Diffuselet method for three-dimensional turbulent mixing of a cloudy air filament

The mixing properties of vapor content, temperature, and particle fields are of paramount importance in cloud turbulence as they pertain to essential processes, such as cloud water droplet evaporation and entrainment. Our study examines the mixing of a single cloudy air (which implies droplet-laden) filament with its clear air environment, a characteristic process at the cloud edge, in two ways. The first consists of three-dimensional combined Euler-Lagrangian direct numerical simulations which describe the scalar supersaturation as an Eulerian field and the individual cloud water droplets as an ensemble of Lagrangian tracers. The second way builds on the recently developed diffuselet method, a kinematic Lagrangian framework that decomposes a scalar filament into a collection of small sections subject to deformation by local stirring and cross-sheet diffusion. The Schmidt number is <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mtext>Sc</a:mtext><a:mo>=</a:mo><a:mn>0.7</a:mn></a:mrow></a:math>. The entrainment process causes a deformation of the supersaturated cloud filament in combination with diffusion until the system reaches a well-mixed equilibrium state, which implies for the present configuration that all droplets are evaporated. We compare the time dependence of the mean square and probability density function of the supersaturation field. For the initial period of the mixing process, they agree very well; at later stages, deviations caused by nonzero mean of the conserved scalar are observed. For the cases including cloud water droplets, we also investigate the impact of droplet number density and condensation growth response. Turbulence causes deviations from the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mi>d</b:mi><b:mn>2</b:mn></b:msup></b:math> law similar to recent experiments in sprays. A simulation at a Schmidt number that is by a factor of 100 larger than in clouds improves the agreement between simulation and diffuselet method significantly. The latter result promotes the diffuselet framework as an efficient parametrization for turbulent high-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mtext>Sc</c:mtext></c:math> mixing which can reduce the resolution efforts of the viscous-convective range of scalar turbulence.