Abstract. Numerical experiments of the emergence of magnetic flux from the uppermost layers of the solar interior to the photosphere and its further eruption into the low atmosphere and corona are carried out. We use idealized models for the initial stratification and magnetic field distribution below the photosphere similar to those used for multidimensional flux emergence experiments in the literature. The energy equation is adiabatic except for the inclusion of ohmic and viscous dissipation terms, which, however, become important only at interfaces and reconnection sites. Three-dimensional experiments for the eruption of magnetic flux both into an unmagnetized corona and into a corona with a preexisting ambient horizontal field are presented. The shocks preceding the rising plasma present the classical structure of nonlinear Lamb waves. The expansion of the matter when rising into the atmosphere takes place preferentially in the horizontal directions: a flattened (or oval) low plasma-β ball ensues, in which the field lines describe loops in the corona with increasing inclination away from the vertical as one goes toward the sides of the structure. Magnetograms and velocity field distributions on horizontal planes are presented simultaneously for the solar interior and various levels in the atmosphere. Since the background pressure and density drop over many orders of magnitude with increasing height, the adiabatic expansion of the rising plasma yields very low temperatures. To avoid this, the entropy of the rising fluid elements should be increased to the high values of the original atmosphere via heating mechanisms not included in the present numerical experiments. The eruption of magnetic flux into a corona with a preexisting magnetic field pointing in the horizontal direction yields a clear case of essentially three-dimensional reconnection when the upcoming and ambient field systems come into contact. The coronal ambient field is chosen at time t = 0 perpendicular to the direction of the tube axis and thus, given the twist of the magnetic tube, almost anti-parallel to the field lines at the upper boundary of the rising plasma ball. A thin, dome-shaped current layer is formed at the interface between the two flux systems, in which ohmic dissipation and heating are taking place. The reconnection proceeds by merging successive layers on both sides of the reconnection site; however, this occurs not only at the cusp of the interface, but, also, gradually along its sides in the direction transverse to the ambient magnetic field. The topology of the magnetic field in the atmosphere is thereby modified: the reconnected field lines typically are part of the flanks of the tube below the photosphere but then join the ambient field system in the corona and reach the boundaries of the domain as horizontal field lines.

To contribute to the understanding of heating and dynamic activity in boundary‐driven, low‐beta plasmas such as the solar corona, we investigate how an initially homogeneous magnetic field responds to random large‐scale shearing motions on two boundaries, by numerically solving the dissipative MHD equations, with resolutions ranging from 243 to 1363. We find that even a single application of large‐scale shear, in the form of orthogonal sinusoidal shear on two boundaries, leads to the formation of tangential discontinuities (current sheets). The formation time scales logarithmically with the resistivity and is of the order of a few times the inverse shearing rate for any reasonable resistivity, even though no mathematical discontinuity would form in a finite time in the limit of vanishing resistivity. The reason for the formation of the current sheets is the interlocking of two magnetic flux systems. Reconnection in the current sheets is necessary for the field lines to straighten out. The formation of current sheets causes a transition to a very dynamic plasma state, where reconnection drives supersonic and super‐Alfvénic jet flows and where these, in turn, cause the formation of smaller‐scale current sheets. A statistically steady state level for the average Poynting flux and the average Joule dissipation is reached after a few correlation times, but both boundary work and Joule dissipation are highly fluctuating in time and space and are only weakly correlated. Strong and bursty Joule dissipation events are favored when the volume has a large length/diameter ratio and is systematically driven for periods longer than the Alfvèn crossing time. The understanding of the reason for the current sheet formation allows a simple scaling law to be constructed for the average boundary work. Numerical experiments over a range of parameter values, covering over 3 orders of magnitude in average dissipation, obey the scaling law to within a factor of 2. The heating rate depends on the boundary velocity amplitude and correlation time, the Alfvén speed, and the initial magnetic field strength but appears to be independent of the resistivity because of the formation of a hierarchy of current sheets. Estimates of the photospheric boundary work on the solar coronal magnetic field using the scaling law are consistent with estimates of the required coronal heating rates. We therefore conclude that the work supplied to the solar corona as a consequence of the motion of the magnetic foot points in the solar photosphere and the emergence of new flux is a significant contributor to coronal heating and flaring and that it quite plausibly is the dominant one.

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Aims. We investigate the effects of varying the magnetic field strength and the twist of a flux tube as it rises through the solar interior and emerges into the atmosphere. Methods. Using a 3D numerical MHD code, we consider a simple stratified model, comprising of one solar interior layer and three overlying atmospheric layers. We set a horizontal, twisted flux tube in the lowest layer. The specific balance of forces chosen results in the tube being fully buoyant and the temperature is decreased in the ends of the tube to encourage the formation of an Ω-shape along the tube's length. We vary the magnetic field strength and twist independently of each other so as to give clear results of the individual effects of each parameter. Results. We find a self-similar evolution in the rise and emergence of the flux tube when the magnetic field strength of the tube is modified. During the rise through the solar interior, the height of the crest and axis, the velocity of the crest and axis, and the decrease in the magnetic field strength of the axis of the tube are directly dependent upon the initial magnetic field strength given to the tube. No such self-similarity is evident when the twist of the flux tube is changed, due to the complex interaction of the tension force on the rise of the tube. For low magnetic field strength and twist values, we find that the tube cannot fully emerge into the atmosphere once it reaches the top of the interior since the buoyancy instability criterion cannot be fulfilled. For those tubes that do advance into the atmosphere, when the magnetic field strength has been modified, we find further self-similar behaviour in the amount of tube flux transported into the atmosphere. For the tubes that do emerge, the variation in the twist results in the buoyancy instability, and subsequent emergence, occurring at different locations along the tube's length.

A three-dimensional numerical experiment of the launching of a hot and fast coronal jet followed by several violent eruptions is analyzed in detail. These events are initiated through the emergence of a magnetic flux rope from the solar interior into a coronal hole. We explore the evolution of the emerging magnetically-dominated plasma dome surmounted by a current sheet and the ensuing pattern of reconnection. A hot and fast coronal jet with inverted-Y shape is produced that shows properties comparable to those frequently observed with EUV and X-Ray detectors. We analyze its 3D shape, its inhomogeneous internal structure, and its rise and decay phases, lasting for some 15-20 min each. Particular attention is devoted to the field-line connectivities and the reconnection pattern. We also study the cool and high-density volume that appears encircling the emerged dome. The decay of the jet is followed by a violent phase with a total of five eruptions. The first of them seems to follow the general pattern of tether-cutting reconnection in a sheared arcade, although modified by the field topology created by the preceding reconnection evolution. The two following eruptions take place near and above the strong field-concentrations at the surface. They show a twisted, Ω-loop like rope expanding in height, with twist being turned into writhe, thus hinting at a kink instability (perhaps combined with a torus-instability) as the cause of the eruption. The succession of a main jet ejection and a number of violent eruptions that resemble mini-CME's and their physical properties suggest that this experiment may provide a model for the blowout jets recently proposed in the literature.