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This article examines three-dimensional ideal flow and presents related mathematical concepts. The flow function is defined, providing a useful geometric interpretation. When combined with the velocity potential, the flow function generates a monogenic flow potential. This potential is monogenic in the sense of quaternion analysis. Finally, we apply the integration theory of monogenic functions and derive the velocity potential and stream function using their boundary values.

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Three Dimensional Stream Functions and Monogenic Flow Potentials

  • 章节

  • 发表日期：

    2025年

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  • Heikki Orelma

摘要

This article examines three-dimensional ideal flow and presents related mathematical concepts. The flow function is defined, providing a useful geometric interpretation. When combined with the velocity potential, the flow function generates a monogenic flow potential. This potential is monogenic in the sense of quaternion analysis. Finally, we apply the integration theory of monogenic functions and derive the velocity potential and stream function using their boundary values.