Oscillatory disintegration of a trans-Alfvenic shock: A magnetohydrodynamic simulation

Nonlinear evolution of a trans-Alfvenic shock wave (TASW), at which the flow velocity passes over the Alfven velocity, is computed in a magnetohydrodynamic approximation. The analytical theory suggests that an infinitesimal perturbation of a TASW results in its disintegration, i.e., finite variation of the flow, or transformation into some other unsteady configuration. In the present paper, this result is confirmed by numerical simulations. It is shown that the disintegration time is close to its minimum value equal to the shock thickness divided by a relative velocity of the emerging secondary structures. The secondary TASW that appears after the disintegration is again unstable with respect to disintegration. When the perturbation has a cyclic nature, the TASW undergoes oscillatory disintegration, during which it repeatedly transforms into another TASW. This process manifests itself as a train of shock and rarefaction waves, which consecutively emerge at one edge of the train and merge at the other edge.Comment: REVTEX, 8 pages, 13 PostScript figures, uses epsfig.st

The Linear Instability of Astrophysical Flames in Magnetic Fields

Supernovae of Type Ia are used as standard candles for cosmological observations despite the as yet incomplete understanding of their explosion mechanism. In one model, these events are thought to result from subsonic burning in the core of an accreting Carbon/Oxygen white dwarf that is accelerated through flame wrinkling and flame instabilities. Many such white dwarfs have significant magnetic fields. Here we derive the linear effects of such magnetic fields on one flame instability, the well-known Landau-Darrieus instability. When the magnetic field is strong enough that the flame is everywhere sub-Alfvenic, the instability can be greatly suppressed. Super-Alfvenic flames are much less affected by the field, with flames propagating parallel to the field somewh at destabilized, and flames propagating perpendicular to the field somewhat stabili zed. Trans-Alfvenic parallel flames, however, like trans-Alfvenic parallel shocks, are seen to be non-evolutionary; understanding the behavior of these flames will require careful numerical simulation.Comment: 31 pp, 11 fig, submitted to Ap

Proton, Electron, and Ion Heating in the Fast Solar Wind from Nonlinear Coupling Between Alfvenic and Fast-Mode Turbulence

In the parts of the solar corona and solar wind that experience the fewest Coulomb collisions, the component proton, electron, and heavy ion populations are not in thermal equilibrium with one another. Observed differences in temperatures, outflow speeds, and velocity distribution anisotropies are useful constraints on proposed explanations for how the plasma is heated and accelerated. This paper presents new predictions of the rates of collisionless heating for each particle species, in which the energy input is assumed to come from magnetohydrodynamic (MHD) turbulence. We first created an empirical description of the radial evolution of Alfven, fast-mode, and slow-mode MHD waves. This model provides the total wave power in each mode as a function of distance along an expanding flux tube in the high-speed solar wind. Next we solved a set of cascade advection-diffusion equations that give the time-steady wavenumber spectra at each distance. An approximate term for nonlinear coupling between the Alfven and fast-mode fluctuations is included. For reasonable choices of the parameters, our model contains enough energy transfer from the fast mode to the Alfven mode to excite the high-frequency ion cyclotron resonance. This resonance is efficient at heating protons and other ions in the direction perpendicular to the background magnetic field, and our model predicts heating rates for these species that agree well with both spectroscopic and in situ measurements. Nonetheless, the high-frequency waves comprise only a small part of the total Alfvenic fluctuation spectrum, which remains highly two-dimensional as is observed in interplanetary space.Comment: Accepted for publication in the Astrophysical Journal. 30 pages (emulateapj style), 18 figure

Solar Wind Turbulence and the Role of Ion Instabilities

International audienc

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions

On Identifying the Formation Pressure and Filtration Coefficients of Two Gaz-bearing Formations

In the practice of gas field exploitation, there arises a problem of the production rates calculation for two gas-bearing formations opened by a single well. Its solution requires knowledge of the formation pressures and flow coefficients. While solving the problem, an important concept of the turning points has been introduced. They play a key role in developing a system of equations. In practice, no information on the formation flow coefficients and pressures is available; therefore, a question now arises of how they can be determined. It is possible to use downhole measurements, although doing this appears to be technically challenging. Wellhead measurements are simpler, but they provide only total production rate values under a fixed wellhead pressure. In [9], the authors are of the opinion that “measuring the flow coefficients of two gas-bearing formations opened by a single well without downhole measurements is currently impossible.”The problem under studying may have 13 different variants of setting up, depending on the placement of the wellhead pressure that is measured with respect to the turning points. It is unknown in advance which of the aforementioned variants is the case while measuring; therefore, it is necessary to study each of them individually. One of the most difficult cases is considered in the present article. Mathematically, the problem is reduced to solving a system of equations with 30 unknown quantities, and only 6 out of these equations are linear. Among the unknowns, there are the formation pressure and flow coefficients 3+3=6 of the upper and lower formations as well as 24 unknowns at each formation flow rate measuring: 6+6=12 and 6+6=12 wellbore pressures.It is reasonable to take the upper formation flow rates as the main unknowns in 1, 3, and 5 measurements, in which case the unknown formation pressures and flow coefficients are determined: they turn out to be the functions of the main unknowns, which in their turn satisfy a system of a three nonlinear equations' polynomial over the first unknown of the seventh degree. Therewith, it is shown that two other main parameters are changed within the bounded domain, the boundary of which is explicitly described. This fact significantly simplifies solving the problem, whereas the desired formation pressures and filtration coefficients are a priori unbounded