[show abstract][hide abstract] ABSTRACT: Recently, Silvers, Vasil, Brummell, & Proctor (2009), using numerical
simulations, confirmed the existence of a double diffusive magnetic buoyancy
instability of a layer of horizontal magnetic field produced by the interaction
of a shear velocity field with a weak vertical field. Here, we demonstrate the
longer term nonlinear evolution of such an instability in the simulations. We
find that a quasi two-dimensional interchange instability rides (or "surfs") on
the growing shear-induced background downstream field gradients. The region of
activity expands since three-dimensional perturbations remain unstable in the
wake of this upward-moving activity front, and so the three-dimensional nature
becomes more noticeable with time.
Proceedings of the International Astronomical Union 08/2011; 271.
[show abstract][hide abstract] ABSTRACT: A dynamo is a process by which fluid motions sustain magnetic fields against dissipative effects. Dynamos occur naturally in many astrophysical systems. Theoretically, we have a much more robust understanding of the generation and maintenance of magnetic fields at the scale of the fluid motions or smaller, than that of magnetic fields at scales much larger than the local velocity. Here, via numerical simulations, we examine one example of an ``essentially nonlinear'' dynamo mechanism that successfully maintains magnetic field at the largest available scale (the system scale) without cascade to the resistive scale. In particular, we examine whether this new type of dynamo at the system scale is still effective in the presence of other smaller-scale dynamics (turbulence).
Proceedings of the International Astronomical Union 01/2011; 271:367-368.
[show abstract][hide abstract] ABSTRACT: We investigate dynamo action in compressible convection via numerical simulations in a Cartesian domain. We directly compare the dynamo properties of a fully convective domain with the same domain extended to include an underlying stable region. These simulations extend models of fully convective domains with open lower boundary conditions to a more self-consistent model. We examine whether the extremely slow recirculation of the lower region affects the dynamo properties in the convection zone. We find that the dynamo properties of the upper convective region are essentially unchanged by the addition of the lower stable region. After a transient period, dynamo action in the convective region not only proceeds as normal, but also extends into the region of overshooting flow in the stable region. Downward magnetic pumping, long recirculation times and the low percentage of rising elements that transit the vertical extent of the domain all fail to eliminate the dynamo. Sufficient magnetic field is recirculated or remains in the convective region to fuel the local dynamo there. The independence of the convective layer from the conditions of the lower layer makes the dynamo truly local.
[show abstract][hide abstract] ABSTRACT: 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.
The Astrophysical Journal 01/2009; 473(1):494. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: A plausible scenario for solar dynamo action is that the large-scale organized toroidal magnetic field is generated by the action of strong radial shear at the base of the solar convection zone, whereas the weaker poloidal field is regenerated by cyclonic convection throughout the convection zone. We show, using high-resolution three-dimensional numerical simulations, that the required transport of magnetic field from the convection zone to the overshoot region can be achieved on a convective rather than diffusive timescale by a pumping mechanism in turbulent penetrative compressible convection. A layer of magnetic field initially placed in the convection zone is swept down by strong sinking plumes, locally amplified, and deposited in the stable region at the base of the convection zone, despite the opposing action of magnetic buoyancy. The rate of transport is insensitive to the strength of the initial imposed field.
The Astrophysical Journal 01/2009; 502(2):L177. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Previous theoretical work has speculated about the existence of double-diffusive magnetic buoyancy instabilities of a dynamically evolving horizontal magnetic layer generated by the interaction of forced vertically sheared velocity and a background vertical magnetic field. Here we confirm numerically that if the ratio of the magnetic to thermal diffusivities is sufficiently low then such instabilities can indeed exist, even for high Richardson number shear flows. Magnetic buoyancy may therefore occur via this mechanism for parameters that are likely to be relevant to the solar tachocline, where regular magnetic buoyancy instabilities are unlikely. Comment: Submitted to ApJL
The Astrophysical Journal 01/2009; · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Using numerical simulations of a compressible, stably stratified, magnetohydrodynamical (MHD) flow, we investigate a mechanism for producing a series of rising tubelike magnetic structures. In this process, a steadily forced shear flow stretches a weak poloidal background magnetic field to create a strong toroidal field that is magnetically buoyant. The subsequent evolution of this system depends on the parameters: At moderate magnetic Reynolds numbers (Rm), the system reaches a stable nonstatic equilibrium. At larger values of Rm, this equilibrium becomes unstable to a shear-buoyant instability, involving a modification of the background velocity shear by the magnetically induced buoyant poloidal flow. The system then produces a series of buoyant magnetic structures at regular intervals that are expelled from the region of strong velocity shear. Even higher Rm causes the magnetic intensity of the structures to strengthen and the intervals between expulsion events to become irregular. For large enough kinetic Reynolds numbers (Re), the magnetic modification of the background shear can trigger a secondary three-dimensional Kelvin-Helmholtz instability that can twist the magnetic structures into a helical shape.
The Astrophysical Journal 12/2008; 588(1):630. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: We present the results of a series of high-resolution, three-dimensional numerical experiments that investigate the nature of turbulent compressible convective motions extending from a convection zone into a stable layer below. In such convection, converging flows in the near-surface cellular convecting network create strong downflowing plumes that can traverse the multiple scale heights of the convection zone. Such structures can continue their downward motions beyond the convecting region, piercing the stable layer, where they are decelerated by buoyancy braking. If these motions mix entropy to an adiabatic state below the convection zone, the process is known as penetration; otherwise it is termed overshooting. We find that in three-dimensional turbulent compressible convection at the parameters studied, motions generally overshoot a significant fraction of the local pressure scale height but do not establish an adiabatic penetrative region, even at the highest Péclet numbers considered. This is mainly due to the low filling factor of the turbulent plumes. The scaling of the overshooting depth with the relative stability S of the two layers is affected by this lack of true penetration. Only an S-1 dependence is exhibited, reflecting the existence of a thermal adjustment region without a nearly adiabatic penetration zone. Rotation about a vertical axis decreases the depth of overshooting, owing to horizontal mixing induced by the rotation. For rotation about an inclined axis, turbulent rotational alignment of the strong downflow structures decreases the overshooting further at mid-latitudes, but the laminar effects of cellular roll solutions take over at low latitudes. Turbulent penetrative convection is quite distinct from its laminar counterpart and from the equivalent motions in a domain confined by impenetrable horizontal boundaries. Although overshooting would not be so deep in the solar case, the lack of true penetration extending the adiabatic region may explain why helioseismic inferences show little evidence of the expected abrupt change between the convection zone and the radiative interior. These results may also provide insight into how overshooting motions can provide a coupling between the solar convection zone and the tachocline.
The Astrophysical Journal 12/2008; 570(2):825. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: We present direct numerical simulations based on the full MHD equations of dynamo action in a nonrotating, convectively stable layer containing a forced, localized velocity shear. The dynamo operates by the interaction of two MHD processes: the production of toroidal magnetic field from poloidal field by the shear, and the regeneration of poloidal loops from toroidal field due to the combined action of magnetic buoyancy and Kelvin-Helmholtz instabilities. The nature of the dynamo process is such that it can occur only if the initial magnetic fields exceed a critical value that typically depends on the magnetic Reynolds number. As such, this dynamo does not operate in the kinematic limit. Several different behaviors are observed, including steady dynamo production and cyclic as well as chaotic activity. In the cyclic regimes, the dynamo process exhibits polarity reversals and periods of reduced activity.
The Astrophysical Journal 12/2008; 599(2):1449. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: We discuss a series of high-resolution fully nonlinear MHD numerical simulations relevant to processes that are expected to operate in the solar tachocline. We study the generation of a strong toroidal magnetic field by the stretching action of velocity shear on a weak background poloidal magnetic field, a process often referred to in solar dynamo theory as the Ω-effect. Here we specifically study the generation of a strong layer of horizontal magnetic field by the action of vertical shear on weak vertical magnetic field in a subadiabatically stratified atmosphere, and we examine the buoyancy properties of the resulting magnetic configurations. We find that magnetic layers can indeed be generated, and that magnetic buoyancy instabilities of this layer can exist and lead to rising magnetic structures that resemble arching tubes. However, the conditions for the instabilities to occur are much more demanding than might be anticipated from previous results where a magnetic layer was initially prescribed, rather than shear-generated. Furthermore, the magnetic flux transport by the buoyancy instabilities in this case is decidedly inefficient. These issues, stemming from the feedback of strong magnetic field on the generating shear, raise serious questions for the efficacy of this process in the current solar dynamo paradigm.
The Astrophysical Journal 12/2008; 686(1):709. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: We present the results of a series of numerical experiments that investigate the transport of magnetic fields by turbulent penetrative compressible convection. We find that magnetic flux is preferentially transported downward out of a turbulent convecting region and stored in a stably stratified region below. This pumping mechanism is believed to be a crucial component for the operation of a large-scale solar interface dynamo since it may be responsible for the transport of flux from the solar convection zone to the stable overshoot region. The high-resolution three-dimensional simulations show that efficient pumping occurs as a result of the action of strong coherent downflowing plumes. The properties of the transport are evaluated as a function of magnetic field strength, rotation rate, supercriticality, stiffness of the interface, and configuration. The turbulent pumping of magnetic flux is remarkably robust and more efficient than its laminar counterpart. The turbulent convection naturally amplifies magnetic energy from any existing mean field. The transport of flux from the convection zone removes the source for this local amplification there, and thus the peak magnetic energy also comes to reside in the stable region. This is important for an effective interface dynamo.
The Astrophysical Journal 12/2008; 549(2):1183. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: In a recent paper (Vasil & Brummell 2008), we found that the action of vertical (radial) shear on the vertical component of poloidal magnetic field could induce magnetic buoyancy instabilities that produced rising, undulating tubular magnetic structures as often envisaged arising from the solar tachocline, but only under extreme circumstances. Herein, we examine, in greater detail, the reasons underpinning the difficulties in obtaining magnetic buoyancy. Under a variety of assumptions about the maintenance of the shear, we herein discuss some analytic limits on the ability of the Ω-effect to produce toroidal magnetic field. Firstly, we consider the Ω-effect in a local time-dependent context, where an unmaintained shear is allowed to build a magnetic layer over time. In this case, we find amplitude estimates of the magnetic field made through such a process in terms of the shear-flow Richardson number. Secondly, we consider the Ω-effect in a local time-independent context, where the shear is forced, such that under certain circumstances it would be maintained. In this situation, we derive a variety of mathematical bounds on the toroidal magnetic energy that can be realized, and its gradients, in terms of the magnitude and the magnetic Prandtl number. This result implies that at low σ M , unreasonably strong shear flows must be forced to produce magnetic buoyancy, as was found in our earlier paper. Conversely, for high σ M , magnetic buoyancy can be realized for reasonable forcing, and this is confirmed with a new simulation. Our results imply that the maintenance of tachocline shear and the production of magnetic structures cannot be separated, and a comprehensive approach must likely be adopted.
The Astrophysical Journal 12/2008; 690(1). · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: We address the problem of parity mixing, where the projection of a variable expressed as a finite series of half-period cosine (sine) functions onto a half-period sine (cosine) function basis is not finite. We propose new fast methods for computing these complicated projections exactly up to some arbitrary degree using fast Fourier transforms. This method has immediate applications for pseudospectral solutions of many systems of partial differential equations.
Journal of Computational Physics 09/2008; 227(17):7999-8016. · 2.14 Impact Factor
[show abstract][hide abstract] ABSTRACT: To demonstrate the utility of the parity filtering methods described by Vasil et al. [G. Vasil, N. Brummell, K. Julien, A new method for fast transforms in parity-mixed PDEs: Part I. Numerical techniques and analysis, J. Comput. Phys. (2008)], we introduce a numerical code designed to solve for Rayleigh–Bénard convection in a confined rotating box using the new methods we have formulated. That is, using a straightforward pseudospectral framework, we incorporate techniques for efficiently computing parity-mixed Coriolis accelerations in a time-dependent numerical solver. The goals of the presented numerical code are to provide a tool to investigate aspects of confined rotating convection experiments with a simple model, and to illustrate the application of parity filtering. In our numerical tests, we find that a correct accounting for parity leads to clear and interesting behavior that has been observed in laboratory experiments but that has not been observed in previous numerical simulations in periodic domains.
Journal of Computational Physics 01/2008; 227(17):8017-8034. · 2.14 Impact Factor
[show abstract][hide abstract] ABSTRACT: The filamentary structure of a sunspot penumbra is believed to be magnetoconvective in origin. In the outer pen-umbra there is a difference in inclination of up to 30 Y40 between the magnetic fields associated with bright and dark filaments, and the latter fields plunge downward below the surface toward the edge of the spot. We have proposed that these fields are dragged downward by magnetic pumping caused by the external granular convection. In this paper we model this process in a more elaborate idealized configuration that includes the curvature force exerted by an arched magnetic field in addition to magnetic buoyancy, and demonstrate that magnetic pumping remains an efficient mech-anism for holding flux submerged. We discuss the implications of these results for the magnetic structure of the outer penumbra.
The Astrophysical Journal 01/2008; 686. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Highly resolved numerical simulations are used to study three-dimensional, compressible convection. The viscous dissipation is sufficiently low that the flow divides itself in depth into two distinct regions: (i) an upper thermal boundary layer containing a smooth flow with a granular appearance, and (ii) a turbulent interior pierced by the strongest downflows from the surface layer. Such downflows span the whole depth of the unstable layer, are temporally coherent, and are thermodynamically well correlated. A remarkable property of such convection, once it becomes turbulent, is that the enthalpy and kinetic fluxes carried by the strong downflows nearly cancel, for they are of opposite sense and nearly equal in amplitude. Thus, although the downflows serve to organize the convection and are the striking feature that emerges from effects of compressibility, it is the small-scale, disorganized turbulent motions (between the coherent downflow structures that serve as the principal carriers of net convected flux.
[show abstract][hide abstract] ABSTRACT: We study the topology of field lines threading buoyant magnetic flux structures. The magnetic structures, visually resembling idealized magnetic flux tubes, are generated self-consistently by numerical simulation of the interaction of magnetic buoyancy and a localized velocity shear in a stably stratified atmosphere. Depending on the parameters, the system exhibits varying degrees of symmetry. By integrating along magnetic field lines and constructing return maps, we show that, depending on the type of underlying behaviour, the stages of the evolution, and therefore the degree of symmetry, the resulting magnetic structures can have field lines with one of three distinct topologies. When the x-translational and y-reflectional symmetries remain intact, magnetic field lines lie on surfaces but individual lines do not cover the surface. When the y symmetry is broken, magnetic field lines lie on surfaces and individual lines do cover the surface. When both x and y symmetries are broken, magnetic field lines wander chaotically over a large volume of the magnetically active region. We discuss how these results impact our simple ideas of a magnetic flux tube as an object with an inside and an outside, and introduce the concept of ‘leaky’ tubes.
Monthly Notices of the Royal Astronomical Society 12/2005; 365(3):727 - 734. · 5.52 Impact Factor
[show abstract][hide abstract] ABSTRACT: This paper offers the first coherent picture of the interactions between convection and magnetic fields that lead to the formation of the complicated filamentary structure of a sunspot penumbra. Recent observations have revealed the intricate interlocking-comb structure of the penumbral magnetic field. Some field lines, with associated Evershed outflows, plunge below the solar surface near the edge of the spot. We claim that these field lines are pumped downward by small-scale granular convection outside the sunspot. This mechanism is demonstrated in numerical experiments. Magnetic pumping is a key new ingredient that links several theoretical ideas about penumbral structure and dynamics; it explains not only the abrupt appearance of a penumbra as a pore increases in size but also the behavior of moving magnetic features outside a spot.
The Astrophysical Journal 01/2004; 600. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: The structure of a sunspot is determined by the local interaction between magnetic fields and convection near the Sun's surface. The dark central umbra is surrounded by a filamentary penumbra, whose complicated fine structure has only recently been revealed by high-resolution observations. The penumbral magnetic field has an intricate and unexpected interlocking-comb structure and some field lines, with associated outflows of gas, dive back down below the solar surface at the outer edge of the spot. These field lines might be expected to float quickly back to the surface because of magnetic buoyancy, but they remain submerged. Here we show that the field lines are kept submerged outside the spot by turbulent, compressible convection, which is dominated by strong, coherent, descending plumes. Moreover, this downward pumping of magnetic flux explains the origin of the interlocking-comb structure of the penumbral magnetic field, and the behaviour of other magnetic features near the sunspot.