Mechanisms of particle clustering in Gaussian and non-Gaussian synthetic turbulence

We use synthetic turbulence simulations to study how inertial particles cluster in a turbulent flow, for a wide range of Stokes numbers. Two different types of synthetic turbulence are used: one Gaussian, where the time evolution of the velocity field is a simple phase shift, and one non-Gaussian, where convection is used to evolve the velocity field in time. In both flow types we observe significant particle clustering over a wide range of scales and Stokes numbers. The clustering found at low Stokes numbers can be attributed to the vortex centrifuge effect, where heavy particles are expelled from regions dominated by vorticity. This mechanism is much more effective in the non-Gaussian turbulence, because local flow structures are convected with the particles. The preferential sampling of regions with low vorticity is almost negligible in the Gaussian turbulence. At higher Stokes numbers, caustics are formed in a very similar manner in both Gaussian and non-Gaussian synthetic turbulence. In non-Gaussian turbulence, heavy particles cluster in regions of low fluid kinetic energy, while the opposite is true in Gaussian turbulence. Our results show that synthetic simulations cannot correctly predict how the particle clustering correlates with local fluid flow properties, without including convection.

Figure 1

Probability density function of $\partial u/\partial x$ in Gaussian (solid line) and non-Gaussian (dashed line) turbulence. The symbols represent a Gaussian probability distribution.

Figure 2

Probability density function of $Q$ in Gaussian (solid line) and non-Gaussian (dashed line) turbulence.

Figure 3

Time spectrum $\psi \left(\omega \right)$ $\left({\int }_0^{\infty }\psi d\omega =\frac{1}{2}\mathbf{u}·\mathbf{u}\right)$ for Gaussian (solid line) and non-Gaussian (dashed line) synthetic turbulence, plotted as function of nondimensional frequency $\omega \lambda$.

Figure 4

Degree of particle clustering measured using $1000\varphi$ for (a) Gaussian synthetic turbulence and (b) non-Gaussian synthetic turbulence.

Figure 5

Probability density function of $Q$ in non-Gaussian synthetic turbulence sampled on the particle paths for fluid tracer particles (solid line), particles with $\mathrm{St}=0.067$ (dashed line) and particles with $\mathrm{St}=0.19$ (dotted line).

Figure 6

Skewness of PDF for $Q$ sampled on particle paths for Gaussian synthetic turbulence (solid line, circles) and non-Gaussian synthetic turbulence (dashed line, squares). The symbols mark the simulated values, and the lines are interpolants. Horizontal dotted lines mark the skewness of $Q$ for fluid tracers in Gaussian (lower line) and non-Gaussian (upper line) turbulence.

Figure 7

Lagrangian autocorrelation of $Q$ along particle trajectories for fluid tracers (sold line), particles with $\mathrm{St}=0.11$ (dashed line) and $\mathrm{St}=1.3$ (dotted line), in Gaussian (gray lines) and non-Gaussian (black lines) synthetic turbulence.

Figure 8

Lagrangian integral time scale for $Q$ along particle trajectories in Gaussian (solid line, circles) and non-Gaussian (dashed line, squares) synthetic turbulence. The horizontal (dotted) lines represent the integral time scales for fluid tracers in Gaussian (lower line) and non-Gaussian (upper line) turbulence.

Figure 9

Power-law exponent of first-order particle velocity structure function in the dissipative range, in Gaussian (solid line, circles) and non-Gaussian (dashed line, squares) synthetic turbulence.

Figure 10

Power-law exponent ${\xi }_p$ of particle velocity structure function in the dissipative range, for $p=1$ (solid line), $p=2$ (dashed line) and $p=3$ (dotted line) in non-Gaussian turbulence. Dash-dot line is $-0.5log\mathrm{St}$.

Figure 11

Average fluid kinetic energy sampled on the particle paths, for Gaussian (solid line, circles) and non-Gaussian (dashed line, squares) turbulence. The horizontal dotted line marks the kinetic energy sampled for fluid tracers.

Figure 12

Average velocity gradient $\langle \left|\Delta V\right|/r\rangle$ for $r<{10}^{-3}$ in Gaussian (solid line, circles) and non-Gaussian (dashed line, squares) synthetic turbulence.