Neal E. Hurlburt

Turbulent compressible convection

Numerical simulations with high spatial resolution (up to 96-cubed gridpoints) are used to study three-dimensional, compressible convection. A sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent. 39 refs.

Nonlinear compressible convection penetrating into stable layers and producing internal gravity waves

Penetrative convection spanning multiple scale heights is studied within a simple stellar envelope consisting of three layers: a convectively unstable middle layer bounded above and below by stably stratified polytropes. Two-dimensional numerical simulations are used to investigate the fully compressible nonlinear motions that ensue. The cellular flows display prominent downward-directd plumes surrounded by broader regions of upflow. Such asymmetry arises because pressure fluctuations accentuate buoyancy driving in the concentrated plumes and can even lead to weak buoyancy braking in the surrounding ascending flows. As the plumes plunge downward into a region of stable stratification, they serve to excite a broad spectrum of internal gravity waves there. The induced waves are not passive, for they feed back upon the plumes by deflecting them sideways, thereby modulating the amplitude of the convection in time even in the unstable layer. The penetrative motions that billow upward into the upper stable zone are distinctly weaker, and they cascade back downward toward the unstable zone over a broad horizontal scale. The strong excitation of gravity waves by the convection has implications for gradual mixing deep within a star.

Turbulent Compressible Convection with Rotation. I. Flow Structure and Evolution

The effects of Coriolis forces on compressible convection are studied using three-dimensional numerical simulations carried out within a local modified f-plane model. The physics is simplified by considering a perfect gas occupying a rectilinear domain placed tangentially to a rotating sphere at various latitudes, through which a destabilizing heat flux is driven. The resulting convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers, evaluating conditions where the influence of rotation is both weak and strong. Given the computational demands of these high-resolution simulations, the parameter space is explored sparsely to ascertain the differences between laminar and turbulent rotating convection. The first paper in this series examines the effects of rotation on the flow structure within the convection, its evolution, and some consequences for mixing. Subsequent papers consider the large-scale mean shear flows that are generated by the convection, and the effects of rotation on the convective energetics and transport properties.It is found here that the structure of rotating turbulent convection is similar to earlier nonrotating studies, with a laminar, cellular surface network disguising a fully turbulent interior punctuated by vertically coherent structures. However, the temporal signature of the surface flows is modified by inertial motions to yield new cellular evolution patterns and an overall increase in the mobility of the network. The turbulent convection contains vortex tubes of many scales, including large-scale coherent structures spanning the full vertical extent of the domain involving multiple density scale heights. Remarkably, such structures align with the rotation vector via the influence of Coriolis forces on turbulent motions, in contrast with the zonal tilting of streamlines found in laminar flows. Such novel turbulent mechanisms alter the correlations which drive mean shearing flows and affect the convective transport properties. In contrast to this large-scale anisotropy, small-scale vortex tubes at greater depths are randomly orientated by the rotational mixing of momentum, leading to an increased degree of isotropy on the medium to small scales of motion there. Rotation also influences the thermodynamic mixing properties of the convection. In particular, interaction of the larger coherent vortices causes a loss of correlation between the vertical velocity and the temperature leaving a mean stratification which is not isentropic.

TURBULENT COMPRESSIBLE CONVECTION WITH ROTATION. II. MEAN FLOWS AND DIFFERENTIAL ROTATION

The e†ects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of di†erential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity pro-le with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional Nows that are produced by convection inNuenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent Now conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the e†ects of rotation on the resulting laminar cellular convec- tion leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean Nows, inter- pretable as di†erential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted Nuid particle trajectories, with few clear corre- lations between vertical and horizontal motions, punctuated by an evolving and intricate downNow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downNow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the prin- cipal correlated motions and thus Reynolds stresses and subsequently mean Nows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and strati-cation. Such structure is here found to play a crucial role in de-ning the mean zonal and meridional Nows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean Nows are determined by a com- bination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters pro- duces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity pro-le that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a de-nite handedness, with the direction of the persistent mean Nows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deduc- tions. The mean helicity has a pro-le that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection. Subject headings: convection E stars: interiors E stars: rotation E Sun: rotation E turbulence

Penetration below a convective zone

Two-dimensional numerical simulations are used to investigate how fully compressible nonlinear convection penetrates into a stably stratified zone beneath a stellar convection zone. Estimates are obtained of the extent of penetration as the relative stability S of the stable to the unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The dynamics is dominated by downward-directed plumes which can extend far into the stable material and which can lead to the excitation of a broad spectrum of internal gravity waves in the lower stable zone. The convection is highly time dependent, with the close coupling between the lateral swaying of the plumes and the internal gravity waves they generate serving to modulate the strength of the convection. The depth of penetration delta, determined by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kinetic energy carried into the stable layer by the plumes and the buoyancy braking they experience there. A passive scalar is introduced into the unstable layer to evaluate the transport of chemical species downward. Such a tracer is effectively mixed within a few convective overturning times down to a depth of delta within the stable layer. Analytical estimates based on simple scaling laws are used to interpret the variation of delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exceeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S(exp -1) and S(exp -1/4). These estimates are in accord with the penetration results from the simulations.

Magnetic fields interacting with nonlinear compressible convection

Two-dimensional numerical simulations are used to study fully compressible convection in the presence of an imposed magnetic field. Highly nonlinear flows are considered that span multiple density scale heights. The convection tends to sweep the initially uniform vertical magnetic field into concentrated flux sheets with significant magnetic pressures. These flux sheets are partially evacuated, and effects of buoyancy and Lorentz forces there can serve to suppress motions. The flux sheets can be surrounded by a sheath of descending flow. If the imposed magnetic field is sufficiently strong, the convection can become oscillatory. The unstably stratified fluid layer has an initial density ratio (bottom to top of layer) of 11. Surveys of solutions at fixed Rayleigh number sample Chandrasekhar numbers from 1 to 1000 and magnetic Prandtl numbers from 1/16 to 1. These nonlinear simulations utilize a two-dimensional numerical scheme based on a modified two-step Lax-Wendroff method. 46 references.

Laboratory Experiments on Planetary and Stellar Convection Performed on Spacelab 3

Experiments on thermal convection in a rotating, differentially heated hemispherical shell with a radial buoyancy force were conducted in an orbiting microgravity laboratory. A variety of convective structures, or planforms, were observed, depending on the magnitude of the rotation and the nature of the imposed heating distribution. The results are compared with numerical simulations that can be conducted at the more modest heating rates, and suggest possible regimes of motion in rotating planets and stars.

INTERNETWORK CHROMOSPHERIC BRIGHT GRAINS OBSERVED WITH IRIS AND SST

The Interface Region Imaging Spectrograph (IRIS) reveals small-scale rapid brightenings in the form of bright grains all over coronal holes and the quiet Sun. These bright grains are seen with the IRIS 1330, 1400, and 2796 A slit-jaw filters. We combine coordinated observations with IRIS and from the ground with the Swedish 1 m Solar Telescope (SST) which allows us to have chromospheric (Ca II 8542 A, Ca II H 3968 A, Hα, and Mg II k 2796 A) and transition region (C II 1334 A, Si IV1403 A) spectral imaging, and single-wavelength Stokes maps in Fe I 6302 A at high spatial (  0 .3 3), temporal, and spectral resolution. We conclude that the IRIS slit-jaw grains are the counterpart of so-called acoustic grains, i.e., resulting from chromospheric acoustic waves in a nonmagnetic environment. We compare slit-jaw images (SJIs) with spectra from the IRIS spectrograph. We conclude that the grain intensity in the 2796 A slit-jaw filter comes from both the Mg II k core and wings. The signal in the C II and Si IV lines is too weak to explain the presence of grains in the 1300 and 1400 A SJIs and we conclude that the grain signal in these passbands comes mostly from the continuum. Although weak, the characteristic shock signatures of acoustic grains can often be detected in IRIS C II spectra. For some grains, a spectral signature can be found in IRIS Si IV. This suggests that upward propagating acoustic waves sometimes reach all the way up to the transition region.

NONLINEAR THREE-DIMENSIONAL MAGNETOCONVECTION AROUND MAGNETIC FLUX TUBES

Magnetic flux in the solar photosphere forms concentrations from small scales, such as flux elements, to large scales, such as sunspots. This paper presents a study of the decay process of large magnetic flux tubes, such as sunspots, on a supergranular scale. Three-dimensional nonlinear resistive magnetohydrodynamic numerical simulations are performed in a cylindrical domain, initialized with axisymmetric solutions that consist of a well-defined central flux tube and an annular convection cell surrounding it. As the nonlinear convection evolves, the annular cell breaks up into many cells in the azimuthal direction, allowing magnetic flux to slip between cells away from the central flux tube (turbulent erosion). This lowers magnetic pressure in the central tube, and convection grows inside the tube, possibly becoming strong enough to push the tube apart. A remnant of the central flux tube persists with nonsymmetric perturbations caused by the convection surrounding it. Secondary flux concentrations form between convection cells away from the central tube. Tube decay is dependent on the convection around the tube. Convection cells forming inside the tube as time-dependent outflows will remove magnetic flux. (This is most pronounced for small tubes.) Flux is added to the tube when flux caught in the surrounding convection is pushed toward it. The tube persists when convection inside the tube is sufficiently suppressed by the remaining magnetic field. All examples of persistent tubes have the same effective magnetic field strength, consistent with the observation that pores and sunspot umbrae all have roughly the same magnetic field strength.

Two and Three-Dimensional Simulations of Compressible Convection

We present some results of numerical studies of compressible, nonlinear convection in highly stratified fluids. Both two and three-dimensional flows are considered. In three dimensions the flow forms an irregular cellular pattern near the surface with downflows at the cellular boundaries and upflows at the cellular centers. At greater depth the downflows collapse into isolated columns surrounded by gentler upflows. The two dimensional simulations show that at high Rayleigh numbers convection becomes supersonic near the upper boundary. Non-stationary shock systems appear which interact with the thermal boundary layer giving rise to a vigorous time dependence.