Diffusion of turbulence following both stable and unstable step stratification perturbations

Abstract

We have studied the evolution of a two-phase, air and unsaturated water vapor, time decaying, shearless, turbulent mixing layer in the presence of both stable and unstable perturbations of the temperature profile.The top interface between a warm vapor cloud and clear air in the absence of water droplets -the liquid phase -is the reference dynamics. Three dimensional direct numerical simulations were performed within a 6m x 6m wide and 12m high cloud portion which is hypothesized to be located close to an interface between the warm cloud and clear air. The Taylor micro-scale Reynolds number, Re λ , inside the cloud portion is 250. The squared Froude number, Fr 2 , varies over the [0.4:1038.5] and [-4.2:-20.8] intervals.The presence of a sufficiently intense stratification (Fr 2 of the order of 1) changes the mixing dynamics to a great extent. The formation of a sub-layer inside the shearless layer is observed. Under a stable thermal stratification condition, the sub-layer behaves like a pit of kinetic energy. On the other hand, a kinetic energy transient growth takes place under unstable conditions, which leads to the formation of an energy peak just below the center of the shearless layer.The scaling law of the energy time variation inside the interface region has been quantified: this is an algebraic law with an exponent which depends on the perturbation stratification intensity. The presence of an unstable stratification increases the differences in statistical behavior among the longitudinal velocity derivatives with respect to the unstratified case. In stable cases, since the mixing process is suppressed, so is the small-scale anisotropy.