Enhancement of coalescence due to droplet inertia in turbulent clouds

In the EMPM (Explicit Mixing Parcel Model), turbulent advection of fluid is implemented by rearranging the fluid cells in a segment of the 1D domain. Each permutation represents an individual turbulent eddy, and is called a ``triplet map.'' This implementation of the triplet map captures flow processes as small as the smallest turbulent eddy (Kolmogorov microscale), but the response of small droplets to turbulence has important features at scales as small as the droplet radius. Namely, droplet motion relative to the fluid at scales less than the Kolmogorov microscale induces droplet clustering that is estimated to increase droplet collision rates significantly. We have developed (Kerstein and Krueger 2006), implemented, and tested a 3D triplet map for droplets that captures this clustering effect at small particle Stokes numbers (such as those of cloud droplets). We have also implemented a collision detection algorithm so that we can simulate collisions and coalescence between finite-inertia particles. There is excellent agreement between our results (for radial distribution functions and collision kernels) at small particle Stokes numbers and DNS (direct numerical simulation) results obtained by Reade and Collins (2000) (without gravity) and good agreement with the results obtained by Franklin et al. (2005) and Ayala et al. (2008a,b) (both with gravity). We are currently testing an extension of our model that is intended to be applicable for all particle Stokes numbers.