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Register a new userA closure model with plumes I. The solar convection
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Kevin Belkacem K. B
Publication date
2006
fields
Physics
and research's language is
English
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Oscillations of stellar p modes, excited by turbulent convection, are investigated. We take into account the asymmetry of the up and downflows created by turbulent plumes through an adapted closure model. In a companion paper, we apply it to the formalism of excitation of solar p modes developed by Samadi & Goupil 2001. Using results from 3D numerical simulations of the upper most part of the solar convection zone, we show that the two-scale-mass-flux model (TFM) is valid only for quasi-laminar or highly skewed flows (Gryanik & Hartmann 2002). We build a generalized-Two-scale-Mass-Flux Model (GTFM) model which takes into account both the skew introduced by the presence of two flows and the effects of turbulence in each flow. In order to apply the GTFM to the solar case, we introduce the plume dynamics as modelled by Rieutord & Zahn (1995) and construct a Closure Model with Plumes (CMP). When comparing with 3D simulation results, the CMP improves the agreement for the fourth order moments, by approximatively a factor of two compared with the use of the quasi-normal approximation or a skewness computed with the classical TFM. The asymmetry of turbulent convection in the solar case has an important impact on the vertical-velocity fourth-order moment which has to be accounted for by models. The CMP is a significant improvement and is expected to improve the modelling of solar p-mode excitation.
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Our goal is to improve the theoretical modelling of stochastic excitation of p modes by turbulent convection. With the help of the closure model with plume (CMP) developed in a companion paper, we refine the theoretical description of the excitation by the turbulent Reynolds stress term. The CMP is generalized for two-point correlation products so as to apply it to the formalism developed by Samadi & Goupil (2001). The excitation source terms are then computed with this improvement, and a comparison with solar data from the GOLF instrument is performed. The present model provides a significant improvement when comparing absolute values of theoretical ampplitudes with observational data. It gives rise to a frequency dependence of the power supplied to solar p modes, which agrees with GOLF observations. It is shown that the asymmetry of the turbulent convection zone (up- and downflows) plays a major role in the excitation processes. Despite an increase in the Reynolds stress term contribution due to our improved description, an additional source of excitation, identified as the entropy source term, is still necessary for reproducing the observational data. Theoretical excitation rates in the frequency range [2.5 mHz, 4 mHz] now are in agreement with the observational data from the GOLF instrument. However, at lower frequencies, it exhibits small discrepancies at the maximum level of a few per cent. Improvements are likely to come from a better physical description of the excitation by entropy fluctuations in the superadiabatic zone.
The process referred to as semi-convection in astrophysics and double-diffusive convection in the diffusive regime in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the numerically accessible planetary parameter regime, and can easily be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.
Solar coronal plumes long seemed to possess a simple geometry supporting spatially coherent, stable outflow without significant fine structure. Recent high-resolution observations have challenged this picture by revealing numerous transient, small-scale, collimated outflows (jetlets) at the base of plumes. The dynamic filamentary structure of solar plumes above these outflows, and its relationship with the overall plume structure, have remained largely unexplored. We analyzed the statistics of continuously observed fine structure inside a single representative bright plume within a mid-latitude coronal hole during 2016 July 2-3. By applying advanced edge-enhancement and spatiotemporal analysis techniques to extended series of high-resolution images from the Solar Dynamics Observatorys Atmospheric Imaging Assembly, we determined that the plume was composed of numerous time-evolving filamentary substructures, referred to as plumelets in this paper, that accounted for most of the plume emission. The number of simultaneously identifiable plumelets was positively correlated with plume brightness, peaked in the fully formed plume, and remained saturated thereafter. The plumelets had transverse widths of 10 Mm and intermittently supported upwardly propagating periodic disturbances with phase speeds of 190-260 km/s and longitudinal wavelengths of 55-65 Mm. The characteristic frequency (3.5 mHz) is commensurate with that of solar p-modes. Oscillations in neighboring plumelets are uncorrelated, indicating that the waves could be driven by p-mode flows at spatial scales smaller than the plumelet separation. Multiple independent sources of outflow within a single coronal plume should impart significant fine structure to the solar wind that may be detectable by Parker Solar Probe and Solar Orbiter.
We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Benard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Gamma=D/L=1/2 and Gamma=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio Gamma=1 sample at $Ra=1times10^8$ and $5times10^8$ the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Gamma=1/2 sample with $Pr=0.7$ at $Ra=1times10^8$ the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For $Ra=1times10^8$ we find that this relative LSC strength is significantly lower in a Gamma=1/2 sample than in a Gamma=1 sample, reflecting that the LSC is much more pronounced in a Gamma=1 sample than in a Gamma=1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.
Within the Babcock-Leighton framework for the solar dynamo, the strength of a cycle is expected to depend on the strength of the dipole moment or net hemispheric flux during the preceding minimum, which depends on how much flux was present in each hemisphere at the start of the previous cycle and how much net magnetic flux was transported across the equator during the cycle. Some of this transport is associated with the random walk of magnetic flux tubes subject to granular and supergranular buffeting, some of it is due to the advection caused by systematic cross-equatorial flows such as those associated with the inflows into active regions, and some crosses the equator during the emergence process. We aim to determine how much of the cross-equatorial transport is due to small-scale disorganized motions (treated as diffusion) compared with other processes such as emergence flux across the equator. We measure the cross-equatorial flux transport using Kitt Peak synoptic magnetograms, estimating both the total and diffusive fluxes. Occasionally a large sunspot group, with a large tilt angle emerges crossing the equator, with flux from the two polarities in opposite hemispheres. The largest of these events carry a substantial amount of flux across the equator (compared to the magnetic flux near the poles). We call such events cross-equatorial flux plumes. There are very few such large events during a cycle, which introduces an uncertainty into the determination of the amount of magnetic flux transported across the equator in any particular cycle. As the amount of flux which crosses the equator determines the amount of net flux in each hemisphere, it follows that the cross-equatorial plumes introduce an uncertainty in the prediction of the net flux in each hemisphere. This leads to an uncertainty in predictions of the strength of the following cycle.
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