Abstract
A transient, two-dimensional acoustic boundary element solver is developed using double-layer potentials accelerated by the fast multiple method for application to multibody, external field problems. The formulation is validated numerically against canonical radiation and scattering configurations of single and multiple bodies, and special attention is given to assessing model error. The acoustic framework is applied to model the vortex sound generation of schooling fish encountering 2S and 2P classes of vortex streets. Vortex streets of fixed identity are moved rectilinearly in a quiescent fluid past representative schools of two-dimensional fish, which are composed of four stationary NACA0012 airfoils arranged in a diamond pattern. The induced velocity on the fish-like bodies determines the time-dependent input boundary condition for the acoustic method to compute the sound observed in the acoustic far field. The resulting vortex noise is examined as a function of Strouhal number, where a maximum acoustic intensity is found for \(St \approx 0.2\), and an acoustic intensity plateau is observed for swimmers in the range of \(0.3< St < 0.4\). In the absence of background mean flow effects, numerical results further suggest that the value of Strouhal number can shift the acoustic directivity of an idealized school in a vortex wake to radiate noise in either upstream or downstream directions, which may have implications for the the study of predator-prey acoustic field interactions and the design of quiet bio-inspired underwater devices.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alvarez, A., Ye, Z.: Effects of fish school structures on acoustic scattering. ICES J. Mar. Sci. 56(3), 361–369 (1999)
Banjai, L., Sauter, S.: Rapid solution of the wave equation in unbounded domains. SIAM J. Numer. Anal. 7, 227–249 (2011)
Cottet, G.H., Koumoutsakos, P.D.: Vortex Methods: Theory and Practice. Cambridge University Press (2000)
Eloy, C.: Optimal strouhal number for swimming animals. J. Fluids Struct. 30, 205–218 (2012)
Fay, R.R.: Fish Bioacoustics. Springer (2009)
Feuillade, C., Nero, R., Love, R.: A low-frequency acoustic scattering model for small schools of fish. J. Acoust. Soc. Am. 99(1), 196–208 (1996)
Fish, F., Lauder, G.: Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193–224 (2006)
Gimbutas, Z., Greengard, L.: FMMLIB2D, FORTRAN libraries for fast multiple method in two dimensions (2012). http://www.cims.nyu.edu/cmcl/fmm3dlib/fmm3dlib.html
Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(2), 325–348 (1987)
Hassell, M., Sayas, F.J.: Convolution quadrature for wave simulations. In: Numerical Simulation in Physics and Engineering, pp. 71–159. Springer (2016)
Junger, M.C., Feit, D.: Sound, Structures, and Their Interaction, vol. 225. MIT press Cambridge, MA (1986)
Kirkup, S.M.: The Boundary Element Method in Acoustics. Integrated Sound Software (2007)
Ladich, F., Fine, M.L.: Sound-generating mechanisms in fishes: a unique diversity in vertebrates. Commun. Fishes 1, 3–43 (2006)
Lauder, G.V.: Fish locomotion: recent advances and new directions. Ann. Rev. Mar. Sci. 7, 521–545 (2015)
Leonard, A.: Vortex methods for flow simulation. J. Comput. Phys. 37(3), 289–335 (1980)
Liu, Y.: Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press (2009)
Lubich, C.: Convolution quadrature revisited. BIT Numer. Math. 44, 503–514 (2004)
Moored, K.W., Fish, F.E., Kemp, T.H., Bart-Smith, H.: Batoid fishes: inspiration for the next generation of underwater robots. Mar. Technol. Soc. J. 45(4), 99–109 (2011)
Partridge, B.L.: The structure and function of fish schools. Sci. Am. 246(6), 114–123 (1982)
Raveau, M.P., Feuillade, C.: Time domain investigations of acoustical scattering from schools of swim bladder fish. J. Acoust. Soc. Am. 135(4), 2177–2177 (2014)
Read, D.A., Hover, F., Triantafyllou, M.: Forces on oscillating foils for propulsion and maneuvering. J. Fluids Struct. 17(1), 163–183 (2003)
Rokhlin, V.: Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys. 86, 414–439 (1990)
Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)
Schnipper, T., Andersen, A., Bohr, T.: Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423 (2009)
Weihs, D.: Hydromechanics of fish schooling. Nature 241(5387), 290–291 (1973)
Acknowledgements
This work was supported by the Lehigh University CORE grant. The authors would like to thank Dr. Matthew Hassel for discussions on the convolution quadrature method.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Wagenhoffer, N., Moored, K.W., Jaworski, J.W. (2019). Accelerated Acoustic Boundary Element Method and the Noise Generation of an Idealized School of Fish. In: Ciappi, E., et al. Flinovia—Flow Induced Noise and Vibration Issues and Aspects-II. FLINOVIA 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-76780-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-76780-2_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76779-6
Online ISBN: 978-3-319-76780-2
eBook Packages: EngineeringEngineering (R0)