer. Regardless of initial geometry, magnetic fields are amplified and stabilize the mixing layer via magnetic tension, producing almost laminar flow and depressing column densities. NEI effects can boost column densities by factors of a few. Suppression of cooling by NEI or photoionization can in principle also increase OVI column densities, but in practice is unimportant for CGM conditions. To explain observations, sightlines must pierce hundreds or thousands of mixing layers, which may be plausible if the CGM exists as a `fog of tiny cloudlets.
The space-borne missions have provided a wealth of highly accurate data. However, our inability to properly model the upper-most region of solar-like stars prevents us from making the best of these observations. This problem is called surface effect and a key ingredient to solve it is turbulent pressure for the computation of both the equilibrium models and the oscillations. While 3D hydrodynamic simulations help to include properly the turbulent pressure in the equilibrium models, the way this surface effect is included in the computation of stellar oscillations is still subject to uncertainties. We aim at determining how to properly include the effect of turbulent pressure and its Lagrangian perturbation in the adiabatic computation of the oscillations. We also discuss the validity of the gas-gamma model (GGM) and reduced gamma model (RGM) approximations, which have been used to compute adiabatic oscillations of equilibrium models including turbulent pressure. We use a patched model of the Sun with an inner part constructed by a 1D stellar evolution code (CESTAM) and an outer part by the 3D hydrodynamical code (CO$^5$BOLD). Then, the adiabatic oscillations are computed using the ADIPLS code for the GGM and RGM and with the MAD code imposing the adiabatic condition on an existing time-dependent convection (TDC) formalism. We show that the computation of the oscillations using the TDC formalism in the adiabatic limit improves significantly the agreement with the observed frequencies compared to the GGM and RGM. Of the components of the turbulent pressure perturbation, the perturbation of the density and advection term is found to contribute most to the frequency shift. We propose a formalism to evaluate the frequency shift due to the inclusion of the term with the turbulent pressure perturbation in the variational principle in order to extrapolate our result to other stars.
We present a series of numerical simulations of the quiet Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Suns atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.
The stationary condition (Hopf equation) for the ($n$+1) point correlation function of a passive scalar advected by turbulent flow is argued to have an approximate $SL(n, R)$ symmetry which provides a starting point for the perturbative treatment of less symmetric terms. The large scale anisotropy is found to be a relevant field, in contradiction with Kolmogorov phenomenology, but in agreement with the large scalar skewness observed in shear flows. Exponents are not universal, yet quantitative predictions for experiments to test the $SL(n, R)$ symmetry can be formulated in terms of the correlation functions.
Turbulent spectra of magnetic fluctuations in the free solar wind are studied from MHD to electron scales using Cluster observations. We discuss the problem of the instrumental noise and its influence on the measurements at the electron scales. We confirm the presence of a curvature of the spectrum $sim exp{sqrt{krho_e}}$ over the broad frequency range $sim[10,100]$ Hz, indicating the presence of a dissipation. Analysis of seven spectra under different plasma conditions show clearly the presence of a quasi-universal power-law spectrum at MHD and ion scales. However, the transition from the inertial range $sim k^{-1.7}$ to the spectrum at ion scales $sim k^{-2.7}$ is not universal. Finally, we discuss the role of different kinetic plasma scales on the spectral shape, considering normalized dimensionless spectra.
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