Uncoupling the effects of Euler and Coriolis acceleration on the transient dynamics over a rotating wing

During the steady phase of insect-wing rotation, Coriolis acceleration significantly influences the leading-edge vortex (LEV) dynamics and lift generation. However, its role during the transient phase, where Euler acceleration is dominant, has received limited attention. This study decouples the effects of Euler and Coriolis accelerations to assess their relative contributions to the transient dynamics over a rotating wing. By isolating wing acceleration ( $\alpha ^*$ ) from the Rossby number, we systematically examine how these rotational accelerations govern transient behaviour. Results show that increasing Euler acceleration or decreasing Coriolis acceleration produces similar effects on lift generation and global flow-field evolution; specifically, transient lift (and thus the maximum lift) increases, and the LEV evolves earlier with respect to wing displacement. Nevertheless, the mechanisms driving LEV growth differ for the two accelerations. Higher Euler acceleration increases shear-layer flux while reducing secondary-vorticity generation, thereby accelerating LEV growth. In contrast, reduced Coriolis acceleration increases shear-layer flux while diminishing spanwise vorticity flux, also causing the LEV to grow earlier in time. These findings underscore the critical roles of both accelerations in the transient phase and indicate that considering both is essential for a comprehensive understanding of rotating-wing dynamics.