Turbulent dispersion analysis via distance-neighbor graphs inside a top cloud boundary in temporal decay

We expand on the original studies on atmospheric diffusion shown on a distance neighbour graph, Q, by Lewis F. Richardson (1926), a quantity that effectively defines a distribution of particles over a separation distance, ℓ. Because of its definition we expect Q to evolve according to an equation of type ∂Q/∂t = ∂/∂l (F(l)∂Q∂l). Particular emphasis was put on the search for a correct form of the diffusion function F. Richardson originally proposed an F ∼ l^(4/3) law. His studies have then been revisited by many, among which Obukhov, leading to the so-called Richardson-Obukhov l^2 ∼ t^3 theory, which holds in the homogeneous, isotropic turbulence regime. Our analysis is carried out on direct numerical simulations (DNS) of a time-decaying turbulent shear-free layer which represents a small portion of a top warm cloud boundary, a multiphase simulation where air, water vapor and water drops have been included.