A unified phase-matching mechanism for bio-inspired propulsion and vortex-induced energy harvesting in Kármán streets

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.