Angilella J R
Nancy-Université, LAEGO, Rue du Doyen Roubault, 54501 Vandoeuvre-les-Nancy, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):066310. doi: 10.1103/PhysRevE.78.066310. Epub 2008 Dec 18.
Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment, and fold" mechanism is close to the so-called blinking vortex effect, which is responsible for chaotic transport of perfect tracers, except that in the present case the vortex motion is replaced by gravitational settling. In the present work this phenomenon is analyzed for heavy Stokes particles moving under the sole effect of gravity and of a linear drag. The vortex is taken to be a fixed isolated point vortex, the intensity of which varies under the effect of either boundary conditions or volume force. When the unsteadiness of the vortex is weak and the free-fall velocity is of the order of the fluid velocity, and the particle response time is small, the particle motion equation can be written asymptotically as a perturbed Hamiltonian system, the phase portrait of which displays a homoclinic trajectory. A homoclinic bifurcation is therefore likely to occur, and the contribution of particle inertia to the occurrence of this bifurcation is analyzed asymptotically by using Melnikov's method.
在重力足以在涡旋关闭或较弱时使颗粒云发生位移的情况下，强度随时间变化的固定水平涡旋附近的颗粒沉降可能是混沌的。这种“拉伸、沉降和折叠”机制与所谓的闪烁涡旋效应相近，闪烁涡旋效应是造成理想示踪剂混沌输运的原因，只是在当前情况下，涡旋运动被重力沉降所取代。在本研究中，针对仅在重力和线性阻力作用下运动的重斯托克斯颗粒分析了这一现象。涡旋被视为一个固定的孤立点涡旋，其强度在边界条件或体积力的作用下发生变化。当涡旋的非定常性较弱、自由落体速度与流体速度相当且颗粒响应时间较小时，颗粒运动方程可以渐近地写为一个受扰哈密顿系统，其相图显示出一条同宿轨道。因此很可能发生同宿分岔，并且通过使用梅尔尼科夫方法渐近地分析了颗粒惯性对该分岔发生的贡献。
