The paper presents an analytical solution for helical vortices with a Gaussian vorticity distribution in the core, which is confirmed by experimental and numerical simulations. This result is obtained by extending the Dyson method to the Biot–Savart law. Previously, analytical solutions were found and studied only for vortices with constant vorticity distribution in the core (a Rankine-type vortex core). One of the important issues raised during the discussion is the difference between self-induced movements of helical structures with both types of vortex core. The proposed solutions are important for the fundamental understanding and description of the behavior of helical eddy flows in various fields of industry and in nature. Examples include tip vortices behind the rotors of wind or hydro turbines, tornadoes, or axial vortices in aerodynamic devices such as vortex apparatuses and generators; cyclone separators, combustion chambers, etc.

本文提出了一种在中心具有高斯涡度分布的螺旋涡旋的解析解，这一点已通过实验和数值模拟得到了证实。通过将戴森方法扩展到Biot-Savart定律可获得此结果。以前，仅针对核心（兰金型涡旋核心）中具有恒定涡度分布的涡旋发现并研究了解析解。讨论中提出的重要问题之一是两种类型的涡旋核的螺旋结构的自感应运动之间的差异。所提出的解决方案对于在工业的各个领域和自然界中对螺旋涡流的行为的基本理解和描述很重要。例子包括风力涡轮机或水力涡轮机转子后面的尖端涡旋，龙卷风，或空气动力学装置（如涡流装置和发生器）中的轴向涡流；旋风分离器，燃烧室等