Turbulent enhancement of droplet collision rates at cloud Reynolds numbers

For water droplets of radii 10 to 40 micron in air turbulence with $\mathrm{Re}_{\lambda} \sim 10^4$ and $\epsilon \sim 10 \text{ to } 1000\ \mathrm{cm}^2/\mathrm{s}^3$, including gravity, hydrodynamic interactions and non-continuum lubrication, compute the collision kernel and its enhancement over gravitational collection. DNS with resolved Kolmogorov scales reach $\mathrm{Re}_{\lambda}$ of only a few hundred to about $10^3$, so the $\mathrm{Re}_{\lambda}$ dependence must be established.

DNS or laboratory measurements over at least a decade in $\mathrm{Re}_{\lambda}$ establishing the scaling of the kernel, extrapolated with a validated theory to $\mathrm{Re}_{\lambda} \sim 10^{4}$.