The essence of generating vortex-within-a-vortex structures behind forked caudal fins

This work focuses on vortex-within-a-vortex (VV) structures behind three different shapes of forked caudal fin with a heaving-pitching motion. The results show that the synchronization of trailing-edge vortex separation and the shedding of the leading-edge vortex contributes to the generation of the VV structure. The VV structures of caudal fins with different chord lengths can be observed almost simultaneously. The Strouhal number not only determines the number of shedding vortices in the wake but also reflects the activation time and the superimposed effect of the leading-edge vortex and trailing-edge vortex on propulsion performance. This study provides an important theoretical reference for the design and control of fork propellers for use in underwater vehicles.