Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA.
Bull Math Biol. 2011 Aug;73(8):1841-56. doi: 10.1007/s11538-010-9594-4. Epub 2010 Oct 26.
We study the dynamics of plankton in the wake of a jellyfish. Using an analytical approach, we derive a reduced-order equation that governs the prey motion which is modeled as neutrally-buoyant inertial particle. This modified equation takes into account both the effects of prey inertia and self-propulsion and enables us to calculate both the attracting and repelling Lagrangian coherent structures for the prey motion. For the case of zero self-propulsion, it is simplified to the equation of motion for infinitesimal fluid particles. Additionally, we determine the critical size of prey over which instabilities on its motion occur resulting in different dynamics from those predicted by the reduced-order equation even for the case of zero self-propulsion. We illustrate our theoretical findings through an experimentally measured velocity field of a jellyfish. Using the inertial equation, we calculate the Lagrangian coherent structures that characterize prey motion as well as the instability regions over which larger prey will have different dynamics even for the case of zero self-propulsion.
我们研究了水母尾流中浮游生物的动力学。使用解析方法，我们推导出一个控制猎物运动的降阶方程，将其建模为中性浮力惯性粒子。该修正方程考虑了猎物惯性和自推进的影响，使我们能够计算猎物运动的吸引和排斥拉格朗日相干结构。对于零自推进的情况，它简化为无穷小流体粒子的运动方程。此外，我们确定了猎物的临界尺寸，超过这个尺寸，猎物的运动就会出现不稳定性，导致与降阶方程预测的不同的动力学，即使在零自推进的情况下也是如此。我们通过水母的实验测量速度场来说明我们的理论发现。使用惯性方程，我们计算了拉格朗日相干结构，这些结构表征了猎物的运动以及不稳定性区域，在这些区域中，即使在零自推进的情况下，较大的猎物也会有不同的动力学。
