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

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.