Particle size effects on Lagrangian turbulence

Abstract

Perturbation methods are used to show that the equations of motion for a small rigid sphere in a steady laminar flow take the form of a dynamical system in which phase volume is not conserved. In the absence of stagnation points, particle inertia and virtual mass effects destroy Lagrangian turbulence and the particles are captured by periodic or quasiperiodic orbits that are associated with the vortices of the flow. When gravitational effects are included, it is found that point particles can sediment chaotically, but that particle inertia and virtual mass effects tend to eliminate the chaotic behavior. An interesting consequence of the latter phenomenon is that finite particles which are denser than the fluid can be permanently suspended in three-dimensional cellular flows. Numerical results are presented for the Arnold–Beltrami–Childress [C. R. Acad. Sci. Paris 261, 17 (1965)] flows.