Data-driven reduced-order modelling of wake dynamics in hovering flapping flight

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As insects flap their wings, they generate complex wake structures critical to their aerodynamic force production. Specific flow structures such as the leading-edge vortex have been studied for decades; however, a complete understanding of the transient dynamics and energy exchange mechanisms in insect wakes remains elusive. To help bridge this gap, we employ data-driven reduced-order modelling techniques to identify a simple and interpretable model for a hovering hawkmoth’s wake. We begin by using an in-house immersed-boundary-method computational fluid dynamics solver to simulate hovering hawkmoth flight. We then perform dynamic mode decomposition to distil the resulting flow field into a set of time-varying modes. Finally, we employ sparse regression to identify a model capturing the driving modes’ temporal evolution, ranging from quiescent flow to periodic steady state. Notably, the model takes the form of a Stuart–Landau oscillator with higher-order nonlinear terms. The presence of a limit-cycle dynamics suggests a balance between energy input from wing motion and energy lost due to advective energy transfer and viscous dissipation. Using an impulse-based wake survey method, we show that this model provides an accurate estimation (mean absolute error within 3.5 % of body weight) of the hawkmoth’s long-term lift production. These findings highlight the significance of stability and energy transfer in flapping-flight aerodynamics, offering a framework for future studies of biological flight systems. Furthermore, by linking the wake dynamics to simple dynamic equations, this work provides inspiration for the design and control of bio-inspired micro-aerial vehicles.