Ghorai S, Hill N A
Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India.
J Theor Biol. 2002 Nov 21;219(2):137-52. doi: 10.1006/jtbi.2002.3077.
In three-dimensional bioconvection, the regions of rising and sinking fluid are dissimilar. This geometrical effect is studied for axisymmetric bioconvection in a cylindrical cell with stress-free (i.e. normal velocity and tangential stress vanish) lateral and top boundaries, and rigid bottom boundary. Using the continuum model of Pedley et al. (1988, J. Fluid Mech.195, 223-237) for bioconvection in a suspension of swimming, gyrotactic microorganisms, the structure and stability of an axisymmetric plume in a deep chamber are investigated. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a microorganism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. Comparisons are made with two-dimensional bioconvection.
在三维生物对流中，流体上升和下沉的区域并不相同。针对具有无应力（即法向速度和切向应力消失）的侧向和顶部边界以及刚性底部边界的圆柱形细胞中的轴对称生物对流，研究了这种几何效应。利用佩德利等人（1988年，《流体力学杂志》195卷，223 - 237页）提出的用于游动、趋旋微生物悬浮液中生物对流的连续介质模型，研究了深腔中轴对称羽流的结构和稳定性。该系统由不可压缩流体的纳维 - 斯托克斯方程与微生物守恒方程耦合控制。这些方程使用守恒有限差分格式进行数值求解。并与二维生物对流进行了比较。
