Computational analysis of fish-foil pairing and wake energy extraction in low-speed flow

The energetic consequences of swimming within a neighboring fish's vortex street remain a central question in collective locomotion. Recent flume experiments in which a flapping hydrofoil generated a biomimetic wake demonstrated that a trout can station-keep behind the foil while displaying kinematics markedly different from those used in uniform flow. To examine the underlying hydrodynamics, we accurately replicate the fish-foil system by first reproducing the experimentally recorded motions using a joint-based kinematic reconstruction method, and then we simulate the fluid dynamics with three-dimensional computational fluid dynamics. A companion simulation without the foil is also conducted to isolate wake effects. Relative to uniform-flow swimming, the presence of the foil wake reduces the trout's cycle-averaged hydrodynamic power expenditure by 11.4 ± 0.0003%, a benefit that arises because vortex columns shed by the foil create coherent negative-pressure corridors along the fish's lateral surface. Power reduction is realized when the trout's long-wavelength body wave remains phase-locked with the downstream advection of these vortex structures, enabling the fish to harvest pressure-induced thrust while minimizing added-mass losses. These findings provide a mechanistic explanation for wake exploitation in schooling fish, establish phase synchrony as a key control parameter for hydrodynamic benefit, and offer design guidelines for paired biomimetic underwater vehicles that seek to emulate schooling to improve propulsive efficiency.