Data-Driven Reduced-Order Modeling of a Flying Hawkmoth’s Wake

Computational fluid dynamics (CFD) simulations offer precise insight into complex flow phenomena yet are often prohibitively time- and resource-intensive. To address this challenge, this study applies reduced-order modeling (ROM) to the problem of insect flight. We begin by simulating a hawkmoth's wake using an in-house immersed-boundary-method-based CFD solver. Then, dynamic mode decomposition (DMD) is used to decompose the wake into a set of time-varying modes. Finally, we employ sparse identification of nonlinear dynamics (SINDy) principles to formulate a low-dimensional model of the wake dynamics. Using these techniques, we demonstrate that the wake can be effectively modeled by a Stuart-Landau oscillator, providing a simple and interpretable representation of the complex flow dynamics as a limit cycle. This approach allows us to create a concise dynamic model of the hawkmoth's wake without relying on computationally expensive full-scale CFD simulations. Notably, our methodology produces a model that captures both transient and fully periodic wake dynamics. Furthermore, we explore the extension of this approach across multiple flight speeds, demonstrating its versatility in capturing wake dynamics across various flow conditions. The simplicity and efficiency of this ROM approach have significant implications for the design and control of bio-inspired micro-aerial vehicles (MAVs), offering a powerful tool for rapid analysis and optimization of flight performance.