Improvement of the Bulk Formulation at the Cloud Boundary

How does dry air mix into a cloud? The rate at which a cloud entrains dry air determines the cloud lifetime before dissipation and therefore it is a key parameter for modeling clouds. However estimations of entrainment are difficult because the mixing is turbulent involving a wide range of length scales, from big eddies down to the Kolmogorov length. Besides, small scale features like local supersaturation or preferential concentration might interact with the small turbulent scales and play an important role for the mixing. Typical cloud simulations using LES can resolve whole clouds but usually lack a good parametrization of small scale processes. Therefore LES entrainment values remain suspicious until a better model of mixing is provided. On the other end, Lagrangian Direct Numerical Simulations (LDNS) provide a much complete picture of the small scales of the flow. However the domain size in LDNS is severely limited by the number of droplets that computer clusters can handle (around 10⁸ droplets in 30 cm³). One of the main goals of LDNS studies is to improve the parametrization used in LES but the big gap between the typical scales of LES and LDNS makes it difficult any validation. We present an improved bulk formulation for the study of cloud boundary mixing. On one hand, this approach relies on Direct Numerical Simulations and resolves down to the Komogorov scales without any parametrization. On the other hand, the droplets are described in a continuous manner. Finite time thermodynamic (supersaturation), particle inertia and settling velocity have been included in the formulation. Contrary to the LDNS, this method is pure Eulerian reducing problems for parallelization. This allows for the simulation of bigger domains. The formulation has thus the potential to connect the results coming from LDNS to be used in LES. As an example we show results of the study of the Cloud Top Instability in a two dimensional domain. This instability is caused by the mixture of dry and cloud air at the top of stratocumulus clouds, at scales of the order of few meters. It is thus very sensitive to the small scales of the flow and a perfect test for the hypothesis that small scales might have an important role for clouds. We show how supersaturation and inertial effects influence the instability.