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<p>Vortices, or swirling flows, are fundamental features in many physical systems, ranging from ocean currents and weather patterns to superfluids and plasmas. However, accurately modeling these flows, particularly those with complex topological structures, has remained a significant challenge. This study introduces a mathematical framework for capturing the dynamics of vortex flows via a non-trivial lifting process from spherical vorticity maps to spherical velocity maps, enabling the velocity field to be expressed as a quaternion-valued wave function representing vortex tubes of arbitrary topology. The framework has broad applications across diverse fields, including turbulence, fluid dynamics, superfluid vortices, ocean circulation, and plasma physics, offering valuable insights into the topological evolution and stability of vortex structures in both natural and engineered systems.</p>

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Quaternionic lifting of spherical Clebsch maps in helical flows

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Yanru Wang,
  • Lei Pang,
  • Zhenkun Li,
  • Yukun Yan,
  • Linlin Kang,
  • Qinghai Zhang,
  • Shiying Xiong

摘要

Vortices, or swirling flows, are fundamental features in many physical systems, ranging from ocean currents and weather patterns to superfluids and plasmas. However, accurately modeling these flows, particularly those with complex topological structures, has remained a significant challenge. This study introduces a mathematical framework for capturing the dynamics of vortex flows via a non-trivial lifting process from spherical vorticity maps to spherical velocity maps, enabling the velocity field to be expressed as a quaternion-valued wave function representing vortex tubes of arbitrary topology. The framework has broad applications across diverse fields, including turbulence, fluid dynamics, superfluid vortices, ocean circulation, and plasma physics, offering valuable insights into the topological evolution and stability of vortex structures in both natural and engineered systems.