Kinematic control of vortex shedding in maneuvering zebrafish via an equivalent bluff-body mechanism

To reveal the physical mechanisms governing precise flow control during unsteady aquatic maneuvers, this study investigates the vortex shedding dynamics of maneuvering zebrafish using time-resolved particle image velocimetry. We identify a significant kinematic phase lag in active body deformation, where the moment of maximum bending distinctly lags behind the moment of maximum tail-beat amplitude. Based on this kinematics, we establish a spatiotemporal decoupling framework for vortex prediction. Spatially, a “head-steering” geometric criterion is discovered, exhibiting a strong linear correlation (R2 = 0.94) between the initial head orientation and the wake topology orientation. This implies that the head acts as a “geometric rudder,” pre-determining the symmetry-breaking direction of the wake regardless of the subsequent body undulation. Temporally, the non-dimensional vortex shedding timing demonstrates independence from the Reynolds number (Re = 300–1600). This robustness confirms that, despite the laminar nature of the flow, the shedding process is insensitive to Reynolds number variations, indicating that viscous effects play a secondary role in determining the shedding timing. This validates the applicability of universal inertial scaling laws (i.e., Strouhal number scaling). Furthermore, by introducing an “equivalent rectangular bluff-body” hypothesis, we demonstrate that the active tail sweep amplitude (A) functions as the transverse blockage width (short side), while the body length (L) acts as the streamwise chord (long side). Consequently, a modified Strouhal number scaling law, governed by the effective aspect ratio (L/A), successfully predicts the shedding frequency of actively deforming fish. These findings suggest that complex biological maneuvering wakes are governed by low-dimensional kinematic scaling laws, providing an empirical model for simplifying control strategies.