Ice crystals settling through a turbulent cloud are rotated by turbulent velocity gradients. In the same way, turbulence affects the orientation of aggregates of organic matter settling in the ocean. In fact most solid particles encountered in Nature are not spherical, and their orientation affects their settling speed, as well as collision rates between particles. Therefore it is important to understand the distribution of orientations of non-spherical particles settling in turbulence. Here we study the angular dynamics of small prolate spheroids settling in homogeneous isotropic turbulence. We consider a limit of the problem where the fluid torque due to convective inertia dominates, so that rods settle essentially horizontally. Turbulence causes the orientation of the settling particles to fluctuate, and we calculate their orientation distribution for prolate spheroids with arbitrary aspect ratios for large settling number Sv (a dimensionless measure of the settling speed), assuming small Stokes number St (a dimensionless measure of particle inertia). This overdamped theory predicts that the orientation distribution is very narrow at large Sv, with a variance proportional to Sv−4. By considering the role of particle inertia, we analyse the limitations of the overdamped theory, and determine its range of applicability. Our predictions are in excellent agreement with numerical simulations of simplified models of turbulent flows. We contrast our results with those of an alternative theory predicting that the orientation variance scales as Sv−2 at large Sv. Joint work with K. Gustavsson, M. Z. Sheikh, D. Lopez, A. Naso, E. Leveque, J. Jucha & A. Pumir.

References

K. Gustavsson, M. Z. Sheikh, D. Lopez, A. Naso, A. Pumir, B. Mehlig https://arxiv.org/abs/1904.00481

M. Z. Sheikh, K. Gustavsson, D. Lopez, B. Mehlig, A. Pumir, A. Naso https://arxiv.org/abs/1904.07575

K. Gustavsson, J. Jucha, A. Naso, E. Leveque, A. Pumir, B. Mehlig, Phys. Rev. Lett. 119, 254501 (2017)

Biography

Bernhard Mehlig, 瑞典哥德堡大学教授, 1994 年获得斯图加特大学物理学博士。2001-2002 年期间在哥德堡大学担任副教授，2002 年至今担任哥德堡大学教授。曾获得马普学会奥托-哈恩奖章（1995）、自然科学和医学研究基金会和瑞典皇家科学院的物理学中的“Gustafsson Priset”（2010）、哥德堡皇家艺术与科学院成员（2015）、哥德堡大学自然科学学术部物理学奖（2017）。Bernhard Mehlig 教授长期从事复杂系统的研究工作，在Advances in Physics, Phys. Rev. Lett, Journal of Fluid Mechanics, Journal of Mathematical Physics 等重要物理期刊上共发表文章100 余篇，内容涉及统计物理、生物物理和种群生物学等相关领域。