On the control of surface waves by a vertical magnetic field

We consider the magnetic damping of surface gravity waves by a vertical magnetic field. The damping mechanism is, in principle, quite simple. The motion of a conducting fluid in the presence of an imposed magnetic field leads to electric currents, and hence to Ohmic dissipation. As the fluid heats up, there is a corresponding loss in the mechanical energy of the wave motion. When the fluid is infinite in the horizontal plane, or else bounded by perfectly conducting vertical walls, the induced currents have a simple spatial distribution and so the analysis of such waves is straightforward [L. E. Franekel, J. Fluid. Mech. 7, 81 (1959); P. Rivat, J. Etay, and M. Garnier, Eur. J. Mech. B/Fluids 10, 537 (1991)]. However, in most practical applications of magnetic damping the fluid is bounded by nonconducting vertical walls. This leads to a complex distribution of electric currents and to a much weaker form of damping. In this paper, we extend the simple classical theory to accommodate nonconducting sidewalls, and show that the characteristic damping time increases by a factor of ∼30 due to the presence of these walls. Experiments are described for both conducting and insulating sidewalls. The results of the experiments are in good agreement with the theory.