Stratification perturbation of a turbulent mixing. Effect on small-scale anisotropy

Warm clouds as stratocumuli swathe a significant part of earth’s surface and play a major role in the global dynamics of atmosphere by strongly reflecting incoming solar radiation so that an accurate representation of their dynamics is important in large-scale analyses of atmoshperic flows [Wood 2012].The mixing and entrainment processes at the cloud top have been identified as fundamental to determine the internal structure of warm clouds, so that a clear and complete understanding of their physics is required [Gerber et al 2013]. The aim of this work is to study some of the basic phenomena which occur at a stratified interface focusing on the smallest scales of the flow which influence. These scales are important to understand the global dynamic of clouds, as pointed out by Malinowski et al (2013). To achieve the results, a campaign of high-resolution simulation of the local transport through a dry/moist air were performed by the means of Direct Numerical Simulations (DNS) using our home produced computational code that implements a de-aliased pseudospectral Fourier-Galerkin spatial discretization and an explicit low storage fourth order Runge-Kutta time integration scheme [Iovieno et al 2001]. We consider the interface between clear air and moist air in a 6m × 6m × 12m parallelepipedic domain coupling two homogeneous and isotropic turbulent regions with different kinetic energy that interact through a mixing layer. The energy ratio is of the same order of the ones measured in warm clouds (see, e.g., [Malinowski et al 2013]) and, furthermore, it allows us to compare our results with experiments on shearless mixing (see [Veeravalli & Warhaft 1989, Tordella & Iovieno 2011]) in absence of any stratification. For each simulation two interfaces have been obtained, one in highly stably stratified condition, and one in unstable condition. The dynamics of interfaces is analyzed through an initial temperature perturbation located across one of the vapor/clear air interfaces thus generating a local stable layer; the water vapor is treated as a passive scalar. The level of stratification is quantified with the Froude number. For the stable cases, the Froude numbers considered ranges from 12.7 (weak stratification) to 0.6 (intense stratification), while for the unstable cases Fr^2 ranges from -250 to -16. In both stable and unstable cases the evolution of the system can be split in two different phases. In the first one, the buoyancy terms are negligible, and there are no significant differences with respect to a non-stratified case. As the system evolves, the effect of stratification becomes relevant (as soon as the stratification is intense). About the unstable case layer we observe a high intermittency and an intense growth rate of the layer, which becomes overdiffusive in the case Fr^2 = −16. In particular, the entrainment, after an initial decay, asimptotically always shows a positive growth rate. Here, for reason of space, we give details about the stably stratified layer which presents a more complex dynamics associated to the onset of a pocket very low turbulent kinetic energy. It can be observed the onset of a sub-layer characterized by the presence of low values of kinetic turbulent energy. At about 8 time scales, we observe the 8% of the energy in the wapor cloud and the 50% of the kinetic energy in the clear-air region. A similar trend was also observed in the LES cloud topped boundary layer simulations carried out by using Deardoff TKE model (NCAR group) and by using the ARAP TKE model (WVU group) [Moeng et al 1996]. The presence of such sublayer induces the formation of two local interfaces. Both of these interfaces present an intermittent behavior, and the entrainment (flux of dry air into the moist one) is blocked; the velocity of the moist air front can be considered a characteristic parameter, since the entrainment of clear air is responsible of the growth of the cloud [Mellado 2010, Moeng 2000]. As a consequence, the entrainment of clear air is confined to a thin interfacial layer. Also the dissipative terms inside the pit becomes relatively more important compared to the kinetic energy, making the pit deeper and deeper with respect to the external regions.