Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T17:57:22.902Z Has data issue: false hasContentIssue false
  • English
  • Français

Scanning currents in Stokes flow and the efficient feeding of small organisms

Published online by Cambridge University Press:  21 April 2006

S. Childress ,
M. A. R. Koehl  and
M. Miksis
S. Childress
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
M. A. R. Koehl
Affiliation:
Department of Zoology, University of California, Berkeley, CA 94720, USA
M. Miksis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60201, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The feeding behaviour of many small, free-swimming organisms involves the creation of a scanning current by the coordinated movement of a group of appendages. In this paper, we study the generation of scanning currents in Stokes flow in a number of simple models, utilizing the movement of Stokeslets, spheres, or stalks to set up an average scanning drift in a suitable far-field formulation. Various mechanisms may then be classified by the rate of decay at infinity of the mean scanning current. In addition, optimal scanning can be investigated by minimizing the mean power-required to create a current of prescribed amplitude. The simple mechanisms for scanning described here provide a framework within which the appendage movements of small aquatic organisms can be analysed and the relative merits of scanning and swimming strategies can be investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 407 - 436
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303–310.Google Scholar
Blake, J. R. 1972 A model for the micro-structure of ciliated organisms. J. Fluid Mech. 55, 1–23.Google Scholar
Blake, J. R., Liron, N. & Aldis, G. K. 1982 Flow patterns around ciliated microorganisms and in ciliated ducts. J. Theoret. Biol. 98, 127–41.Google Scholar
Chia, F. S., Buckland-Nicks, J. & Young, C. M. 1981 Locomotion of marine invertebrate: A review. Can. J. Zool. 62, 1025–1222.Google Scholar
Chwang, Allen T. & Yao-Tsu Wu, T. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67, 787–815.Google Scholar
Conover, R. J. 1981 Nutritional strategies for feeding on small suspended particles. In Analysis of Marine Ecosystems (ed. J. R. Longhurst), pp. 363–395. Academic Press.
Cowles, T. J. & Strickler, J. R. 1983 Characterization of feeding activity patterns in the planktonic copepod. Centropages typicus Kroyer under various food conditions. Limnol. Oceanogr. 28, 106–115.Google Scholar
Emlet, R. B. & Strathman, R. R. 1985 Gravity, drag, and feeding currents of small zooplankton. Science 228, 1016–1017.Google Scholar
Fenchel, T. 1986 Protozoan filter feeding. In Progress in Protistology (in press).
Gavis, J. 1976 Munk and Riley revisited: Nutrient diffusion transport and rates of phytoplankton growth. J. Mar. Res. 34, 161–179.Google Scholar
Gerritsen, J. & Strickler, J. R. 1977 Encounter probabilities and community structure in zooplankton: a mathematical model. J. Fish. Res. Board Can. 34, 73–82.Google Scholar
Gill, C. W. & Crisp, D. J. 1985 Sensitivity of intact and antennule amputated copepods to water disturbance. Mar. Ecol. Prog. Ser. 21, 221–227.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Haury, L. & Weihs, D. 1976 Energetically efficient swimming behavior of negatively buoyant zooplankton. Limnol. Oceanogr. 21, 797–803.Google Scholar
Higdon, J. J. L. 1979a A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 90, 685–711.Google Scholar
Higdon, J. J. L. 1979b The generation of feeding currents by flagellar motions. J. Fluid Mech. 94, 305–330.Google Scholar
Higdon, J. J. L. 1979c The hydrodynamics of flagellar propulsion: helical waves. J. Fluid Mech. 94, 331–351.Google Scholar
Jahnke, E. & Emde, F. 1945 Tables of Functions. Dover.
Koehl, M. A. R. 1984 Mechanisms of particle capture by copepods at low Reynolds numbers: possible modes of selective feeding. In Trophic Dynamics within Aquatic Ecosystems (eds D. G. Meyers & J. R. Strickler), pp. 135–166. Westview Press.
Lighthill, M. J. 1975 Mathematical Biofluiddynamics. SIAM vol. 17, Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia.
Lochead, J. H. 1977 Unsolved problems of interest in the locomotion of crustacea. In Scale Effects in Animal Locomotion (ed. T. J. Pedley), pp. 257–268. Academic.
Lunec, J. 1975 Fluid flow induced by smooth flagella. In Swimming and Flying in Nature (ed. T. Y.-T. Wu, C. J. Brokaw & C. Brennen), vol. 1, pp. 143–159. Plenum.
Pironneau, O. & Katz, D. F. 1974 Optimal swimming of flagellated microorganisms. J. Fluid Mech. 66, 391–415.Google Scholar
Strickler, J. R. 1982 Calanoid copepod feeding currents, and the role of gravity. Science 218, 158–160.Google Scholar
Vidal, J. 1980 Physioecology of zooplankton. III. Effects of phytoplankton concentration, temperature, and body size on the metabolic rate of Calanus pacificus. Mar. Biol. 56, 195–202.Google Scholar
Zaret, R. E. 1980 The animal and its viscous environment. In Evolution and Ecology of Zooplankton Communities (ed. W. C. Kerfoot), pp. 3–9. University Press of New England.