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  • Letter
  • Open Access

Orientation dynamics of two-dimensional concavo-convex bodies

S. Ravichandran*

J. S. Wettlaufer†

  • Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm SE 10691, Sweden and Interdisciplinary Programme in Climate Studies, Indian Institute of Technology Bombay, Mumbai 400076, India

  • Departments of Earth & Planetary Sciences, Mathematics and Physics, Yale University, New Haven, Connecticut 06520, USA and Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm SE 10691, Sweden

  • *sravichandran@iitb.ac.in
  • †john.wettlaufer@su.se
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Phys. Rev. Fluids 8, L062301 – Published 2 June, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.L062301

Abstract

We study the orientation dynamics of two-dimensional concavo-convex solid bodies that are denser than the fluid through which they fall under gravity. We show that the orientation dynamics of the body, quantified in terms of the angle ϕ relative to the horizontal, undergoes a transcritical bifurcation at a Reynolds number Rec(1) and a subcritical pitchfork bifurcation at a Reynolds number Rec(2). For Re<Rec(1), the concave-downwards orientation of ϕ=0 is unstable and bodies overturn into the ϕ=π orientation. For Rec(1)<Re<Rec(2), the falling body has two stable equilibria at ϕ=0andϕ=π for steady descent. For Re>Rec(2), the concave-downwards orientation of ϕ=0 is again unstable and bodies that start concave-downwards exhibit overstable oscillations about the unstable fixed point, eventually tumbling into the stable ϕ=π orientation. The Rec(2)≈15 at which the subcritical pitchfork bifurcation occurs is distinct from the Re for the onset of vortex shedding, which causes the ϕ=π equilibrium to also become unstable, with bodies fluttering about ϕ=π. The complex orientation dynamics of irregularly shaped bodies evidenced here are relevant in a wide range of settings, from the tumbling of hydrometeors to the settling of mollusk shells.

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Information

Phys. Rev. Fluids 8, L062301– Published 2 June, 2023
  • Received 22 December 2022
  • Accepted 28 April 2023
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