Invariant manifold approach for quantifying the dynamics of highly inertial particles in steady and time-periodic incompressible flows

The dynamics of finite-sized particles with large inertia are investigated in steady and time-dependent flows through the numerical solution of the invariance equation, describing the spatiotemporal evolution of the slow/inertial manifold representing the effective particle velocity field. This approach allows for an accurate reconstruction of the effective particle divergence field, controlling clustering/dispersion features of particles with large inertia for which a perturbative approach is either inaccurate or not even convergent. The effect of inertia on heavy and light particles is quantified in terms of the rate of contraction/expansion of volume elements along a particle trajectory and of the maximum Lyapunov exponent for systems exhibiting chaotic orbits, such as the time-periodic sine-flow on the 2D torus and the time-dependent 2D cavity flow.

Automated summary

The dynamics of finite-sized particles with large inertia in steady and time-dependent flows are investigated using numerical methods. The effectiveness of perturbative methods for particles with large inertia is examined and accurate reconstructions of the particle divergence field are performed. The effect of inertia on heavy and light particles is quantified in terms of contraction/expansion rates of volume elements along particle trajectories and the maximum Lyapunov exponent for chaotic systems.