Experimental Study on Thrust Prediction for Zebrafish Unsteady Maneuvering at St > 1: A Wake-Vortex-Based Linear Scaling Law

Aquatic organisms exhibit remarkable propulsion capabilities during explosive maneuvers (such as turning and escaping), stemming from their precise control over highly unsteady flow fields. Under highly unsteady operating conditions where the Strouhal number (St > 1) far exceeds the steady-state cruise range, establishing a thrust scaling law that reflects the physical essence and possesses real-time predictive capabilities is a core bottleneck in the development of highly agile biomimetic underwater vehicles (AUVs). This paper aims to explore the linear mechanism of force-vortex coupling during the turning process of zebrafish through live zebrafish autonomous swimming experiments. This study utilized 200 Hz high-frequency particle image velocimetry (PIV) to systematically reconstruct the transient velocity field of zebrafish during maneuvering. To address the complexity of the biological motion boundary, a rigorous quantitative assessment of experimental uncertainties was conducted, ensuring the spatial accuracy of the velocity vectors. Through data post-processing methods, the velocity circulation and vortex radius in the vortex core region were objectively quantified from the complex flow field topology. The results show that zebrafish swimming and wake vortex evolution are highly synchronized within the St range of 1-10. The core finding indicates that despite the high nonlinearity and transient mixing of the turning flow field, there is a very strong linear correlation between the mean thrust and local vortex core parameters. Linear regression analysis shows a fitting coefficient of up to 0.96, and this scaling law exhibits excellent universality across different Reynolds numbers (Re between 100 and 2000). This study demonstrates that in highly unsteady propulsion, complex global momentum exchange can be reduced to simple local vortex core geometry-dynamics. High-precision fitting provides strong evidence for the physical logic that thrust generation is dominated by the main vortex core. This scaling law, due to its extremely low computational cost, can be directly converted into a real-time force sensing algorithm for AUVs, laying a theoretical foundation for realizing closed-loop agile control based on flow field feedback.