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<p>Three-dimensional hydrodynamic equations of ideal incompressible fluid in Lagrangian form are considered. Their explicit solution is obtained. The trajectories of fluid particles are complex spatial curves depending on four frequencies. The vortex lines precess around the vertical axis. Their shape is determined by an arbitrary function depending on the axial Lagrangian coordinate. It is shown that the rotation axis is directed to the plane of vortex lines at some nonzero angle.</p>

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Three-Dimensional Flow of Ideal Fluid with Precessing Vortex Lines (Exact Solutions)

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • A. A. Abrashkin

摘要

Three-dimensional hydrodynamic equations of ideal incompressible fluid in Lagrangian form are considered. Their explicit solution is obtained. The trajectories of fluid particles are complex spatial curves depending on four frequencies. The vortex lines precess around the vertical axis. Their shape is determined by an arbitrary function depending on the axial Lagrangian coordinate. It is shown that the rotation axis is directed to the plane of vortex lines at some nonzero angle.