Hydrodynamic wake resonance as an underlying principle of efficient unsteady propulsion

TLDR

The study develops a wake resonance theory to explain the mechanics and energetics of unsteady self‑propulsion. A linear spatial stability analysis of wake velocity profiles from a flexible robotic elliptical fin is used to identify the hydrodynamic resonant frequency, and experimental data validate the resulting theory. Propulsive efficiency peaks when the fin’s flapping frequency matches the jet’s resonant frequency, multiple resonant modes produce multiple efficiency peaks, and the one‑dimensional analysis accurately predicts three‑dimensional propulsor performance, demonstrating broad applicability.

Abstract

Abstract A linear spatial stability analysis is performed on the velocity profiles measured in the wake of an actively flexible robotic elliptical fin to find the frequency of maximum spatial growth, that is, the hydrodynamic resonant frequency of the time-averaged jet. It is found that: (i) optima in propulsive efficiency occur when the driving frequency of a flapping fin matches the resonant frequency of the jet profile; (ii) there can be multiple wake resonant frequencies and modes corresponding to multiple peaks in efficiency; and (iii) some wake structures transition from one pattern to another when the wake instability mode transitions. A theoretical framework, termed wake resonance theory, is developed and utilized to explain the mechanics and energetics of unsteady self-propulsion. Experimental data are used to validate the theory. The analysis, although one-dimensional, captures the performance exhibited by a three-dimensional propulsor, showing the robustness and broad applicability of the technique.