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<p>This paper considers the propagation of two-dimensional steady periodic waves with constant vorticity under the influence of a vertical electric field. By employing conformal mappings, the free boundary problem is reformulated as a fixed boundary problem. This reformulation allows us to provide the necessary criteria for the existence of critical layers in the local flow. We then construct continuous curves of large-amplitude electrohydrodynamic waves with constant vorticity using analytic global bifurcation theory. Moreover, it is demonstrated that the global bifurcation curves cannot form closed loops.</p>

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The Existence and Geometric Structure of Periodic Solutions to Rotational Electrohydrodynamic Waves Problem

  • 期刊论文

  • 发表日期：

    2025年4月23日

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  • Guowei Dai,
  • Tingting Feng,
  • Yong Zhang

摘要

This paper considers the propagation of two-dimensional steady periodic waves with constant vorticity under the influence of a vertical electric field. By employing conformal mappings, the free boundary problem is reformulated as a fixed boundary problem. This reformulation allows us to provide the necessary criteria for the existence of critical layers in the local flow. We then construct continuous curves of large-amplitude electrohydrodynamic waves with constant vorticity using analytic global bifurcation theory. Moreover, it is demonstrated that the global bifurcation curves cannot form closed loops.