Magnetic flux emerges from the solar surface as dark filaments connecting small sunspots with opposite polarities. The regions around the dark filaments are often bright in X-rays and are associated with jets. This implies plasma heating and acceleration, which are important for coronal heating. Previous two-dimensional simulations of such regions showed that magnetic reconnection between the coronal magnetic field and the emerging flux produced X-ray jets and flares, but left unresolved the origin of filamentary structure and the intermittent nature of the heating. Here we report three-dimensional simulations of emerging flux showing that the filamentary structure arises spontaneously from the magnetic Rayleigh-Taylor instability, contrary to the previous view that the dark filaments are isolated bundles of magnetic field that rise from the photosphere carrying the dense gas. As a result of the magnetic Rayleigh-Taylor instability, thin current sheets are formed in the emerging flux, and magnetic reconnection occurs between emerging flux and the pre-existing coronal field in a spatially intermittent way. This explains naturally the intermittent nature of coronal heating and the patchy brightenings in solar flares.

Computer simulations have been playing an important role in the development of our understanding of the geodynamo, but direct numerical simulation of the geodynamo with a realistic parameter regime is still beyond the power of today's supercomputers. Difficulties in simulating the geodynamo arise from the extreme conditions of the core, which are characterized by very large or very small values of the non-dimensional parameters of the system. Among them, the Ekman number, E, has been adopted as a barometer of the distance of simulations from real core conditions, in which E is of the order of 10(-15). Following the initial computer simulations of the geodynamo, the Ekman number achieved has been steadily decreasing, with recent geodynamo simulations performed with E of the order of 10(-6). Here we present a geodynamo simulation with an Ekman number of the order of 10(-7)-the highest-resolution simulation yet achieved, making use of 4,096 processors of the Earth Simulator. We have found that both the convection flow and magnetic field structures are qualitatively different from those found in larger-Ekman-number dynamos. The convection takes the form of sheet plumes or radial sheet jets, rather than the columnar cell structures that are usually found. We have found that this sheet plume convection is an effective dynamo and the generated current is organized as a set of coils in the shape of helical springs or at times as a torus.

We performed laboratory experiments of Rayleigh-Bénard convection with liquid gallium under various intensities of a uniform imposed horizontal magnetic field. An ultrasonic velocity profiling method was used to visualize the spatiotemporal structure of the flows with simultaneous monitoring of the temperature fluctuations in the liquid gallium layer. The explored Rayleigh numbers Ra range from the critical value for onset of convection to 10 5 ; the Chandrasekhar number Q covers values up to 1100. A regime diagram of the convection patterns was established in relation to the Ra and Q values for a square vessel with aspect ratio 5. We identified five flow regimes: (I) a fluctuating large-scale pattern without rolls, (II) weakly constrained rolls with fluctuations, (III) a continuous oscillation of rolls, (IV) repeated roll number transitions with random reversals of the flow direction, and (V) steady two-dimensional (2D) rolls. These flow regimes are classified by the Ra/Q values, the ratio of the buoyancy to the Lorentz force. Power spectra from the temperature time series indicate that regimes I and II have the features of developed turbulence, while the other regimes do not. The region of steady 2D rolls (Busse balloon) extends to high Ra values in the present setting by a horizontal magnetic field and regime V is located inside the Busse balloon. Concerning the instabilities of the steady 2D rolls, regime III is the traveling wave convection developed from the oscillatory instability. Regime IV can be regarded as a state of phase turbulence, which is induced by intermittent occurrences of the skewed-varicose instability.

We present the results of three-dimensional magnetohydrodynamic simulations of solar emerging flux and its interaction with preexisting coronal field. In order to resolve the fine structures and the current sheets, we used high-resolution grids with up to $800 \times 400 \times 620$ points; the calculation was carried out using the Earth Simulator. The model set up is an extension of a previous two-dimensional simulation by Yokoyama and Shibata (1995) to include the variation along the third direction. Based on the same simulation result, we reported in our previous paper (Isobe et al. 2005): (1) Dense filaments similar to H$\alpha$ arch filament system are spontaneously formed in the emerging flux by the magnetic Rayleigh–Taylor type instability. (2) Filamentary current sheets are created in the emerging flux due to a nonlinear development of the magnetic Rayleigh-Taylor instability, which may cause an intermittent, nonuiform heating of the corona. (3) A magnetic reconnection between the emerging flux and preexisting coronal field occurs in a spatially intermittent way. In this paper we describe the simulation model and discuss the origin and the properties of the magnetic Rayleigh-Taylor instability in detail. It is shown that the top-heavy configuration that causes the instability is formed by the intrinsic dynamics of the emerging flux.

Zonal jets are very common in nature. Well-known examples are those in the atmospheres of giant planets and the alternating jet streams found in the Earth's world ocean. Zonal flow formation in nuclear fusion devices is also well studied. A common feature of these zonal flows is that they are spontaneously generated in turbulent systems. Because the Earth's outer core is believed to be in a turbulent state, it is possible that there is zonal flow in the liquid iron of the outer core. Here we report an investigation at the current low-viscosity limit of numerical simulations of the geodynamo. We find a previously unknown convection regime of the outer core that has a dual structure comprising inner, sheet-like radial plumes and an outer, westward cylindrical zonal flow. We numerically confirm that the dual-convection structure with such a zonal flow is stable under a strong, self-generated dipole magnetic field.

We performed three-dimensional MHD numerical simulations for solar coronal magnetic loop oscillations and found: (1) The loop oscillation period is determined by its Alfvén time. (2) The amplitude of oscillation decreases exponentially in time. This is explained as energy transport by fast-mode MHD waves. The damping rate, $\omega _\mathrm{damp}$, is described as $\omega _\mathrm{damp} \propto V_\mathrm{a}/R$, where $V_\mathrm{a}$ is the Alfvén speed around loops and $R$ is the radius of the loop. Because of computer resources limitations, the plasma $\beta$ value is much larger than that of the real corona. We thus applied a scaling law derived from numerical simulation results to the real corona parameter ranges and analyzed the results.

We studied solar coronal X-ray jets by MHD numerical simulations with thermal conduction effects based on the magnetic reconnection model. Key physical processes are included, such as the emergence of magnetic fluxes from the convection zone, magnetic reconnection with the coronal magnetic fields, heat conduction to the chromosphere, and chromospheric evaporation. High-density evaporation jets were successfully reproduced in the simulations. The mass of the evaporation jets M is described as # 12 15/7 6 5/14 M p 6.8 # 10 g(B/10 G) (T /10 K) cor , where B is the magnetic field strength, is the coronal temperature, is the 12/7 (s /5000 km) (t/400 s) T s flare cor flare loop height, and t is the duration of the ejection.

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