Solar Convection Research Articles

The amplitude of the cross-covariance function of solar oscillations as a diagnostic tool for wave attenuation and geometrical spreading

Context. In time-distance helioseismology, wave travel times are measured from the two-point cross-covariance function of solar oscillations and are used to image the solar convection zone in three dimensions. There is, however, also information in the amplitude of the cross-covariance function, for example about seismic wave attenuation. Aims. Here we develop a convenient procedure to measure the amplitude of the cross-covariance function of solar oscillations. Methods. In this procedure, the amplitude of the cross-covariance function is linearly related to the cross-covariance function and can be measured even for high levels of noise. Results. As an example application, we measure the amplitude perturbations of the seismic waves that propagate through the sunspot in active region NOAA 9787. We can recover the amplitude variations due to the scattering and attenuation of the waves by the sunspot and associated finite-wavelength effects. Conclusions. The proposed definition of cross-covariance amplitude is robust to noise, can be used to relate measured amplitudes to 3D perturbations in the solar interior under the Born approximation, and will provide independent information from the travel times.

Supergranulation and multiscale flows in the solar photosphere

The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future high-resolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate.

Internal Gravity Waves in the Magnetized Solar Atmosphere. I. Magnetic Field Effects

Abstract Observations of the solar atmosphere show that internal gravity waves are generated by overshooting convection, but are suppressed at locations of magnetic flux, which is thought to be the result of mode conversion into magnetoacoustic waves. Here, we present a study of the acoustic-gravity wave spectrum emerging from a realistic, self-consistent simulation of solar (magneto)convection. A magnetic field free, hydrodynamic simulation and a magnetohydrodynamic (MHD) simulation with an initial, vertical, homogeneous field of 50 G flux density were carried out and compared with each other to highlight the effect of magnetic fields on the internal gravity wave propagation in the Sun’s atmosphere. We find that the internal gravity waves are absent or partially reflected back into the lower layers in the presence of magnetic fields and argue that the suppression is due to the coupling of internal gravity waves to slow magnetoacoustic waves still within the high-β region of the upper photosphere. The conversion to Alfvén waves is highly unlikely in our model because there is no strongly inclined magnetic field present. We argue that the suppression of internal waves observed within magnetic flux concentrations may also be due to nonlinear breaking of internal waves due to vortex flows that are ubiquitously present in the upper photosphere and the chromosphere.

THE ROLE OF MAGNETIC HELICITY IN STRUCTURING THE SOLAR CORONA

ABSTRACT Two of the most widely observed and striking features of the Sun's magnetic field are coronal loops, which are smooth and laminar, and prominences or filaments, which are strongly sheared. Loops are puzzling because they show little evidence of tangling or braiding, at least on the quiet Sun, despite the chaotic nature of the solar surface convection. Prominences are mysterious because the origin of their underlying magnetic structure—filament channels—is poorly understood at best. These two types of features would seem to be quite unrelated and wholly distinct. We argue that, on the contrary, they are inextricably linked and result from a single process: the injection of magnetic helicity into the corona by photospheric motions and the subsequent evolution of this helicity by coronal reconnection. In this paper, we present numerical simulations of the response of a Parker (1972) corona to photospheric driving motions that have varying degrees of helicity preference. We obtain four main conclusions: (1) in agreement with the helicity condensation model of Antiochos (2013), the inverse cascade of helicity by magnetic reconnection in the corona results in the formation of filament channels localized about polarity inversion lines; (2) this same process removes most complex fine structure from the rest of the corona, resulting in smooth and laminar coronal loops; (3) the amount of remnant tangling in coronal loops is inversely dependent on the net helicity injected by the driving motions; and (4) the structure of the solar corona depends only on the helicity preference of the driving motions and not on their detailed time dependence. We discuss the implications of our results for high-resolution observations of the corona.

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ∇ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ∇ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ∇ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.

An opaque Sun? The potential for future, higher opacities to solve the solar abundance problem

Last year Bailey et al. announced their measurement of iron opacity that increases the Rosseland mean at the base of the solar convection zone by 7%. I ask what happens if the absorption by other elements is also stronger than predicted so far.Artificially increasing the absorption by other elements, proportional to the number of bound electrons in the absorber (reflecting our remaining ignorance of atomic physics) gives an opacity increase for a solar model, that has the potential to solve the long-standing solar abundance problem.Conclusion: Opacities are the likely source of the solar abundance problem, and the solar abundances are likely closer to those of Asplund et al. (2009) than to the various classic sets of abundances.

Intensity contrast of the average supergranule

While the velocity fluctuations of supergranulation dominate the spectrum of solar convection at the solar surface, very little is known about the fluctuations in other physical quantities like temperature or density at supergranulation scale. Using SDO/HMI observations, we characterize the intensity contrast of solar supergranulation at the solar surface. We identify the positions of ${\sim}10^4$ outflow and inflow regions at supergranulation scales, from which we construct average flow maps and co-aligned intensity and magnetic field maps. In the average outflow center, the maximum intensity contrast is $(7.8\pm0.6)\times10^{-4}$ (there is no corresponding feature in the line-of-sight magnetic field). This corresponds to a temperature perturbation of about $1.1\pm0.1$ K, in agreement with previous studies. We discover an east-west anisotropy, with a slightly deeper intensity minimum east of the outflow center. The evolution is asymmetric in time: the intensity excess is larger 8 hours before the reference time (the time of maximum outflow), while it has almost disappeared 8 hours after the reference time. In the average inflow region, the intensity contrast mostly follows the magnetic field distribution, except for an east-west anisotropic component that dominates 8 hours before the reference time. We suggest that the east-west anisotropy in the intensity is related to the wave-like properties of supergranulation.

A PROPOSED PARADIGM FOR SOLAR CYCLE DYNAMICS MEDIATED VIA TURBULENT PUMPING OF MAGNETIC FLUX IN BABCOCK–LEIGHTON-TYPE SOLAR DYNAMOS

ABSTRACT At present, the Babcock–Leighton flux transport solar dynamo models appear to be the most promising models for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun’s convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10% of the Sun) and more complex than previously thought. Taken together, these observations raise serious concerns on the validity of the flux transport paradigm. By accounting for the turbulent pumping of magnetic flux, as evidenced in magnetohydrodynamic simulations of solar convection, we demonstrate that flux transport dynamo models can generate solar-like magnetic cycles even if the meridional flow is shallow. Solar-like periodic reversals are recovered even when meridional circulation is altogether absent. However, in this case, the solar surface magnetic field dynamics does not extend all the way to the polar regions. Very importantly, our results demonstrate that the Parker–Yoshimura sign rule for dynamo wave propagation can be circumvented in Babcock–Leighton dynamo models by the latitudinal component of turbulent pumping, which can generate equatorward propagating sunspot belts in the absence of a deep, equatorward meridional flow. We also show that variations in turbulent pumping coefficients can modulate the solar cycle amplitude and periodicity. Our results suggest the viability of an alternate magnetic flux transport paradigm—mediated via turbulent pumping—for sustaining solar-stellar dynamo action.

THE EMERGENCE OF SOLAR SUPERGRANULATION AS A NATURAL CONSEQUENCE OF ROTATIONALLY CONSTRAINED INTERIOR CONVECTION

We investigate how rotationally-constrained, deep convection might give rise to supergranulation, the largest distinct spatial scale of convection observed in the solar photosphere. While supergranulation is only weakly influenced by rotation, larger spatial scales of convection sample the deep convection zone and are presumably rotationally influenced. We present numerical results from a series of nonlinear, 3-D simulations of rotating convection and examine the velocity power distribution realized under a range of Rossby numbers. When rotation is present, the convective power distribution possesses a pronounced peak, at characteristic wavenumber $\ell_\mathrm{peak}$, whose value increases as the Rossby number is decreased. This distribution of power contrasts with that realized in non-rotating convection, where power increases monotonically from high to low wavenumbers. We find that spatial scales smaller than $\ell_\mathrm{peak}$ behave in analogy to non-rotating convection. Spatial scales larger than $\ell_\mathrm{peak}$ are rotationally-constrained and possess substantially reduced power relative to the non-rotating system. We argue that the supergranular scale emerges due to a suppression of power on spatial scales larger than $\ell\approx100$ owing to the presence of deep, rotationally-constrained convection. Supergranulation thus represents the largest non-rotationally-constrained mode of solar convection. We conclude that the characteristic spatial scale of supergranulation bounds that of the deep convective motions from above, making supergranulation an indirect measure of the deep-seated dynamics at work in the solar dynamo. Using the spatial scale of supergranulation in conjunction with our numerical results, we estimate an upper bound of 10 m s$^{-1}$ for the Sun's bulk rms convective velocity.

SUPERGRANULATION AS THE LARGEST BUOYANTLY DRIVEN CONVECTIVE SCALE OF THE SUN

ABSTRACT The origin of solar supergranulation remains a mystery. Unlike granulation, the size of which is comparable to both the thickness of the radiative boundary layer and local scale-height in the photosphere, supergranulation does not reflect any obvious length scale of the solar convection zone. Moreover, recent observations of flows in the photosphere using Doppler imaging or correlation or feature tracking show a monotonic decrease in horizontal flow power at scales larger than supergranulation. Both local area and global spherical shell simulations of solar convection by contrast show the opposite, an increase in horizontal flow amplitudes to a low wavenumber. We examine these disparities and investigate how the solar supergranulation may arise as a consequence of nonlocal heat transport by cool diving plumes. Using three-dimensional anelastic simulations with surface driving, we show that the kinetic energy of the largest convective scales in the upper layers of a stratified domain reflects the depth of transition from strong buoyant driving to adiabatic stratification below caused by the dilution of the granular downflows. This depth is quite shallow because of the rapid increase of the mean density below the photosphere. We interpret the observed monotonic decrease in solar convective power at scales larger than supergranulation to be a consequence of this rapid transition, with the supergranular scale the largest buoyantly driven mode of convection in the Sun.

Meteorological and physical conditions of Salt Pan Areas with Filtering-Threaded Technology (TUF) in Cirebon Regency, Indonesia

Salt pans in Indonesia are commonly set in batch operation and highly depend on the meteorological condition. Moreover, the common salt pans are considerably limited in the area (averagely 0.5-1 Ha) as it is not organized by industries or governments; local farmers instead. However, with such confinement, there are some salt pans particularly with filtering-threaded technology system (TUF system) that successfully produce salt with high production (>100 tons/Ha/season) and grade-1 quality. The present study was aimed to get insight on the meteorological condition at the salt pans using TUF system and the physical condition of the sea brine obtained from the TUF in the local salt pans in Cirebon Regency. Measurements on temperatures (air, brine and soil), humidity, wind direction and speed, brine conductivity, brine density and salinity were conducted at the pre-crystallizer pond, brine storage pond, channels, the condenser, and the reservoir. The meteorological parameters were recorded hourly using Automatic Weather Station and the data were taken during 49 hours ly, from August 26-28, 2014 started at 04.00 pm. Meanwhile, the physical parameters of the brine were measured every three hours using water quality meter. The results showed that the meteorological condition, brine physical condition, and the process occurred during salt production were still in agreement and met the theoretical condition or modeling. Even though the relative humidity and some wind speed in the present study area were out of the standard criteria recommended (5m/s for wind speed), the study showed that salt still can be produced in condition of relative humidity (52-88%), wind speed (0.2-5.7 m/s), and ambient temperature (23.2-32.4 oC). Interestingly, it is found that brine thickness and volume could be adjusted to get an optimum temperature of brine (reached 36.2 oC), in order to enhance the evaporation process. The highest soil temperature (34.7 oC) was found at 15.00 in the pre-crystallizer ponds. Meanwhile, the lowest temperature (26.7oC) was found early morning at 04.00 in the reservoir pond. Brine in the pre-crystallizer had highest thermal storage capacity during daytime (06.00-16.00), whereas soil in the pre-crystallizer tended to store heat during the nighttime (18.00-22.00). Brine and soil temperature fluctuation indicate that solar irradiation and convection process transferring heat energy from soil to brine occurs and also took an important part in the evaporation process. It therefore can be concluded that by understanding the condition of meteorology at the salt pan areas and the brine characteristic obtained, the appropriate technology resulting high-quality and quantity salt production could be devised.

DOUBLE DYNAMO SIGNATURES IN A GLOBAL MHD SIMULATION AND MEAN-FIELD DYNAMOS

ABSTRACT The 11 year solar activity cycle is the most prominent periodic manifestation of the magnetohydrodynamical (MHD) large-scale dynamo operating in the solar interior, yet longer and shorter (quasi-) periodicities are also present. The so-called “quasi-biennial” signal appearing in many proxies of solar activity has been gaining increasing attention since its detection in p-mode frequency shifts, which suggests a subphotospheric origin. A number of candidate mechanisms have been proposed, including beating between co-existing global dynamo modes, dual dynamos operating in spatially separated regions of the solar interior, and Rossby waves driving short-period oscillations in the large-scale solar magnetic field produced by the 11 year activity cycle. In this article, we analyze a global MHD simulation of solar convection producing regular large-scale magnetic cycles, and detect and characterize shorter periodicities developing therein. By constructing kinematic mean-field α 2Ω dynamo models incorporating the turbulent electromotive force (emf) extracted from that same simulation, we find that dual-dynamo behavior materializes in fairly wide regions of the model’s parameters space. This suggests that the origin of the similar behavior detected in the MHD simulation lies with the joint complexity of the turbulent emf and differential rotation profile, rather that with dynamical interactions such as those mediated by Rossby waves. Analysis of the simulation also reveals that the dual dynamo operating therein leaves a double-period signature in the temperature field, consistent with a dual-period helioseismic signature. Order-of-magnitude estimates for the magnitude of the expected frequency shifts are commensurate with helioseismic measurements. Taken together, our results support the hypothesis that the solar quasi-biennial oscillations are associated with a secondary dynamo process operating in the outer reaches of the solar convection zone.

What drives the solar magnetic cycle?

Solar magnetic activities show an about 11-year cycle period with the variations of the amplitudes. The increasing technological advancement induces the stronger influence of the solar magnetic cycle on humans. The magnetic cycle is believed to be caused by a magnetohydrodynamic (MHD) dynamo process in the solar interior, where the flows and the magnetic fields interact in the strongly turbulent convective zone. The intrinsic features of the solar interior, e.g., the stratification, the turbulence and the nonlinearities, make the global MHD simulations of solar convection with the realistic parameters of the Sun extremely hard. The past substantial progress in understanding the solar magnetic cycle benefitted from the simplified models, e.g., the axisymmetric kinematic ones. The mean field electrodynamics and the helioseismology laid the foundation of the progress. Under the effects of the large-scale flows, the poloidal and the toroidal components of the magnetic field sustain each other, which persists the cycle variations of the solar magnetic field. The key ingredients in the dynamo process include the mechanism and the location of the toroidal field generation, the mechanism and the location of the poloidal field generation, the rising of toroidal field to form the sunspots with tilts and the mechanism for the equatorward migration of the sunspots. So far, only the generation of the toroidal field by differential rotations is less controversial. The current dynamo models usually do not include the toroidal flux tube emergence, which was investigated as a separated topic. As the workhorse to understand the solar cycle during the past decade, the Babcock-Leighton (BL) type flux transport dynamos is a popular paradigm for explaining the cyclic nature of solar magnetic activity. They were even used to predict future solar cycles by assimilating observed surface flows and fields into the models. Recently the flux transport dynamos faces some challenges, such as the depth variation of the equatorward flow, the strong turbulent diffusivity, and so on. But the BL mechanism which is due to the decay of the tilt sunspot groups on the solar surface to regenerate the poloidal field, is most probably at the heart of the solar cycle. The further understanding of the solar magnetic cycle will benefit from the constraints of the solar historical data, the helioseismology, the different magnetic cycles of different types of stars, and the global MHD numerical simulations. These fields will be developed in parallel with the kinematic dynamo and fertilize each other. The three dimensional Babcock-Leighton type dynamo models coupled with the toroidal flux tube emergence is expected to be the workhorse of the next generation of solar dynamo.

The turbulent diffusion of toroidal magnetic flux as inferred from properties of the sunspot butterfly diagram

In order to match observed properties of the solar cycle, flux-transport dynamo models require the toroidal magnetic flux to be stored in a region of low magnetic diffusivity, typically located at or below the bottom of the convection zone. We infer the turbulent magnetic diffusivity affecting the toroidal field on the basis of empirical data. We consider the time evolution of mean latitude and width of the activity belts of solar cycles 12--23 and their dependence on cycle strength. We interpret the decline phase of the cycles as a diffusion process. The activity level of a given cycle begins to decline when the centers of its equatorward propagating activity belts come within their width (at half maximum) from the equator. This happens earlier for stronger cycles because their activity belts are wider. From that moment on, the activity and the belt width decrease in the same manner for all cycles, independent of their maximum activity level. In terms of diffusive cancellation of opposite-polarity toroidal flux across the equator, we infer the turbulent diffusivity experienced by the toroidal field, wherever it is located, to be in the range 150--450~km$^2$s$^{-1}$. Strong diffusive latitudinal spreading of the toroidal flux underneath the activity belts can be inhibited by an inflow towards the toroidal field bands in the convection zone with a magnitude of several meters per second. The inferred value of the turbulent magnetic diffusivity affecting the toroidal field agrees, to order of magnitude, with estimates based on mixing-length models for the solar convection zone. This is at variance with the requirement of flux-transport dynamo models. The inflows required to keep the toroidal field bands together before they approach the equator are similar to the inflows towards the activity belts observed with local helioseismology.

The shrinking Sun: A systematic error in local correlation tracking of solar granulation

Context. Local correlation tracking of granulation (LCT) is an important method for measuring horizontal flows in the photosphere. This method exhibits a systematic error that looks like a flow converging towards disk center, also known as the shrinking-Sun effect. Aims. We aim at studying the nature of the shrinking-Sun effect for continuum intensity data and at deriving a simple model that can explain its origin. Methods. We derived LCT flow maps by running the local correlation tracking code FLCT on tracked and remapped continuum intensity maps provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We also computed flow maps from synthetic continuum images generated from STAGGER code simulations of solar surface convection. We investigated the origin of the shrinking-Sun effect by generating an average granule from synthetic data from the simulations. Results. The LCT flow maps derived from HMI and from the simulations exhibit a shrinking-Sun effect of comparable magnitude. The origin of this effect is related to the apparent asymmetry of granulation originating from radiative transfer effects when observing with a viewing angle inclined from vertical. This causes, in combination with the expansion of the granules, an apparent motion towards disk center.

Angular momentum fluxes caused by [formula omitted]-effect and meridional circulation structure of the Sun

Using mean-field hydrodynamic models of the solar angular momentum balance we show that the non-monotonic latitudinal dependence of the radial angular momentum fluxes caused by Λ-effect can affect the number of the meridional circulation cells stacking in the radial direction in the solar convection zone. In particular, our results show the possibility of a complicated triple-cell meridional circulation structure. This pattern consists of two large counterclockwise circulation cells (the N-hemisphere) and a smaller clockwise cell located at low latitudes at the bottom of the convection zone. Similar triple-cell circulation patterns were previously earlier found in a number of 3D global simulations models. The effect is demonstrated for the first time using the mean-field parametrization of the Λ-effect.

Analysis of combined solar photovoltaic-nanostructured thermoelectric generator system

ABSTRACTIn this paper, a combined solar photovoltaic (PV) and thermoelectric (TE) generator system is investigated. The TE generator converts the temperature gradient into electricity eventually improving the overall performance of the system. A nanostructured TE material is used in this investigation and its power generation performance is compared with the traditional TE material. Using the analytical solutions, different performance parameters (e.g. heat input, power output, efficiency) are calculated and expressed graphically as a function of solar radiation and convection heat transfer coefficient. In addition to this, different performance parameters were also compared between traditional and nanostructured TE materials. Moreover, the nanostructured TE material leads to improvement in performance of TE generator due to the reduction in thermal conductivity and improvement in electrical conductivity. The TE generators have a large impact on the overall efficiency of the combined system at higher radiation.

Characterisation of the turbulent electromotive force and its magnetically-mediated quenching in a global EULAG-MHD simulation of solar convection

We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos and Charbonneau (2014). The turbulent electromotive force (emf) operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation’s meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. (2011), we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed α-tensor shows good agreement with that obtained by Racine et al. (2011), who did not include derivatives of the mean-field in their fit, as well as with the α-tensor extracted by Augustson et al. (2015) from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor β is positive definite and reaches values of 5.0×107m2s−1 in the middle of the convecting fluid layers. The spatial variations of both αϕϕ and βϕϕ component are well reproduced by expressions obtained under the Second Order Correlation Approximation, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. By segmenting the simulation data into epochs of magnetic cycle minima and maxima, we also measure α- and β-quenching. We find the magnetic quenching of the α-effect to be driven primarily by a reduction of the small-scale flow’s kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the βϕϕ component, but indicate a weaker quenching, by a factor of ≃1.36, than of the α-effect, which in our simulation drops by a factor of three between the minimum and maximum phases of the magnetic cycle.

Velocity amplitudes in global convection simulations: The role of the Prandtl number and near-surface driving

Several lines of evidence suggest that the velocity amplitude in global simulations of solar convection, U, may be systematically over-estimated. Motivated by these recent results, we explore the factors that determine U and we consider how these might scale to solar parameter regimes. To this end, we decrease the thermal diffusivity κ along two paths in parameter space. If the kinematic viscosity ν is decreased proportionally with κ (fixing the Prandtl number Pr=ν/κ), we find that U increases but asymptotes toward a constant value, as found by Featherstone and Hindman (2016). However, if ν is held fixed while decreasing κ (increasing Pr), we find that U systematically decreases. We attribute this to an enhancement of the thermal content of downflow plumes, which allows them to carry the solar luminosity with slower flow speeds. We contrast this with the case of Rayleigh–Bénard convection which is not subject to this luminosity constraint. This dramatic difference in behavior for the two paths in parameter space (fixed Pr or fixed ν) persists whether the heat transport by unresolved, near-surface convection is modeled as a thermal conduction or as a fixed flux. The results suggest that if solar convection can operate in a high-Pr regime, then this might effectively limit the velocity amplitude. Small-scale magnetism is a possible source of enhanced viscosity that may serve to achieve this high-Pr regime.

Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations.

The 11-year solar magnetic cycle shows a high degree of coherence in spite of the turbulent nature of the solar convection zone. It has been found in recent high-resolution magnetohydrodynamics simulations that the maintenance of a large-scale coherent magnetic field is difficult with small viscosity and magnetic diffusivity (≲10 (12) square centimenters per second). We reproduced previous findings that indicate a reduction of the energy in the large-scale magnetic field for lower diffusivities and demonstrate the recovery of the global-scale magnetic field using unprecedentedly high resolution. We found an efficient small-scale dynamo that suppresses small-scale flows, which mimics the properties of large diffusivity. As a result, the global-scale magnetic field is maintained even in the regime of small diffusivities-that is, large Reynolds numbers.