Skip to main content Accessibility help

Local flow characterization using bioinspired sensory information

  • Brendan Colvert (a1), Kevin Chen (a1) and Eva Kanso (a1)


Most marine creatures exhibit remarkable flow sensing abilities. Their task of discerning hydrodynamic cues from local sensory information is particularly challenging because it relies on local and partial measurements to accurately characterize the ambient flow. This is in contrast to classical flow characterization methods, which invariably depend on the ability of an external observer to reconstruct the flow field globally and identify its topological structures. In this paper, we develop a mathematical framework in which a local sensory array is used to identify select flow features. Our approach consists of linearizing the flow field around the sensory array and providing a frame-independent parameterization of the velocity gradient tensor which reveals both the local flow ‘type’ and ‘intensity’. We show that a simple bioinspired sensory system that measures differences in flow velocities is capable of locally characterizing the flow type and intensity. We discuss the conditions under which such flow characterization is possible. Then, to demonstrate the effectiveness of this sensory system, we apply it in the canonical problem of a circular cylinder in uniform flow. We find excellent agreement between the sensed and actual flow properties. These findings will serve to direct future research on optimal sensory layouts and dynamic deployment of sensory arrays.


Corresponding author

Email address for correspondence:


Hide All
Boxshall, G. A., Yen, J. & Strickler, R. J. 1997 Functional significance of the sexual dimorphism in the cephalic appendages of Euchaeta rimana Bradford. Bull. Mar. Sci. 61, 387398.
Candes, E. J. 2008 The restricted isometry property and its implications for compressed sensing. C. R. Mathematique 346 (9), 589592.
Chen, K. K., Tu, J. H. & Rowley, C. W. 2012 Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses. J. Nonlinear Sci. 22, 887915.
Colvert, B. & Kanso, E. 2016 Fishlike rheotaxis. J. Fluid Mech. 793, 656666.
Coombs, S. & Van Netten, S. 2005 The hydrodynamics and structural mechanics of the lateral line system. Fish Biomechanics, Fish Physiology. vol. 23, pp. 103139. Academic.
Dehnhardt, G., Mauck, B., Hanke, W. & Bleckmann, H. 2001 Hydrodynamic trail-following in harbor seals (Phoca vitulina). Science 293, 102104.
Engelmann, J., Hanke, W., Mogdans, J. & Bleckmann, H. 2000 Neurobiology: hydrodynamic stimuli and the fish lateral line. Nature 408 (6808), 5152.
Fernandez, V. I. 2011 Performance analysis for lateral-line-inspired sensor arrays. PhD thesis, Massachusetts Institute of Technology.
Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A. & Koumoutsakos, P. 2016 Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789, 726749.
Golub, G. H. & Van Loan, C. F. 1996 Matrix Computations, 3rd edn. Johns Hopkins University Press.
Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 126.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of the Summer Program 1988, pp. 193208. Center for Turbulence Research.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Kroese, A. B. & Schellart, N. A. 1992 Velocity- and acceleration-sensitive units in the trunk lateral line of the trout. J. Neurophys. 68 (6), 22122221.
Lagnado, R. R. 1985 The stability of two-dimensional linear flows. PhD thesis, California Institute of Technology.
Marrucci, G. & Astarita, G. 1967 Linear, steady, two-dimensional flows of viscoelastic liquids. AIChE J. 13, 931935.
Montgomery, J. C., Baker, C. F. & Carton, A. G. 1997 The lateral line can mediate rheotaxis in fish. Nature 389 (6654), 960963.
Ristroph, L., Liao, J. C. & Zhang, J. 2015 Lateral line layout correlates with the differential hydrodynamic pressure on swimming fish. Phys. Rev. Lett. 114, 018102.
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411423.
Venturelli, R., Akanyeti, O., Visentin, F., Ježov, J., Chambers, L. D., Toming, G., Brown, J., Kruusmaa, M., Megill, W. M. & Fiorini, P. 2012 Hydrodynamic pressure sensing with an artificial lateral line in steady and unsteady flows. Bioinspir. Biomim. 7, 036004.
Vergassola, M., Villermaux, E. & Shraiman, B. I. 2007 ‘Infotaxis’ as a strategy for searching without gradients. Nature 445 (7126), 406409.
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355381.
Yen, J. & Nicoll, N. T. 1990 Setal array on the first antennae of a carnivorous marine copepod, Euchaeta norvegica. J. Crustac. Biol. 10, 218224.
Yen, J. & Strickler, J. R. 1996 Advertisement and concealment in the plankton: What makes a copepod hydrodynamically conspicuous? Invertebrate Biology 115 (3), 191205.
Yen, J., Weissburg, M. J. & Doall, M. H. 1998 The fluid physics of signal perception by mate-tracking copepods. Phil. Trans. R. Soc. Lond. B 353, 787804.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed