Vortex is the dominant flow structure in hydro-energy machinery, and its swirling features are mainly determined by the rigid rotation part of vorticity. In this study, the rigid vorticity transport equation is proposed based on the vorticity decomposition. The vortex spatial evolution is described by the stretching term RST, the dilatation term RDT, the Lamb term RCT and the viscous term RVT. The shape change of a vortex tube is mainly affected by RST and RDT, while vortex production and dissipation are mainly reflected by RCT and RVT. Compared with the traditional vorticity transport equation, this new theoretical tool can distinguish between rigid rotation and shearing motion of local fluids, and it can better reveal the intuitive evolution characteristics of vortical structures. Two cases with clear engineering demands are analysed by using the transport equation, and the results show that it can provide a practical method for the analysis and control of vortical flows in hydro-energy machinery.

涡流是水能机械中占主导地位的流动结构，其涡流特征主要由涡流的刚性旋转部分决定。本研究在涡度分解的基础上提出了刚性涡度输运方程。涡旋空间演化由拉伸项 RST、膨胀项 RDT、兰姆项 RCT 和粘性项 RVT 描述。涡流管的形状变化主要受 RST 和 RDT 的影响，而涡流的产生和消散主要受 RCT 和 RVT 的影响。与传统的涡量输运方程相比，这种新的理论工具可以区分局部流体的刚性旋转和剪切运动，更好地揭示涡结构的直观演化特征。