Global MHD simulations of stratified and turbulent protoplanetary discs. I. Model properties

We present the results of global 3-D MHD simulations of stratified and turbulent protoplanetary disc models. The aim of this work is to develop thin disc models capable of sustaining turbulence for long run times, which can be used for on-going studies of planet formation in turbulent discs. The results are obtained using two codes written in spherical coordinates: GLOBAL and NIRVANA. Both are time--explicit and use finite differences along with the Constrained Transport algorithm to evolve the equations of MHD. In the presence of a weak toroidal magnetic field, a thin protoplanetary disc in hydrostatic equilibrium is destabilised by the magnetorotational instability (MRI). When the resolution is large enough (25 vertical grid cells per scale height), the entire disc settles into a turbulent quasi steady-state after about 300 orbits. Angular momentum is transported outward such that the standard alpha parameter is roughly 4-6*10^{-3}. We find that the initial toroidal flux is expelled from the disc midplane and that the disc behaves essentially as a quasi-zero net flux disc for the remainder of the simulation. As in previous studies, the disc develops a dual structure composed of an MRI--driven turbulent core around its midplane, and a magnetised corona stable to the MRI near its surface. By varying disc parameters and boundary conditions, we show that these basic properties of the models are robust. The high resolution disc models we present in this paper achieve a quasi--steady state and sustain turbulence for hundreds of orbits. As such, they are ideally suited to the study of outstanding problems in planet formation such as disc--planet interactions and dust dynamics.Comment: 19 pages, 29 figures, accepted in Astronomy & Astrophysic

General Relativistic Magnetohydrodynamic Simulations of Black Hole Accretion Disks

Observations are providing increasingly detailed quantitative information about the accretion flows that power such high energy systems as X-ray binaries and active galactic nuclei. Analytic models of such systems must rely on assumptions such as regular flow geometry and a simple, parameterized stress. Global numerical simulations offer a way to investigate the basic physical dynamics of accretion flows without these assumptions. For black hole accretion studies one solves the equations of general relativistic magnetohydrodynamics. Magnetic fields are of fundamental importance to the structure and evolution of accretion disks because magnetic turbulence is the source of the anomalous stress that drives accretion. We have developed a three-dimensional general relativistic magnetohydrodynamic simulation code to evolve time-dependent accretion systems self-consistently. Recent global simulations of black hole accretion disks suggest that the generic structure of the accretion flow is usefully divided into five regimes: the main disk, the inner disk, the corona, the evacuated funnel, and the funnel wall jet. The properties of each of these regions are summarized.Comment: invited review at the conference "Stellar-mass, Intermediate-mass, and Supermassive Black Holes", held in Kyoto, Japan, Octorber 28-31, 2003, to be published in Progress of Theoretical Physics Supplemen

The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models

This is the first of a series of papers aimed at developing and interpreting simulations of protoplanets interacting with turbulent accretion discs. Here we study the disc models prior to the introduction of a protoplanet.We study models in which a Keplerian domain is unstable to the magnetorotational instability (MRI). Various models with B-fields having zero net flux are considered.We relate the properties of the models to classical viscous disc theory.All models attain a turbulent state with volume averaged stress parameter alpha ~ 0.005. At any particular time the vertically and azimuthally averaged value exhibited large fluctuations in radius. Time averaging over periods exceeding 3 orbital periods at the outer boundary of the disc resulted in a smoother quantity with radial variations within a factor of two or so. The vertically and azimuthally averaged radial velocity showed much larger spatial and temporal fluctuations, requiring additional time averaging for 7-8 orbital periods at the outer boundary to limit them. Comparison with the value derived from the averaged stress using viscous disc theory yielded schematic agreement for feasible averaging times but with some indication that the effects of residual fluctuations remained. The behaviour described above must be borne in mind when considering laminar disc simulations with anomalous Navier--Stokes viscosity. This is because the operation of a viscosity as in classical viscous disc theory with anomalous viscosity coefficient cannot apply to a turbulent disc undergoing rapid changes due to external perturbation. The classical theory can only be used to describe the time averaged behaviour of the parts of the disc that are in a statistically steady condition for long enough for appropriate averaging to be carried out.Comment: 10 pages, 23 figures, accepted for publication in MNRAS. A gzipped postscript version including high resolution figures is available at http://www.maths.qmul.ac.uk/~rp

An Exact, Three-Dimensional, Time-Dependent Wave Solution in Local Keplerian Flow

We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the solution covers an extensive dynamical range in wavenumber space, it is an excellent test of the dissipative properties of numerical codes.Comment: 22 pages, 4 figures. To appear Apj Dec 1 200

Numerical analysis of a downsized 2-stroke uniflow engine

In order to optimize the 2-stroke uniflow engine performance on vehicle applications, numerical analysis has been introduced, 3D CFD model has been built for the optimization of intake charge organization. The scavenging process was investigated and the intake port design details were improved. Then the output data from 3D CFD calculation were applied to a 1D engine model to process the analysis on engine performance. The boost system optimization of the engine has been carried out also. Furthermore, a vehicle model was also set up to investigate the engine in-vehicle performance

Test results for composite specimens and elements containing joints and cutouts

A program was conducted to develop the technology for joints and cutouts in a composite fuselage that meets all design requirements of a large transport aircraft for the 1990s. An advanced trijet derivative of the DC-10 was selected as the baseline aircraft. Design and analysis of a 30-foot-long composite fuselage barrel provided a realistic basis for the test effort. The primary composite material was Hexcel F584 resin on 12 K IM6 fiber, in tape and broadgoods form. Fiberglass broadgoods were used in E-glass and S-glass fiber form in the cutout region of some panels. Additionally, injection-molded chopped graphite fiber/PEEK was used for longeron-to-frame shear clips. The test effort included four groups of test specimens, beginning with coupon specimens of mono-layer and cross-piled laminates, progressing through increasingly larger and more complex specimens, and ending with two 4- by 5-foot curved fuselage side panels. One of the side panels incorporated a transverse skin splice, while the second included two cabin window cutouts

Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport

The magneto-rotational instability is presently the most promising source of turbulent transport in accretion disks. However, some important issues still need to be addressed to quantify the role of MRI in disks; in particular no systematic investigation of the role of the physical dimensionless parameters of the problem on the dimensionless transport has been undertaken yet. First, we complete existing investigations on the field strength dependence by showing that the transport in high magnetic pressure disks close to marginal stability is highly time-dependent and surprisingly efficient. Second, we bring to light a significant dependence of the global transport on the magnetic Prandtl number, with $\alpha\propto Pm^\delta$ for the explored range: $0.12<Pm<8$ and $200<Re<6400$ ($\delta$ being in the range 0.25 to 0.5). We show that the dimensionless transport is not correlated to the dimensionless linear growth rate, contrarily to a largely held expectation. More generally, these results stress the need to control dissipation processes in astrophysical simulations.Comment: 11 pages, 11 figures, accepted to MNRA

A feasibility study for advanced technology integration for general aviation

An investigation was conducted to identify candidate technologies and specific developments which offer greatest promise for improving safety, fuel efficiency, performance, and utility of general aviation airplanes. Interviews were conducted with general aviation airframe and systems manufacturers and NASA research centers. The following technologies were evaluated for use in airplane design tradeoff studies conducted during the study: avionics, aerodynamics, configurations, structures, flight controls, and propulsion. Based on industry interviews and design tradeoff studies, several recommendations were made for further high payoff research. The most attractive technologies for use by the general aviation industry appear to be advanced engines, composite materials, natural laminar flow airfoils, and advanced integrated avionics systems. The integration of these technologies in airplane design can yield significant increases in speeds, ranges, and payloads over present aircraft with 40 percent to 50 percent reductions in fuel used

The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks

We present three-dimensional magnetohydrodynamic simulations of the nonlinear evolution of the magnetorotational instability (MRI) with a non-zero Ohmic resistivity. The properties of the saturated state depend on the initial magnetic field configuration. In simulations with an initial uniform vertical field, the MRI is able to support angular momentum transport even for large resistivities through the quasi-periodic generation of axisymmetric radial channel solutions rather than through the maintenance of anisotropic turbulence. Simulations with zero net flux show that the angular momentum transport and the amplitude of magnetic energy after saturation are significantly reduced by finite resistivity, even at levels where the linear modes are only slightly affected. This occurs at magnetic Reynolds numbers expected in low, cool states of dwarf novae, these results suggest that finite resistivity may account for the low and high angular momentum transport rates inferred for these systems.Comment: 8 figures, accepted for publication in Ap