Formation of weak singularities on the surface of a dielectric fluid in a tangential electric field

The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that singular points are formed at the fluid boundary in a finite time; at these points, the boundary curvature significantly increases and undergoes a discontinuity. The amplitude and slope angles of the boundary remain small. The singular behavior of the system is demonstrated by spectral functions of the fluid surface–they acquire a power dependence. Near the singularity, the boundary curvature demonstrates a self-similar behavior typical for weak root singularities.