Below are some current active research thrusts (non-exhaustive).

Collective motion and avian flocking

Collective patterns of motion emerge across biological taxa: migratory birds flock, starlings form murmurations, fish school, and large mammals such as wildebeests form dynamic herds. This collective motion is both visually beautiful as well as scientifically intriguing. In particular, birds achieve remarkable aerodynamic and biological advantages through coordinated flocking flight -- yet despite decades of modeling, simulation, and observation, there exists no unified framework which explains how these benefits emerge across species or how flow-mediated interactions balance behavioral and sensory imperatives. This line of my research entails a multi-level investigation into avian flocking, which lies at the interface of biology, physics, and emergent organization. The ultimate aim is to characterize the flows of information -- which propagate through fluidic channels, via complex unsteady wake-vortex interactions among birds, as well as through visual, auditory, and behavioral channels -- that together govern emergent collective dynamics.

Flow control via kirigami and porous media

Strategic inclusion of roughness on airfoils is known to replicate the mechanism of vortex generators: flow control devices that introduce high-energy vortices into the boundary layer of an airfoil and thus energize flows, maintain attachment to the airfoil surface, and delay the onset of stall. I am interested in investigating this effect in the context of kirigami, i.e., the Japanese art of paper cutting. Can we adhere kirigami to an airfoil, dynamically actuate it, and control the transition to stall? Can we mathematically model the stress, strain, roughness, and porosity of a sheet of deployed kirigami based on its cut geometry and constitutive properties? How do these properties dictate flow patterns?

Extreme lift-to-drag ratios of free-flying rotors

A cylinder rotating in a viscous fluid establishes circulation and thereby generates lift by the well-known Magnus effect . However, rotary wings are currently viewed as impractical due to their high drag compared to airfoils at the speeds and scales of conventional aviation. Here, we report that rotors incur negligibly low drag for conditions relevant to smaller-scale flight applications, and that such states are naturally sought and stably maintained during free flight. Two-dimensional immersed boundary simulations of a spinning disk moving freely in a fluid reveal a drag-free terminal mode in which the body levitates against gravity and drifts horizontally without leaving a substantial vortex wake. Through experimental tests of an aquatic robot in which a cylinder is driven to spin by internal actuation, we find that Flettner-type rotors with end disks enable similar outcomes in three dimensions. These results should reawaken interest in Magnus-based flight by revealing a form of levitation that is wakeless and thus aerodynamically stealthy and also self-stable. See chapter 5 of my Ph.D. dissertation.