Topology of Reverse Von-Kármán Vortex Street in the Wake of a Swimming Whale Shark
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32918
Topology of Reverse Von-Kármán Vortex Street in the Wake of a Swimming Whale Shark

Authors: Arash Taheri

Abstract:

In this paper, effects of the ventral body planform of a swimming whale shark on the formation of ‘reverse von-Kármán vortex street’ behind the aquatic animal are studied using Fluid-Structure Interaction (FSI) approach. In this regard, incompressible Navier-Stokes equations around the whale shark’s body with a prescribed deflection dynamics are solved with the aid of Boundary Data Immersion Method (BDIM) and Implicit Large Eddy Simulation (ILES) turbulence treatment by WaterLily.jl solver; fully-written in Julia programming language. The whale shark flow simulations here are performed at high Reynolds number, i.e. 1.4 107 corresponding to the swimming of a 10 meter-whale shark at an average speed of 5 km/h. For comparison purposes, vortical flow generation behind a silky shark with a streamlined forehead eidonomy is also simulated at high Reynolds number, Re = 2 106, corresponding to the swimming of a 2 meter-silky shark at an average speed of 3.6 km/h. The results depict formation of distinct wake topologies behind the swimming sharks depending on the travelling wave oscillating amplitudes.

Keywords: Whale shark, vortex street, BDIM, FSI, functional eidonomy, bionics.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1101

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] 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.
[3] I. Borazjani, “Numerical simulations of fluid-structure interaction problems in biological flows”, Ph.D. thesis, Department of Mechanical Engineering, University of Minnesota, 2008.
[4] M.S.U. Khalid, J. Wang, I. Akhtare, H. Dong, M. Liu and 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.
[5] 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.
[6] N. Li, H. Liu and Y. Su, “Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion”, PLoS ONE, vol.12, no.3, 2017.
[7] 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.
[8] 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.
[9] A. Taheri, “On the hydrodynamic effects of the eidonomy of the hammerhead shark’s cephalofoil in the eye bulb region: Winglet-like behaviour”, International Journal of Marine Science and Technology Bulletin, vol. 11, no.1, pp.41-51, 2022.
[10] 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.
[11] A. Taheri, “Hydrodynamic analysis of bionic chimerical wing planforms inspired by manta ray eidonomy”, Indonesian Journal of Engineering and Science, vol.2, no.3, pp.11-28, 2021.
[12] 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.
[13] A. Battista, “Swimming through parameter subspaces of a simple anguilliform swimmer”, Integrative and Comparative Biology, vol.60, no.5, pp. 1221–1235, 2020.
[14] N.A. Battista, “Diving into a Simple Anguilliform Swimmer’s Sensitivity”, Integrative and Comparative Biology, vol.60, no.5, pp. 1236–1250, 2020.
[15] A. Taheri, “Lagrangian flow skeletons captured in the wake of a swimming nematode C. elegans using an immersed boundary fluid-structure interaction approach”, International Journal of Bioengineering and Life Sciences, vol.15, no.7, pp.71-78, 2021.
[16] 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.
[17] 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.
[18] N.A. Battista, A.J. Baird and 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,
[19] 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.
[20] N.A. Battista, “Fluid-Structure Interaction for the Classroom: Interpolation, Hearts, and Swimming!”, SIAM Review, vol.63, no.1, pp. 181-207, 2021.
[21] L. Copmpagno, M. Dando and S. Fowler, Sharks of the world. 1st ed., New Jersey: Princeton University Press, 368 pages, 2005.
[22] C.R. McClain, M.A. Balk, M.C. Benfield, T.A. Branch and C. Chen, “Sizing ocean giants: patterns of intraspecific size variation in marine megafauna”, PeerJ Journal, doi:10.7717/peerj.715, 2015.
[23] Photo from P. Xu, Georgia Aquarium- Atlanta, www.unsplash.com.
[24] C.S. Peskin, “The immersed boundary method”, Acta Numerica Journal, vol.11, pp.479-517, 2002.
[25] G.D. Weymouth and B. Font, “WaterLily.jl: A differentiable fluid simulator in Julia with fast heterogeneous execution”, 34th International Conference on Parallel Computational Fluid Dynamics, Cuenca, Ecuador, 29–31 May, 2023.
[26] G.D. Weymouth, “Simulation of a swimming dogfish shark”, presented at www.Julialang.org, August 2021.
[27] G.D. Weymouth and D.K.P. Yue, “Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems”, Journal of Computational Physics, vol.230, pp.6233-6247, 2011.
[28] A.P. Maertens and G.D. Weymouth, “Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers”, Computer Methods in Applied Mechanics and Engineering, vol.283, pp.106-129, 2015.
[29] M. Lauber, G.D. Weymouth, and G. Limbert, “Immersed boundary simulations of flows driven by moving thin membranes", Journal of Computational Physics, p.111076, 2022.
[30] G.D. Weymouth, “Data-driven multi-grid solver for accelerated pressure projection", Computers & Fluids, vol.246, p.105620, 2022.
[31] www.Julialang.org.
[32] S. Danisch and J. Krumbiegel, “Makie.jl: Flexible high-performance data visualization for Julia”, Journal of Open Source Software, vol.6, no.65, DOI:10.21105/joss.03349, 2021.
[33] D.A. Elbert, On board guide for the identification of pelagic sharks and rays of the western Indian Ocean, Illustrator: M. Dando, Food and Agriculture Organization of The United Nations, 2014.
[34] J. Lighthill, “Note on the swimming of slender fish”, Journal of Fluid Mechanics, vol.9, no.2, pp.305 – 317, 1960.
[35] M. Gazzola, M. Argentina and L. Mahadevan, “Scaling macroscopic aquatic locomotion”, Nature Physics, vol.10, pp.758-761, 2014.