Hydrodynamic optimality of balistiform and gymnotiform locomotion

Authors

  • Brennan Sprinkle Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, USA
  • Rahul Bale Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA
  • Amneet Pal Singh Bhalla Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA
  • Malcolm A. MacIver Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA, Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA and Department of Neurobiology, Northwestern University, Evanston, IL, USA
  • Neelesh A. Patankar Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, USA and Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA

Keywords:

Hydrodynamic optimality, gymnotiform, balistiform, knifefish

Abstract

Some groups of fish have evolved to generate propulsion using undulatory elongated fins while maintaining a relatively rigid body. The fins run along the body axis and can be dorsal, ventral, dorsoventral pairs or left-right pairs. These fish are termed as median/paired fin (MPF) swimmers. The movement of these groups of fish was studied in an influential series of papers by Lighthill and Blake. In this work, we revisit this problem by performing direct numerical simulations. We interrogate two issues. First, we investigate and explain a key morphological feature, which is the diagonal fin insertion found in many MPF swimmers such as the knifefish. Not only are these results of biological relevance, but these are also useful in engineering to design bioinspired highly maneuverable underwater vehicles. Second, we investigate whether there is a mechanical advantage in the form of reduced cost of transport (COT) (energy spent per unit distance traveled) for not undulating the entire body.We find that a rigid body attached to an undulating fin leads to a reduced COT.

Downloads

Download data is not yet available.

References

Albert, J. S., & Crampton, W. G. R. (2005). Diversity and phylogeny of Neotropical electric

fishes (Gymnotiformes), Chapter 13, In T. H. Bullock, C. D. Hopkins, A. N. Popper, & R. R.

Fay, (Eds.), Electroreception (pp. 360–409).New York,NY: Springer Handbook of Auditory

Research.

Bale, R., Bhalla, A. P. S., Neveln, I. D., MacIver, M. A., & Patankar, N. A. (2015). Convergent

evolution of mechanically optimal locomotion in aquatic invertebrates and vertebrates.

PLOS Biology, 13, e1002123.

Bale, R., Shirgaonkar, A. A., Neveln, I. D., Bhalla, A. P. S., MacIver, M. A., & Patankar, N.

A. (2014). Separability of drag and thrust in undulatory animals and machines. Scientific

Reports, 4, 7329.

Bhalla, A. P. S., Bale, R., Griffith, B. E., & Patankar, N. A. (2013, October). A unified

mathematical framework and an adaptive numericalmethod for fluid-structure interaction

with rigid, deforming, and elastic bodies. Journal of Computational Physics, 250, 446–476.

Blake, R. W. (1983). Swimming in the electric eels and knifefishes. Canadian Journal of

Zoology, 61, 1432–1441.

Breder, C. M. (1926). The locomotion of fishes. Zoologica (N. Y.), 4, 159–297.

Crampton, W. G. R., & Albert, J. S. (2006). Evolution of electric signal diversity in

gymnotiform fishes. Communication in Fishes, 2, 647–731.

Jagnandan, K., & Sanford, C. P. (2013). Kinematics of ribbon-fin locomotion in the bowfin,

Amia calva. Journal of Experimental Zoology Part A: Ecological Genetics and Physiology,

, 569–583.

Lighthill, J. (1971, November). Large-amplitude elongated-body theory of fish locomotion.

Proceedings of the Royal Society of London. Series B, Biological Sciences, 179, 125–138.

Lighthill, J. (1990a). Biofluiddynamics of balistiform and gymnotiform locomotion. Part

The pressure distribution arising in two-dimensional irrotational flow from a general

symmetrical. Journal of Fluid Mechanics, 213, 1–10.

Lighthill, J. (1990b). Biofluiddynamics of balistiform and gymnotiform locomotion. Part 3.

Momentum enhancement in the presence of a body of elliptic cross-section. Journal of Fluid

Mechanics, 213, 11–20.

Lighthill, J. (1990c). Biofluiddynamics of balistiform and gymnotiform locomotion. Part 4.

Short-wavelength limitations on momentum enhancement. Journal of Fluid Mechanics,

, 21–28.

Lighthill, J., & Blake, R. W. (1990). Biofluiddynamics of balistiform and gymnotiform

locomotion. Part 1. Biological background, and analysis by elongated-body theory. Journal

of Fluid Mechanics, 212, 183–207.

Loofbourrow, H. (2009). Hydrodynamics of balistiform swimming in the picasso triggerfish,

rhinecanthus aculeatus (Master’s thesis). Vancouver: University of British Columbia.

MacIver, M. A., Fontaine, E., & Burdick, J.W. (2004). Designing future underwater vehicles:

Principles and mechanisms of the weakly electric fish. IEEE Journal of Oceanic Engineering,

, 651–659.

Neveln, I. D., Bale, R., Bhalla, A. P., Curet, O. M., Patankar, N. A., & Maciver, M. A.

(2014, January). Undulating fins produce off-axis thrust and flow structures. The Journal of

Experimental Biology, 217, 201–213.

Ruiz-Torres,R.,Curet,O.M.,Lauder,G.V.,&MacIver,M.A. (2012). Kinematics of the ribbon

fin in hovering and swimming of the electric ghost knifefish. The Journal of Experimental

Biology, 216, 823–834.

Sfakiotakis, M., Lane, D. M., & Davies, J. B. C. (1999). Review of fish swimming modes for

aquatic locomotion. The IEEE Journal of Oceanic Engineering, 24, 237–252.

Shirgaonkar, A. A., Curet, O. M., Patankar, N. A., & MacIver, M. A. (2008). The

hydrodynamics of ribbon-fin propulsion during impulsive motion. The Journal of

Experimental Biology, 211, 3490–3503.

Zhu, Q., Wolfgang, M. J., Yue, D. K. P., & Triantafyllou, M. S. (2002). Three-dimensional

flow structures and vorticity control in fish-like swimming. Journal of Fluid Mechanics,

, 1–28.

Downloads

Published

2019-01-14

How to Cite

Sprinkle, B., Bale, R., Bhalla, A. P. S., MacIver, M. A., & Patankar, N. A. (2019). Hydrodynamic optimality of balistiform and gymnotiform locomotion. European Journal of Computational Mechanics, 26(1-2), 31–43. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/296

Issue

Section

Original Article