Magnetic helicity evolution inside a hexagonal convective cell

Magnetic helicity has received considerable attention in the area of fluid dynamics. Recently, this quantity is attracting the interest of solar physicists and much research has been carried out related to magnetic helicity generation and transport through different solar layers, starting from the interior and the convection zone, towards the photosphere, the corona and finally into the heliosphere. Taking into account the global importance of supergranular cells in convection theories, we study the motion of magnetic features into such a geometrical element simplified as hexagonal cell and we analyse the results in terms of the accumulated magnetic helicity. We compute the emergence of a bipole inside the hexagonal cell and its motion from the centre of the cell towards its sides and its vertices, where the magnetic elements are considered to be sinking down. Multiple bipoles are also considered and phenomena such as cancellation, coalescence and fragmentation are also investigated. We find that the most important process for the accumulation of magnetic helicity is the shear motion between the polarities. The magnetic helicity accumulation changes its trend when one polarity reaches the side of the hexagon, and later the vertex. It has zero value when there is no shear motion inside the hexagonal cell, and it is constant when there is no shear between the two polarities during their motion along the cell sides.