Lagrangian Flow Skeletons Captured in the Wake of a Swimming Nematode C. elegans Using an Immersed Boundary Fluid-Structure Interaction Approach

In this paper, Lagrangian coherent structure (LCS) concept is applied to wake flows generated in the up/down-stream of a swimming nematode C. elegans in an intermediate Re number range, i.e., 250-1200. It materializes Lagrangian hidden structures depicting flow transport barriers. To pursue the goals, nematode swimming in a quiescent fluid flow environment is numerically simulated by a two-way fluid-structure interaction (FSI) approach with the aid of immersed boundary method (IBM). In this regard, incompressible Navier-Stokes equations, fully-coupled with Lagrangian deformation equations for the immersed body, are solved using IB2d code. For all simulations, nematode’s body is modeled with a parametrized spring-fiber built-in case available in the computational code. Reverse von-Kármán vortex street formation and vortex shedding characteristics are studied and discussed in details via LCS approach, including grid resolution, integration time and Reynolds number effects. Results unveil presence of different flow regions with distinct fluid particle fates in the swimming animal’s wake and formation of so-called ‘mushroom-shaped’ structures in attracting LCS identities.


Authors:



References:
[1] A. Taheri, Fluid Dynamics and Bio-Propulsion of Animal Swimming in Nature (Bionics). 1st ed., Tehran: Arshadan Publication, 20 Chapters, 692 pages, 2021.
[2] M.S.U. Khalid, J. Wang, I. Akhtare, H. Dong, M. Liu, A. Hemmati, “Why do anguilliform swimmers perform undulation with wavelengths shorter than their bodylengths?”, Physics of Fluids, vol.33, no.3, 031911, DOI:10.1063/5.0040473, 2021.
[3] A.P. Maertens, A. Gao and M.S. Triantafyllou, “Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers”, Journal of Fluid Mechanics, vol.813, pp.301-345, 2017.
[4] N. Li, H. Liu, Y. Su, “Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion”, PLoS ONE, vol.12, no.3, 2017.
[5] K.N. Lucas, N. Johnson,W.T. Beaulieu, E. Cathcart, G. Tirrell, S.P. Colin, B.J. Gemmell, J.O. Dabiri, and J.H. Costello, “Bending rules for animal propulsion”, Journal of Nature Communications, vol.5, no.3293, , pp.1-7, DOI: 10.1038/ncomms4293, 2014.
[6] A. Taheri, “Lagrangian coherent structure analysis of jellyfish swimming using immersed boundary FSI simulations”, Journal of Mechanical and Civil Engineering, vol.15, no.1, pp.69-74, 2018.
[7] J.G. Miles and N.A. Battista, “Naut your everyday jellyfish model: exploring how tentacles and oral arms impact locomotion”, Fluids, vol.4, no.169, doi:10.3390/fluids4030169, 2019.
[8] A. Taheri, “Hydrodynamic impacts of prominent longitudinal ridges on the ‘whale shark’ swimming”, Research in Zoology, 2020, vol.10, no.1, pp.18-30, 2020.
[9] K. Bang, J. Kim, S.I. Lee and H. Choi, “Hydrodynamic role of longitudinal dorsal ridges in a leatherback turtle swimming”, Scientific Reports, Nature Journal, vol.6, no. 34283, doi:10.1038/srep34283, 2016
[10] A. Taheri, “On the hydrodynamic effects of humpback whale’s ventral pleats”, American Journal of Fluid Dynamics, vol.8, no.2, pp.47-62, 2018.
[11] A. Taheri, “A meta-model for tubercle design of wing planforms inspired by humpback whale flippers”, International Journal of Aerospace and Mechanical Engineering, vol.12, no.3, pp.315-328, 2018.
[12] Photo from Bob Goldstein Lab, Department of Biology, University of North Carolina at Chapel Hill.
[13] B. Weischer and D.J F. Brown, An Introduction to Nematodes: General Nematology: Student's Textbook. Sofia: Pensoft Publication, 183 pages, 2000.
[14] R. Ghosh and S.W. Emmons, “Episodic swimming behavior in the nematode C. elegans”, Journal of Experimental Biology, vol.211, pp. 3703-3711, 2008.
[15] J. Sznitman, X. Shen, R. Sznitman and P.E. Arratia, “Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number”, Physics Of Fluids, vol.22, no.121901, 2010.
[16] K.T. Du Clos, J.O. Dabiri, John H. Costello, S.P. Colin, J.R. Morgan, S.M. Fogerson and B.J. Gemmell, “Thrust generation during steady swimming and acceleration from rest in anguilliform swimmers”, Journal of Experimental Biology, vol.222, jeb212464. doi: 10.1242 /jeb. 212464, 2019.
[17] J.S. Park, D. Kim, J.H. Shina and D.A. Weitz, “Efficient nematode swimming in a shear thinning colloidal suspension”, Soft Matter Journal -Royal Society of Chemistry, doi: 10.1039/c5sm01824b, 2015.
[18] E.D. Tytella, C.Y. Hsub, T.L. Williamsc, A.H. Cohena and L.J. Faucib, “Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming”, PNAS Journal, vol.107, no.46, pp.19832–19837, 2010.
[19] C. S. Peskin, “The immersed boundary method”, Acta Numerica Journal, vol.11, pp.479-517, 2002.
[20] I. Borazjani, ‘Numerical simulations of fluid-structure interaction problems in biological flows’, Ph.D. thesis, Department of Mechanical Engineering, University of Minnesota, 2008.
[21] N.A. Battista, A.J. Baird, L.A. Miller, “A mathematical model and MATLAB code for muscle-fluid-structure simulations”, Journal of Integrative and Comparative Biology, vol.55, no.5, pp.901-911, 2015.
[22] N.A. Battista, W.C. Strickland, and L.A. Miller, “IB2d: a Python and MATLAB implementation of the immersed boundary method”, Bioinspiration and Biomimicry Journal, vol.12, no.3, 036003, 2017.
[23] S.C. Shadden, J.O. Dabiri, and J.E. Marsden, Lagrangian analysis of fluid transport in empirical vortex ring flows, Journal of Physics of Fluid, vol.18, no.047105, pp.1-11, 2006.
[24] N.A. Battista, “Fluid-Structure Interaction for the Classroom: Interpolation, Hearts, and Swimming!”, SIAM Review, vol.63, no.1, pp. 181-207, 2021.
[25] N.A. Battista, “Swimming through parameter subspaces of a simple anguilliform swimmer”, Integrative and Comparative Biology, vol. 60, no. 5, pp. 1221–1235, 2020.
[26] N.A. Battista, “Diving into a Simple Anguilliform Swimmer’s Sensitivity”, Integrative and Comparative Biology, vol. 60, no. 5, pp. 1236–1250, 2020.
[27] U.E. Ogunka, M. Daghooghi, A.M. Akbarzadeh and I. Borazjani, “The ground effect in anguilliform swimming”, Biomimetics Journal, doi:10.3390/biomimetics5010009, 2020.
[28] S.K. Robinson, “Coherent motions in the turbulent boundary layer”, Journal of Fluid Mechanics, vol.23, pp.601-639, 1991.
[29] M.A. Green, C.W. Rowley and Haller G., “Detection of Lagrangian coherent structures in three-dimensional turbulence”, Journal of Fluid Mechanics, vol.572, pp.111-120, 2007.
[30] J.C.R. Hunt, A.A. Wraya and P. Moin, “Eddies, stream, and convergence zones in turbulent flows”, Center for Turbulent Research Report CTR-S88, pp.193-208, 1988.
[31] J. Jeong and F. Hussain, “On the identification of a vortex”, Journal of Fluid Mechanics, vol.285, pp.69-94, 1995.
[32] J. Peng, and J.O. Dabiri, Transport of inertial particles by Lagrangian coherent structures: application to predator-prey interaction in jellyfish feeding, Journal of Fluid Mechanics, vol.623, pp.75–84, 2009.
[33] VTK User’s Guide, Kitware: www.kitware.com.
[34] D. Lipinski, B. Cardwell and K. Mohseni, “A Lagrangian analysis of a two-dimensional airfoil with vortex shedding”, Journal of Physics A: Mathematical and Theoretical, vol.41, no.3444011, pp.1-22, 2008.
[35] J. Peng and J.O. Dabiri, “The upstream wake of swimming and flying animals and its correlation with propulsive efficiency”, Journal of Experimental Biology, vol.211, pp.2669-2677, 2008.
[36] S.P. Colin, J.H. Costello, L.J. Hansson, J. Titelman and J.O. Dabiri, "Stealth predation and the predatory success of the invasive Ctenophre Mnemiopsis leidyi”, PNAS Journal, doi: 10.1073/pnas.100 3170107, pp.1-5, 2010.