Abstract
We study the propagation of surface waves on a current in the presence of an electromagnetic field. A horizontal (vertical) field strengthens (weakens) the counter-current which blocks the waves. We compute the phase space diagrams (blocking velocities versus period of the waves) with and without surface tension. Three new dimensionless numbers are introduced to compare the relative strengths of gravity, surface tension and field effects. This work shows the importance of an electromagnetic field in order to design wave-breakers or in microfluidics applications.
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