Multiscale dynamics of inertial particles in turbulence with and without the effect of gravitational settling

We investigate the dynamics of inertial heavy particles in three-dimensional homogeneous isotropic turbulence, both with and without gravitational settling, by means of direct numerical simulation over a range of Stokes numbers (

) and at a Taylor-microscale Reynolds number

italic Re Subscript lamda Baseline equals 204 Re λ = 204 $ \textit{Re}_\lambda = 204$

. Utilising a modified Voronoi tessellation, we compute the divergence, curl and helicity of particle velocities to quantify particle cloud self-organisation, including clustering, as well as vortical and swirling motions within particle clouds. We perform a novel graph-based multiresolution analysis by applying a wavelet decomposition to the divergence and curl of the particle velocities, and thus assess the clustering dynamics across multiple scales. Scales at which cluster formation and destruction are most active can hence be identified. In addition, we quantify and analyse the impact of the Stokes numbers and gravity on the divergence, rotational and swirling motions of particle clouds. As quantified in the wavelet energy spectra, gravitational settling is shown to affect the scale distribution of divergence and curl. We observe that the dominant particle dynamics is shifted toward larger scales while amplitude decrease for large Stokes numbers. In the absence of gravity the activity becomes increasingly concentrated at smaller scales for large Stokes numbers, consistent with the emergence of caustics. These gravitational effects become more pronounced at higher Stokes numbers, where particle motion transitions from relatively erratic without gravity to more coherent swirling patterns with gravity, as also reflected by the helicity of the particle velocity, which indicates an increased alignment and anti-alignment between the particle velocity and the particle vorticity.