Calculation of three-dimensional compressible laminar and turbulent boundary flows. Three-dimensional compressible boundary layers of reacting gases over realistic configurations

A three-dimensional boundary-layer code was developed for particular application to realistic hypersonic aircraft. It is very general and can be applied to a wide variety of boundary-layer flows. Laminar, transitional, and fully turbulent flows of compressible, reacting gases are efficiently calculated by use of the code. A body-oriented orthogonal coordinate system is used for the calculation and the user has complete freedom in specifying the coordinate system within the restrictions that one coordinate must be normal to the surface and the three coordinates must be mutually orthogonal

Three-Dimensional Inviscid Flow About Supersonic Blunt Cones at Angle of Attack - III: Coupled Subsonic and Supersonic Programs for Inviscid Three-Dimensional Flow

The three-dimensional ideal gas flow in the shock layer of a blunted supersonic cone at an angle of attack is calculated using two asymptotic solutions. The first solution calculates the steady state flow in the subsonic nose region by obtaining a time-dependent solution of the hyperbolic equations using numerical techniques. Internal, nonboundary points are calculated using a Lax-Wendroff numerical type technique. Boundary points, shock and body surface, are computed using a time-dependent method of characteristics. When a steady state solution is reached the flow properties on a surface of constant {theta}, (where the Mach number is everywhere > 1) are used for initial data for the afterbody solution. The afterbody solution, using polar coordinates (r, {theta}, {phi}) assumes at r{sub 0} an arbitrary set of initial conditions provided by the nose region solution and computes the downstream flow as a function of {theta}, {phi}, and r until an asymptotic state independent of r develops. The interior mesh points are again calculated using a Lax- Wendroff type technique and the boundary points by a method of characteristics. This report covers the coupling of the time-dependent and radius (r) dependent solutions. Instructions are given for the operation of the resulting Fortran code. The type of input data required is detailed and sample output is provided. Output data is given in two sets of coordinates. One is wind orientated; the other set is given in body orientated coordinates; The analytical transformation from one coordinate system to the other is given

Three-Dimensional Inviscid Flow About Supersonic Blunt Cones at Angle of Attack - III: Coupled Subsonic and Supersonic Programs for Inviscid Three-Dimensional Flow

The three-dimensional ideal gas flow in the shock layer of a blunted supersonic cone at an angle of attack is calculated using two asymptotic solutions. The first solution calculates the steady state flow in the subsonic nose region by obtaining a time-dependent solution of the hyperbolic equations using numerical techniques. Internal, nonboundary points are calculated using a Lax-Wendroff numerical type technique. Boundary points, shock and body surface, are computed using a time-dependent method of characteristics. When a steady state solution is reached the flow properties on a surface of constant {theta}, (where the Mach number is everywhere > 1) are used for initial data for the afterbody solution. The afterbody solution, using polar coordinates (r, {theta}, {phi}) assumes at r{sub 0} an arbitrary set of initial conditions provided by the nose region solution and computes the downstream flow as a function of {theta}, {phi}, and r until an asymptotic state independent of r develops. The interior mesh points are again calculated using a Lax- Wendroff type technique and the boundary points by a method of characteristics. This report covers the coupling of the time-dependent and radius (r) dependent solutions. Instructions are given for the operation of the resulting Fortran code. The type of input data required is detailed and sample output is provided. Output data is given in two sets of coordinates. One is wind orientated; the other set is given in body orientated coordinates; The analytical transformation from one coordinate system to the other is given

Transport of magnetic flux from the canopy to the internetwork

Recent observations have revealed that 8% of linear polarization patches in the internetwork quiet Sun are fully embedded in downflows. These are not easily explained with the typical scenarios for the source of internetwork fields which rely on flux emergence from below. We explore using radiative MHD simulations a scenario where magnetic flux is transported from the magnetic canopy overlying the internetwork into the photosphere by means of downward plumes associated with convective overshoot. We find that if a canopy-like magnetic field is present in the simulation, the transport of flux from the canopy is an important process for seeding the photospheric layers of the internetwork with magnetic field. We propose that this mechanism is relevant for the Sun as well, and it could naturally explain the observed internetwork linear polarization patches entirely embedded in downflows.Comment: Accepted to Ap

Emergence of small-scale magnetic loops through the quiet solar atmosphere

We investigate the emergence of magnetic flux in the quiet Sun at very small spatial scales, focusing on the magnetic connection between the photosphere and chromosphere. The observational data consist of spectropolarimetric measurements and filtergrams taken with the Hinode satellite and the Dutch Open Telescope. We find that a significant fraction of the magnetic flux present in internetwork regions appears in the form of Omega-shaped loops. The emergence rate is 0.02 loops per hour and arcsec^{-2}, which brings 1.1 x 10^12 Mx s^{-1} arcsec^{-2} of new flux to the solar surface. Initially, the loops are observed as small patches of linear polarization above a granular cell. Shortly afterwards, two footpoints of opposite polarity become visible in circular polarization within or at the edges of the granule and start to move toward the adjacent intergranular space. The orientation of the footpoints does not seem to obey Hale's polarity rules. The loops are continuously buffeted by convective motions, but they always retain a high degree of coherence. Interestingly, 23% of the loops that emerge in the photosphere reach the chromosphere (16 cases out of 69). They are first detected in Fe I 630 nm magnetograms and 5 minutes later in Mg I b 517.3 nm magnetograms. After about 8 minutes, some of them are also observed in Ca II H line-core images, where the footpoints produce small brightness enhancements.Comment: Accepted for publication in Ap

Comparison of transient horizontal magnetic fields in a plage region and in the quiet Sun

Properties of transient horizontal magnetic fields (THMFs) in both plage and quiet Sun regions are obtained and compared. Spectro-polarimetric observations with the Solar Optical Telescope (SOT) on the Hinode satellite were carried out with a cadence of about 30 seconds for both plage and quiet regions located near disk center. We select THMFs that have net linear polarization (LP) higher than 0.22%, and an area larger than or equal to 3 pixels, and compare their occurrence rates and distribution of magnetic field azimuth. We obtain probability density functions (PDFs) of magnetic field strength and inclination for both regions.The occurrence rate in the plage region is the same as for the quiet Sun. The vertical magnetic flux in the plage region is ~8 times larger than in the quiet Sun. There is essentially no preferred orientation for the THMFs in either region. However, THMFs in the plage region with higher LP have a preferred direction consistent with that of the plage-region's large-scale vertical field pattern. PDFs show that there is no difference in the distribution of field strength of horizontal fields between the quiet Sun and the plage regions when we avoid the persistent large vertical flux concentrations for the plage region. The similarity of the PDFs and of the occurrence rates in plage and quiet regions suggests that a local dynamo process due to the granular motion may generate THMFs all over the sun. The preferred orientation for higher LP in the plage indicates that the THMFs are somewhat influenced by the larger-scale magnetic field pattern of the plage.Comment: 11 pages, 7 figures, A&A accepte

Convective Dynamos and the Minimum X-ray Flux in Main Sequence Stars

The objective of this paper is to investigate whether a convective dynamo can account quantitatively for the observed lower limit of X-ray surface flux in solar-type main sequence stars. Our approach is to use 3D numerical simulations of a turbulent dynamo driven by convection to characterize the dynamic behavior, magnetic field strengths, and filling factors in a non-rotating stratified medium, and to predict these magnetic properties at the surface of cool stars. We use simple applications of stellar structure theory for the convective envelopes of main-sequence stars to scale our simulations to the outer layers of stars in the F0--M0 spectral range, which allows us to estimate the unsigned magnetic flux on the surface of non-rotating reference stars. With these estimates we use the recent results of \citet{Pevtsov03} to predict the level of X-ray emission from such a turbulent dynamo, and find that our results compare well with observed lower limits of surface X-ray flux. If we scale our predicted X-ray fluxes to \ion{Mg}{2} fluxes we also find good agreement with the observed lower limit of chromospheric emission in K dwarfs. This suggests that dynamo action from a convecting, non-rotating plasma is a viable alternative to acoustic heating models as an explanation for the basal emission level seen in chromospheric, transition region, and coronal diagnostics from late-type stars.Comment: ApJ, accepted, 30 pages with 7 figure

The horizontal internetwork magnetic field: numerical simulations in comparison to observations with Hinode

Observations with the Hinode space observatory led to the discovery of predominantly horizontal magnetic fields in the photosphere of the quiet internetwork region. Here we investigate realistic numerical simulations of the surface layers of the Sun with respect to horizontal magnetic fields and compute the corresponding polarimetric response in the Fe I 630 nm line pair. We find a local maximum in the mean strength of the horizontal field component at a height of around 500 km in the photosphere, where it surpasses the vertical component by a factor of 2.0 or 5.6, depending on the initial and boundary conditions. From the synthesized Stokes profiles we derive a mean horizontal field component that is, respectively, 1.6 and 4.3 times stronger than the vertical component. This is a consequence of both the intrinsically stronger flux density of, and the larger area occupied by the horizontal fields. We find that convective overshooting expels horizontal fields to the upper photosphere, making the Poynting flux positive in the photosphere, while this quantity is negative in the convectively unstable layer below it.Comment: 4 pages, 3 figures, minor revisions, esp. concerning top boundary cond., ApJL accepte

Solar Flux Emergence Simulations

We simulate the rise through the upper convection zone and emergence through the solar surface of initially uniform, untwisted, horizontal magnetic flux with the same entropy as the non-magnetic plasma that is advected into a domain 48 Mm wide from from 20 Mm deep. The magnetic field is advected upward by the diverging upflows and pulled down in the downdrafts, which produces a hierarchy of loop like structures of increasingly smaller scale as the surface is approached. There are significant differences between the behavior of fields of 10 kG and 20 or 40 kG strength at 20 Mm depth. The 10 kG fields have little effect on the convective flows and show little magnetic buoyancy effects, reaching the surface in the typical fluid rise time from 20 Mm depth of 32 hours. 20 and 40 kG fields significantly modify the convective flows, leading to long thin cells of ascending fluid aligned with the magnetic field and their magnetic buoyancy makes them rise to the surface faster than the fluid rise time. The 20 kG field produces a large scale magnetic loop that as it emerges through the surface leads to the formation of a bipolar pore-like structure.Comment: Solar Physics (in press), 12 pages, 13 figur

Is null-point reconnection important for solar flux emergence?

The role of null-point reconnection in a 3D numerical MHD model of solar emerging flux is investigated. The model consists of a twisted magnetic flux tube rising through a stratified convection zone and atmosphere to interact and reconnect with a horizontal overlying magnetic field in the atmosphere. Null points appear as the reconnection begins and persist throughout the rest of the emergence, where they can be found mostly in the model photosphere and transition region, forming two loose clusters on either side of the emerging flux tube. Up to 26 nulls are present at any one time, and tracking in time shows that there is a total of 305 overall, despite the initial simplicity of the magnetic field configuration. We find evidence for the reality of the nulls in terms of their methods of creation and destruction, their balance of signs, their long lifetimes, and their geometrical stability. We then show that due to the low parallel electric fields associated with the nulls, null-point reconnection is not the main type of magnetic reconnection involved in the interaction of the newly emerged flux with the overlying field. However, the large number of nulls implies that the topological structure of the magnetic field must be very complex and the importance of reconnection along separators or separatrix surfaces for flux emergence cannot be ruled out.Comment: 26 pages, 12 figures. Added one referenc