湍流流场中游动微生物的趋光聚集
Phototactic Clustering of Swimming Micro-organisms in a Turbulent Velocity Field
摘要：
我们研究了由一个模型湍流平流并通过趋光性被吸引到一个局部光源的游动微生物的分布。结果表明，粒子沿着一个具有分形测度的动力学吸引子聚集，该吸引子的维数取决于趋光性的强弱。使用一个有效的扩散近似的流量，我们推导出的趋光增益（增加曝光量的聚合）的解析表达式，并通过扩展的平流动力学和吸引场的统计特性的基础上的分形维数的准确预测。这表明，团聚体的分形特征是由游泳动能与湍流动能的无量纲比决定的。
英文摘要：
We study the distribution of swimming micro-organisms advected by a model turbulent flow and attracted towards a localised light source through phototaxis. It is shown that particles aggregate along a dynamical attractor with fractal measure whose dimension depends on the strength of the phototaxis. Using an effective diffusion approximation for the flow we derive an analytic expression for the phototactic gain (increase in light exposure over the aggregate) and by extension an accurate prediction for the fractal dimension based on the properties of the advection dynamics and the statistics of the attracting field. This shows that the fractal characteristics of the aggregate are determined by the non-dimensional ratio of the kinetic energy of swimming to that of the turbulent flow.
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