Fish swimming in unsteady environments can exploit the Kármán vortex streets generated by upstream obstacles to reduce energetic cost or enhance propulsion, offering inspiration for bio-inspired marine energy harvesting. Using a two-dimensional numerical model, this study systematically examines how the intrinsic body-phase parameter α and the external phase difference φ jointly regulate vortex–body interactions. The resulting α–φ performance maps reveal two distinct operational regimes governed by phase matching. When φ = 0, upward body motion aligns favorably with low-pressure vortex cores, enabling substantial negative work uptake and markedly reduced lateral power expenditure; within this ‘energy-harvesting gait,’ α = π/6 maintains positive thrust, whereas a phase-delayed configuration (α = 7π/6) recovers energy but fails to generate net propulsion. When φ = 2π/3, vortex-body coupling reinforces tail pressure differentials and enlarges the effective propulsive area, defining a ‘performance-enhancing gait’ in which α = 2π/3 produces the strongest thrust and α = 7π/6 achieves the highest quasi-Froude efficiency. These findings identify phase matching as the central mechanism enabling organisms – or engineered systems – to transition between energy-harvesting and thrust-enhancing modes. The results provide a mechanistic basis and quantitative parameter framework for designing bio-inspired underwater vehicles and flexible marine harvesters capable of sensing vortex rhythms and autonomously extracting renewable hydrodynamic energy.
Ren et al. (2026) studied this question.