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Register a new userMeridional Circulation Dynamics in a Cyclic Convective Dynamo
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Surface observations indicate that the speed of the solar meridional circulation in the photosphere varies in anti-phase with the solar cycle. The current explanation for the source of this variation is that inflows into active regions alter the global surface pattern of the meridional circulation. When these localized inflows are integrated over a full hemisphere, they contribute to the slow down of the axisymmetric poleward horizontal component. The behavior of this large scale flow deep inside the convection zone remains largely unknown. Present helioseismic techniques are not sensitive enough to capture the dynamics of this weak large scale flow. Moreover, the large time of integration needed to map the meridional circulation inside the convection zone, also masks some of the possible dynamics on shorter timescales. In this work we examine the dynamics of the meridional circulation that emerges from a 3D MHD global simulation of the solar convection zone. Our aim is to assess and quantify the behavior of meridional circulation deep inside the convection zone, where the cyclic large-scale magnetic field can reach considerable strength. Our analyses indicate that the meridional circulation morphology and amplitude are both highly influenced by the magnetic field, via the impact of magnetic torques on the global angular momentum distribution. A dynamic feature induced by these magnetic torques is the development of a prominent upward flow at mid latitudes in the lower convection zone that occurs near the equatorward edge of the toroidal bands and that peaks during cycle maximum. Globally, the dynamo-generated large-scale magnetic field drives variations in the meridional flow, in stark contrast to the conventional kinematic flux transport view of the magnetic field being advected passively by the flow.
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We investigate the role of magnetic helicity in promoting cyclic magnetic activity in a global, 3D, magnetohydrodynamic (MHD) simulation of a convective dynamo. This simulation is characterized by coherent bands of toroidal field that exist within the convection zone, with opposite polarities in the northern and southern hemispheres. Throughout most of the cycle, the magnetic helicity in these bands is negative in the northern hemisphere and positive in the southern hemisphere. However, during the declining phase of each cycle, this hemispheric rule reverses. We attribute this to a global restructuring of the magnetic topology that is induced by the interaction of the bands across the equator. This band interaction appears to be ultimately responsible for, or at least associated with, the decay and subsequent reversal of both the toroidal bands and the polar fields. We briefly discuss the implications of these results within the context of solar observations, which also show some potential evidence for toroidal band interactions and helicity reversals.
In this paper we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third-order and has cubic nonlinearities whilst the second has only quadratic nonlinearities and describes the interaction of convection and an aperiodically reversing magnetic field. We show how DSS can be utilised to solve for the statistics of these systems of equations both in the presence and the absence of stochastic terms, by truncating the cumulant hierarchy at either second or third order. We compare two different techniques for solving for the statistics, timestepping -- which is able to locate only stable solutions of the equations for the statistics and direct detection of the fixed points. We develop a complete methodology and symbolic package in Python for deriving the statistical equations governing the Low-order dynamic systems in cumulant expansions. We demonstrate that although direct detection of the fixed points is efficient and accurate for DSS truncated at second order, the addition of higher order terms leads to the inclusion of many unstable fixed points that may be found by direct detection of the fixed point by iterative methods. In those cases timestepping is a more robust protocol for finding meaninful solutions to DSS.
A theoretical framework is developed for understanding the transient growth and propagation characteristics of thermodynamically coupled, meridional mode-like structures in the tropics. The model consists of a Gill-Matsuno type steady atmosphere under the longwave approximation coupled via a wind-evaporation-sea surface temperature (WES) feedback to a slab ocean model. When projected onto basis functions for the atmosphere the system simplifies to a non-normal set of equations that describes the evolution of individual sea surface temperature (SST) modes, with clean separation between symmetric and anti-symmetric modes. The following major findings result from analysis of the system: (i) a transient growth process exists whereby specific SST modes propagate toward lower order modes at the expense of the higher-order modes; (ii) the same dynamical mechanisms govern the evolution of symmetric and anti-symmetric SST modes except for the lowest-order wave number, where for symmetric structures the atmospheric Kelvin wave plays a critically different role in enhancing decay; and (iii) the WES feedback is positive for all modes (with a maximum for the most equatorially confined antisymmetric structure) except for the most equatorially confined symmetric mode where the Kelvin wave generates a negative WES feedback. Taken together, these findings explain why equatorially anti-symmetric dipole-like structures may dominate thermodynamically coupled ocean / atmosphere variability in the tropics. The role of non-normality as well as the role of realistic mean states in meridional mode variability are discussed.
A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded conflicting inferences. Here, following a summary of existing results we show how a large center-to-limb systematics (CLS) in the measured travel times of acoustic waves affect the inferences through an analysis of frequency dependence of CLS, using data from the Helioseismic and Doppler Imager (HMI) onboard Solar Dynamics Observatory (SDO). Our results point to the residual systematics in travel times as a major cause of differing inferences on the deep structure of MC.
A turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased in several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on the mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that the ratio of the effective penetration length to the mean penetration length of radiation increases in 2.5 times in the vicinity of the solar surface. The main reason are the compressibility effects that become important in the vicinity of the solar surface where temperature and density fluctuations increase towards the solar surface, enhancing fluctuations of the radiation absorption coefficient and increasing the effective penetration length of radiation.
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