Maintenance mechanism of a circular surface wave in a magnetohydrodynamic cell and limits of its existence

The circular surface wave (CSW) of a low-temperature gallium alloy in the immovable cell with a central bottom electrode and an upper ring electrode exposed to axial magnetic fields is studied experimentally. It is shown that, depending on the force parameter and geometrical characteristics of the cell [cell radius, height of the liquid metal (LM) layer, and position of the circular electrode], three modes can occur in the cell: rest, CSW, or axial rotation with a deep funnel on the surface providing the circular contact of the LM with the electrode. A mode map showing the boundaries of the CSW existence domain is plotted on the parameter plane. The mechanism which provides the existence of a stable CSW is suggested. It is shown that the CSW is a superposition of two intense large-scale vortices. The main vortex, whose axis coincides with the axis of the cylindrical cell, is generated by the Lorentz force localized near the bottom electrode and arising from the interaction of the divergent electric current with the vertical magnetic field. The intensity of the second vortex is an order of magnitude less, and the axis of rotation is directed to the contact area of the liquid metal with the ring electrode, which appears near the crest of the wave. Similar to the main vortex, it exists due to the interaction of the current converging to the contact area with the superimposed magnetic field. The second vortex provides the lifting of the LM ahead of the incoming wave. The intensity of both vortices is proportional to the product of the external field by the total current, which explains the linear relationship between the relative frequency of surface oscillations and their amplitude.