Sedimenting array of ellipsoids: transient growth and nonlinear behaviour*

An array of ellipsoids sedimenting in a viscous fluid can avoid the well-known Crowley clumping instability of spheres and fall in a wave that couples orientational and translation degrees of freedom.  In previous work [cite Chajwa2020] we established, by experiment, theory and simulation, the space of perturbation wave number and lattice spacing that separate this regime of linearly stable waves from the Crowley instability. We also showed that the non-normal character of the dynamical matrix leads to algebraic growth of perturbations ultimately destabilizing even the linearly stable waves.  In this work, we explore the late-time behaviour in both regimes largely by simulations, with some illustrative experiments. We seek to understand whether clumps generically form regardless of the mechanism that first destabilizes the array, and if so, what statistical measures distinguish structures that grow through the (hitherto unexplored) nonlinear regime of the Crowley instability, and structures that develop from algebraic non-modal growth.

[Chajwa2020] Chajwa, R., Menon, N., Ramaswamy, S. and Govindarajan, R., 2020. Waves, algebraic growth, and clumping in sedimenting disk arrays. Physical Review X, 10(4), p.041016.