Development and stability of gyrotactic plumes in bioconvection

Journal of Fluid Mechanics

Volumn 400, Issue , 1999, Pages 1-31

  Ghorai, S ^a   Hill, N A ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002935764     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099006473     Document Type: Article

References (30)

1. BAI, R., CHEN, K. & JOSEPH, D. D. 1992 Lubricated pipelining: stability of core annular flow. Part 5. Experiments and comparison with theory. J. Fluid Mech. 240, 97-132.
2. BATCHELOR, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545-570.
3. BEES, M. A. & HILL, N. A. 1997 Wavelengths of bioconvection patterns. J. Expl Biol. 200, 1515-1526.
4. BEES, M. A. & HILL, N. A. 1998 Linear bioconvection in a suspension of randomly swimming, gyrotactic micro-organisms. Phys. Fluids A 10, 1864-1881.
5. BEES, M. A. & HILL, N. A. 1999 Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms. J. Math. Biol. 38, 135-168.
6. BEES, M. A., HILL, N. A. & PEDLEY, T. J. 1998 Analytical approximations for the orientation distributions of small dipolar particles in steady shear flows. J. Math. Biol. 36, 269-298.
7. CASH, J. R. & MOORE, D. R. 1980 A high order method for the numerical solution of two point boundary value problems. BIT 20, 44-52.
8. CHILDRESS, S., LEVANDOWSKY, M. & SPIEGEL, E. A. 1975 Pattern formation in a suspension of swimming micro-organisms: equations and stability theory modes. J. Fluid Mech. 69, 595-613.
9. GHORAI, S. 1997 Bioconvection and plumes. PhD thesis, University of Leeds.
10. HARASHIMA, A., WATANABE, M. & FUJISHIRO, I. 1988 Evolution of bioconvection patterns in a culture of motile flagellates. Phys. Fluids 31, 764-775.
11. HILL, N. A. & HÄDER, D. P. 1997 A biased random random walk model for the trajectories of swimming micro-organisms. J. Theor. Biol. 186, 503-526.
12. HILL, N. A., PEDLEY, T. J. & KESSLER, J. O. 1989 Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth. J. Fluid Mech. 208, 509-543.
13. KÁLNAY DE RIVAS, P. 1972 On the use of nonuniform grids in finite-difference equations. J. Comput. Phys. 10, 202-210.
14. KESSLER, J. O. 1985a Hydrodynamic focusing of motile algal cells. Nature 313, 218-220.
15. KESSLER, J. O. 1985b Co-operative and concentrative phenomena of swimming micro-organisms. Contemp. Phys. 26, 147-166.
16. KESSLER, J. O. 1986 Individual and collective fluid dynamics of swimming cells. J. Fluid Mech. 173, 191-205.
17. LENNIE, T. B., MCKENZIE, D. P., MOORE, D. R. & WEISS, N. O. 1988 The breakdown of steady convection. J. Fluid Mech. 188, 47-85.
18. LISTER, J. R. 1987 Long wavelength instability of a line plume. J. Fluid Mech. 175, 413-428.
19. PEDLEY, T. J. 1988 Bottom-standing plumes in gyrotactic bioconvection. Bull. Am. Phys. Soc. 33, 2282 (Abstr.).
20. PEDLEY, T. J., HILL, N. A. & KESSLER, J. O. 1988 The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms. J. Fluid Mech. 195, 223-338.
21. PEDLEY, T. J. & KESSLER, J. O. 1987 The orientation of spheroidal micro-organisms swimming in a flow field. Proc. R. Soc. Land. B 231, 47-70.
22. PEDLEY, T. J. & KESSLER, J. O. 1990 A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155-182.
23. PEDLEY, T. J. & KESSLER, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming micro-organisms. Ann. Rev. Fluid Mech. 24, 313-358.
24. PLATT, J. R. 1961 'Bioconvection patterns' in cultures of free-swimming organisms. Science 133, 1766-1767.
25. PLESSET, M. S. & WINET, H. 1974 Bioconvection patterns in swimming micro-organism cultures as an example of Rayleigh-Taylor instability. Nature 248, 441-443.
26. ROBERTS, G. O. 1970 Computational meshes for boundary layer problems. In Second Intl Conf. on Numerical Methods in Fluid Dynamics (ed. M. Holt). Lecture Notes in Physics, vol. 8, pp. 171-177. Springer.
27. SMITH, M. K. 1989 The axisymmetric long-wave instability of a concentric two-phase pipe flow. Phys. Fluids. A 1, 494-506.
28. TIMM, U. & OKUBO, A. 1994 Gyrotaxis: A plume model for self-focusing micro-organisms. Bull. Math. Biol. 56, 187-206.
29. VAHL DAVIS, G. DE 1983 Natural-convection of air in a square cavity - a bench-mark numerical-solution, Intl J. Numer. Meth. Fluids 3, 249-264.
30. WAGER, H. 1911 On the effect of gravity upon the movements and aggregation of Euglena viridis, Ehrb., and other micro-organisms. Phil. Trans. R. Soc. Lond. B 201, 333-390.