How upstream wakes help fish with energy-efficient propulsion

From early flight to modern unmanned vehicles, engineers have often looked to biological systems for inspiration. Schools of fish, in particular, can motivate underwater robotics in their ability to swim in organized formations that take advantage of upstream vortices for passive propulsion. To help develop applications of this behavior, Muhammad Umer Khan Mughal and Leixin Ma studied how vortices in the wakes of upstream bodies affect the motion of fish.

The researchers looked at how a wake — specifically the strength and position of vortices in the wake — affects a fish’s drag and thrust. Using a model of a fish comprised of a fixed head and flexible tail, they found opposing effects, depending on whether the fish is close to or far away from the object causing the wake. Nearby, a strong vortex can pull the fish forward to help it accelerate, but as the vortex weakens downstream, this benefit is replaced with drag.

“The wake can do two jobs at once: It can make the flexible tail flap passively, and it can also generate a forward thrust component,” Ma said. “No prescribed tail beat or muscle-like actuation is needed in the model — the motion emerges from the interaction between the flexible body and the incoming vortices.”

The stiffness of the fishtail also plays a role by interacting with the wake — albeit with a smaller effect than the wake itself. Flexible tails can absorb and redistribute load from the wake, but stiffer tails are more prone to fluctuations.

“In simple terms, vortex strength and spacing control whether the wake helps propel the fish, while tail flexibility controls how strongly the fish feels the fluctuating forces,” Ma said.

In real environments, these types of interactions can occur downstream of bridges, rocks, or anything else that causes the water flow to separate, and tapping into them can help in developing energy-efficient underwater propulsion methods.

“A wake is not necessarily just a disturbance to overcome — it can also be an energy source,” Ma said.

Source: “Passive fish-like body dynamics in bluff-body wakes,” by Muhammad Umer Khan Mughal and Leixin Ma, Physics of Fluids (2026). The article can be accessed at https://doi.org/10.1063/5.0344906 .