Circular surface wave in a cylindrical MHD cell

A circular surface wave (CSW) occurs in liquid metal layers as a rotational motion of the inclined upper surface and can be provided by different mechanisms in shaken and immovable vessels. In this paper we study experimentally the CSW of low-temperature gallium alloy in an immovable cell with a central bottom electrode and an upper ring electrode under an applied axial magnetic field. We confirm that a stationary CSW regime takes place if the forcing parameter exceeds some critical value. Above this value, the characteristic CSW frequency, normalized by the natural frequency of the azimuthal gravity wave in the same cell, approximately follows the law \(f/f_0\sim 1+\sqrt{\text {S}}/2\), where \(\text {S}\) is the interaction parameter. The amplitude of surface oscillations also grows with the increase in forcing. The measured velocity profiles show that the flow has a complicated structure, and the calculations of the electromagnetic force distribution demonstrate that the stationary CSW in the considered problem is provided by the eccentric torque of the Lorentz force.