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

## TL;DR

This study numerically investigates the formation of weak singularities on the surface of a dielectric fluid under a strong tangential electric field, revealing finite-time boundary curvature discontinuities with self-similar behavior.

## Contribution

It demonstrates the development of weak singularities on a fluid surface in a tangential electric field, highlighting the boundary's self-similar curvature behavior near singularities.

## Key findings

- Singular points form in finite time with increased boundary curvature.
- Spectral functions show power-law dependence near singularities.
- Boundary curvature exhibits self-similar behavior characteristic of weak root singularities.

## Abstract

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.