Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms

被引:28
作者
Bees, MA [1 ]
Hill, NA [1 ]
机构
[1] Univ Leeds, Dept Appl Math, Leeds LS2 9JT, W Yorkshire, England
关键词
bioconvection patterns; swimming micro-organisms; gyrotaxis; travelling waves; Fokker-Planck equation; amplitude equation;
D O I
10.1007/s002850050144
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
The non-linear structure of deep, stochastic, gyrotactic bioconvection is explored. A linear analysis is reviewed and a weakly non-linear analysis justifies its application by revealing the supercritical nature of the bifurcation. An asymptotic expansion is used to derive systems of partial differential equations for long plume structures which vary slowly with depth. Steady state and travelling wave solutions are found for the first order system of partial differential equations and the second order system is manipulated to calculate the speed of vertically travelling pulses, Implications of the results and possibilities of experimental validation are discussed.
引用
收藏
页码:135 / 168
页数:34
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