Traveling waves in a continuum model of 1D schools

ORAL

Abstract

We construct and analyze a continuum model of a 1D school of flapping swimmers. Our starting point is a delay differential equation that models the interaction between a swimmer and its upstream neighbors’ wakes, which is motivated by recent experiments in the Applied Math Lab at NYU. We coarse-grain the evolution equations and derive PDEs for the swimmer density and variables describing the upstream wake. We study the equations both analytically and numerically, and find that a uniform density of swimmers destabilizes into a traveling wave. Our model makes a number of predictions about the properties of such traveling waves, and sheds light on the role of hydrodynamics in mediating the structure of swimming schools.

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Authors

  • Anand Oza

    • Courant Institute

  • Eva Kanso

    • University of Southern California
    • Univ of Southern California
    • Aerospace \& Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1191
    • University of Southern California; Center for Computational Biology, Simons Foundation
    • Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles
    • USC, Los Angeles, CA

  • Michael Shelley

    • New York University
    • Applied Mathematics Laboratory, Courant Institute, New York University
    • Courant Institute and Flatiron Institute
    • Courant Institute, NYU; Flatiron Institute, NYC