Thermal Convection Field Research Articles

A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle

We present the first three-dimensional (3D), time-dependent, self-consistent numerical solution of the magneto-hydrodynamic (MHD) equations that describe thermal convection and magnetic field generation in a rapidly rotating spherical fluid shell with a solid conducting inner core. This solution, which serves as a crude analog for the geodynamo, is a self-sustaining supercritical dynamo that has maintained a magnetic field for three magnetic diffusion times, roughly 40 000 years. Fluid velocity in the outer core reaches a maximum of 0.4 cm s −1, and at times the magnetic field can be as large as 560 gauss. Magnetic energy is usually about 4000 times greater than the kinetic energy of the convection that maintains it. Viscous and magnetic coupling to both the inner core below and the mantle above cause time-dependent variations in their respective rotation rates; the inner core usually rotates faster than the mantle and decadal variations in the length of the day of the mantle are similar to those observed for the Earth. The pattern and amplitude of the radial magnetic field at the core-mantle boundary (CMB) and its secular variation are also similar to the Earth's. The maximum amplitudes of the longitudinally averaged temperature gradient, shear flow, helicity, and magnetic field oscillate between the northern and southern hemispheres on a time scale of a few thousand years. However, only once in many attempts does the field succeed in reversing its polarity because the field in the inner core, which has the opposite polarity to the field in most of the outer core, usually does not have enough time to reverse before the field in the outer core changes again. One successful magnetic field reversal occurs near the end of our simulation.

Numerical Simulation of Probability Control for Thermal Convection Cell Pattern Mode Transition.

In a thermal convection field constrained by right and left insulated walls, stable multiple solutions easily exist. In the case of a two-dimensional cavity with aspect ratio of 1.5, whose upper wall is cooled and lower wall is heated at a constant temperature, the two modes of thermal convection cell pattern are stable at Rayleigh number Ra of 2.0 × 105. That is, one-cell-mode and two-cell-mode. However, as Ra increases to 3.5 × 105, both modes become unstable, and appear in similar probability. The objective of this work is to demonstrate the possibility of controlling convection patterns under unstable conditions. We found that estimation using artificial neural network is effective to increase the probability of obtaining a desired mode, even in the slightly higher Ra of 2.5×105.

A Study on Bifurcation Control Using Pattern Recognition of Thermal Convection.

The Benard thermal convection field is known to have multiple solutions for a certain Rayleigh number condition. This means several convection flow patterns can be stably sustained without external control force. This study demonstrates that bimodal switching control is possible by means of estimating flow states. A neural network was used to recognize the transition state of the convection flow pattern. In order to change the flow pattern, an unstable feature of Benard convection was utilized. That is, the chaotic nature of wobbling around multiple solutions contributes to fast switching between stable modes. Numerical simulations were carried out to show the ability of the current controlling method.

Growth pattern formation in Bénard flows

Abstract The effects of Benard flows on diffusion-limited aggregation (DLA) is investigated by a growth pattern formation (GPF) computational model. The GPF introduced consists of a DLA process driven by a thermal convection field in a plane viscous incompresible flow. The flow regime is governed by the Grashoff, Prandtl and Schmidt dimensionless parameters. Moving from low to high Grashoff numbers, the particle motions obtained change from primarily stochastic Brownian trajectories, with Hausdorff dimension 2.0, to mainly deterministic curvilinear trajectories, with Hausdorff dimension 1.0. Correspondingly, the resulting clusters change their Hausdorff dimension from the DLA fractal to 1.0.