Fast Numerical simulations of 2D turbulence using a dynamic model for Subgrid Motions

We present numerical simulation of 2D turbulent flow using a new model for the subgrid scales which are computed using a dynamic equation linking the subgrid scales with the resolved velocity. This equation is not postulated, but derived from the constitutive equations under the assumption that the non-linear interactions of subgrid scales between themselves are equivalent to a turbulent viscosity.The performances of our model are compared with Direct Numerical Simulations of decaying and forced turbulence. For a same resolution, numerical simulations using our model allow for a significant reduction of the computational time (of the order of 100 in the case we consider), and allow the achievement of significantly larger Reynolds number than the direct method.Comment: 35 pages, 9 figure

Scaling laws and vortex profiles in 2D decaying turbulence

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, as predicted by Carnevale et al., and it is observed that viscous effects spoil this scaling regime. This scaling regime shows some trends toward that of the Kirchhoff model, for which a recent theory predicts a decay exponent $\xi=1$. In terms of scaled variables, the vortices have a similar profile close to a Fermi-Dirac distribution.Comment: 4 Latex pages and 4 figures. Submitted to Phys. Rev. Let

Bridging the condensation–collision size gap: a direct numerical simulation of continuous droplet growth in turbulent clouds

In most previous direct numerical simulation (DNS) studies on droplet growth in turbulence, condensational growth and collisional growth were treated separately. Studies in recent decades have postulated that small-scale turbulence may accelerate droplet collisions when droplets are still small when condensational growth is effective. This implies that both processes should be considered simultaneously to unveil the full history of droplet growth and rain formation. This paper introduces the first direct numerical simulation approach to explicitly study the continuous droplet growth by condensation and collisions inside an adiabatic ascending cloud parcel. Results from the condensation-only, collision-only, and condensation–collision experiments are compared to examine the contribution to the broadening of droplet size distribution (DSD) by the individual process and by the combined processes. Simulations of different turbulent intensities are conducted to investigate the impact of turbulence on each process and on the condensation-induced collisions. The results show that the condensational process promotes the collisions in a turbulent environment and reduces the collisions when in still air, indicating a positive impact of condensation on turbulent collisions. This work suggests the necessity of including both processes simultaneously when studying droplet–turbulence interaction to quantify the turbulence effect on the evolution of cloud droplet spectrum and rain formation