Hydrodynamic model of fish orientation in a channel flow

  1. Maurizio Porfiri  Is a corresponding author
  2. Peng Zhang
  3. Sean D Peterson  Is a corresponding author
  1. New York University, United States
  2. University of Waterloo, Canada


For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.

Data availability

The authors declare that the data supporting the findings of this study are available within the paper. The Mathematica notebook used to derive the governing equations, study the planar dynamical, and generate associated figures, together with the CFD data discussed in the text, are also available at https://github.com/dynamicalsystemslaboratory/Rheotaxis

Article and author information

Author details

  1. Maurizio Porfiri

    Department of Biomedical Engineering, New York University, Brooklyn, United States
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-1480-3539
  2. Peng Zhang

    Department of Mechanical and Aerospace Engineering, New York University, Brooklyn, United States
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8237-1259
  3. Sean D Peterson

    Mechanical and Mechatronics Engineering Department, University of Waterloo, Waterloo, Canada
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8746-2491


National Science Foundation (CMMI-1901697)

  • Maurizio Porfiri

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Agnese Seminara, University of Genoa, Italy

Publication history

  1. Received: November 3, 2021
  2. Accepted: May 31, 2022
  3. Accepted Manuscript published: June 6, 2022 (version 1)


© 2022, Porfiri et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. Maurizio Porfiri
  2. Peng Zhang
  3. Sean D Peterson
Hydrodynamic model of fish orientation in a channel flow
eLife 11:e75225.

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