A spherical shell numerical dynamo benchmark with pseudo vacuum magnetic boundary conditions

It is frequently considered that many planetary magnetic fields originate as a result of convection within planetary cores. Buoyancy forces responsible for driving the convection generate a fluid flow that is able to induce magnetic fields; numerous sophisticated computer codes are able to simulate the dynamic behaviour of such systems. This paper reports the results of a community activity aimed at comparing numerical results of several different types of computer codes that are capable of solving the equations of momentum transfer, magnetic field generation and heat transfer in the setting of a spherical shell, namely a sphere containing an inner core. The electrically conducting fluid is incompressible and rapidly rotating and the forcing of the flow is thermal convection under the Boussinesq approximation. We follow the original specifications and results reported in Harder & Hansen to construct a specific benchmark in which the boundaries of the fluid are taken to be impenetrable, non-slip and isothermal, with the added boundary condition for the magnetic field <b>B</b> that the field must be entirely radial there; this type of boundary condition for <b>B</b> is frequently referred to as ‘pseudo-vacuum’. This latter condition should be compared with the more frequently used insulating boundary condition. This benchmark is so-defined in order that computer codes based on local methods, such as finite element, finite volume or finite differences, can handle the boundary condition with ease. The defined benchmark, governed by specific choices of the Roberts, magnetic Rossby, Rayleigh and Ekman numbers, possesses a simple solution that is steady in an azimuthally drifting frame of reference, thus allowing easy comparison among results. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier-finite element code. There is good agreement among codes

Developing horizontal convection against stable temperature stratification in a rectangular container

The effect of background stable temperature stratification in the developing stage of horizontal convection is studied by conducting laboratory experiments. By imposing horizontally differential heating at the top of a layer of low-temperature water, both vertical and horizontal temperature differences are explicitly defined. In developing horizontal convection of the present study, the flow structures are driven only by the baroclinic torque produced by the horizontal temperature difference, and braked by the restoring force of stable temperature stratification. We thus defined a nondimensional stratification parameter, which represents the balance of the braking force and the baroclinic torque, in addition to the Rayleigh number. Various features of the flow structures, maximum velocity, stream function, roll thickness, circulation of the roll, total kinetic energy, and Reynolds number, which are quantified via particle-tracking velocimetry, are summarized in spaces of the two nondimensional parameters. In the developing horizontal convection, the quantified flow features are well organized by power laws of the nondimensional parameters. The finite domain of the fluid container augments the effect of the apparent braking force, and the bulk quantities of the roll structures are suppressed by the stable temperature stratification. These results are the evidences for the significance of the nondimensional stratification parameter in the developing horizontal convection, unlike thermally equilibrated horizontal convection conventionally considering destabilizing thermal buoyancy as the primary driving force

Convection patterns in a liquid metal under an imposed horizontal magnetic field

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 105; 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

Theoretical and Numerical Studies of an Emerging Flux and associated Active Phenomena of the Sun

It is well established that sunspots and active regions are formed by the emergence of magnetic fluxes from the interior of the Sun into the atmosphere. The newly emerged bipolar active regions are called emerging flux regions (EFRs). There are several observational evidences which indicate the emergence and rising motion of magnetic flux tubes in EFRs. The emerging flux causes active phenomena and energy release in the solar corona. The Yohkoh satellite discovered many dynamic phenomena in the solar corona. One of the most interesting findings among such dynamic phenomena is solar coronal X-ray jets, which are observed as transitory X-ray enhancements with an apparent collimated motion. Based on the frequent observations of X-ray jets from emerging flux regions, Shibata et al.(1994) proposed a phenomenological model which explains the occurrence mechanism of these X-ray jets: magnetic energy of X-ray jets are released by magnetic reconnection between the emerging flux and the pre existing coronal magnetic field. The aim of this thesis is to understand the emerging flux and associated active phenomena of the Sun. This thesis is organized as follows: Chapter 1. Introductory Review: In this chapter, we briefly review the observations and theories of the emerging flux and associated active phenomena in the corona. Chapter 2. MID Numerical Simulations of Solar Coronal Jets based on Magnetic Reconnection Model including Anisotropic Heat Conduction Effect: In this chapter, we studied about properties of solar coronal X-ray jets by MHD numerical simulations based on the magnetic reconnection model including anisotropic heat conduction effect. Yokoyama & Shibata (1995, 1996) performed a two dimensional MHD simulation and succeeded to reproduce the plasma collimated flow along magnetic fields. We extended their works to study evaporated dense jets as X-ray brightening feature caused by magnetic reconnection between the emerging flux and pre-existing coronal fields. Key physical processes are included, such as emergence of magnetic fluxes from the convection zone, magnetic reconnection with the coronal magnetic fields, heat conduction to the chromosphere, and the chromospheric evaporation. High density evaporation jets were successfully reproduced in the simulations. Mass of the evaporation jets M is described as M=6.8x10 12g(B/10G)15/7(Tcor/10 6K)5/14(sflare/5000km)(t/400s), where B is the strength of magnetic fields, Tcor is the coronal temrerature, sflare is the height of the reconnection region, and t is the duration of ejection, respectively. Chapter 3. Three-dimensional MHD Numerical Simulations of a Twisted Emerging Flux Tube from below the Photosphere: According to several studies of the emerging flux process from convection zone to the corona, the magnetic field rising through the convection zone have the shape of an isolated tube with twisted magnetic fields. In this chapter, we performed three-dimensional MHD numerical simulations of the isolated magnetic flux tube\u27s emergence. The purpose of this study is to investigate coronal magnetic structure formed by the emerging flux tube. We found that the strength of twists of the magnetic flux tube greatly affects the final magnetic structure in the corona. The S shaped (like a sigmoid) structure is formed when the magnetic flux tube is strongly twisted initially, while helical magnetic structure is formed at the bottom of the tube when the tube is weakly twisted. This is because of the magnetic reconnection caused by convective plasma motion with the flux emergence. Chapter 4. Three-dimensional MHD Numerical Simulations of Coronal Loop Oscillations Associated with Flares: Recently, coronal loop oscillations associated with flares have observed by TRACE(e.g., Nakariakov et al.1999, Aschwanden et al.1999). To investigate these oscillating loops, we performed three dimensional numerical MHD simulations. We found that (1) loop oscillation period is determined by its Alfven time, and (2) the amplitude of oscillation decreases exponentially in time. This is explained as energy transport by fast-mode MHD waves. The damping rate ω damp is described as ω damp～Va/R where Va is the Alfven speed and R is the radius of the loop, respectively. Chapter 5. Summary and Future Directions: Finally summary of the thesis and the future directions are shown in this chapter. We also discuss application of the magnetic flux emergence and magnetic reconnection model to other astronomical objects such as accretion disks, galaxies, and so on