Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers

Wim M. Van Rees, Mattia Gazzola, Petros Koumoutsakos

Research output: Contribution to journalArticlepeer-review


Undulatory locomotion is an archetypal mode of propulsion for natural swimmers across scales. Undulatory swimmers convert transverse body oscillations into forward velocity by a complex interplay between their flexural movements, morphological features and the fluid environment. Natural evolution has produced a wide range of morphokinematic examples of undulatory swimmers that often serve as inspiration for engineering devices. It is, however, unknown to what extent natural swimmers are optimized for hydrodynamic performance. In this work, we reverse-engineer the morphology and gait for fast and efficient swimmers by coupling an evolution strategy to three-dimensional direct numerical simulations of flows at intermediate Reynolds numbers. The fastest swimmer is slender with a narrow tail fin and performs a sequence of C-starts to maximize its average velocity. The most efficient swimmer combines moderate transverse movements with a voluminous head, tapering into a streamlined profile via a pronounced inflection point. These optimal solutions outperform anguilliform swimming zebrafish in both efficiency and speed. We investigate the transition between morphokinematic solutions in the speed-energy space, laying the foundations for the design of high-performance artificial swimming devices.

Original languageEnglish (US)
Pages (from-to)178-188
Number of pages11
JournalJournal of Fluid Mechanics
StatePublished - Jun 19 2015
Externally publishedYes


  • biological fluid dynamics
  • propulsion
  • swimming/flying

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers'. Together they form a unique fingerprint.

Cite this