The evaporatively driven cloud-top mixing layer

Direct numerical simulations of the turbulent temporally evolving cloud-top mixing layer are used to investigate the role of evaporative cooling by isobaric mixing locally at the stratocumulus top. It is shown that the system develops a horizontal layered structure whose evolution is determined by molecular transport. A relatively thin inversion with a constant thickness h = kappa/w(e) live is formed on top and travels upwards at a mean velocity w(e) similar or equal to 0.1(kappa vertical bar b(s)vertical bar chi(2)(c))(1/3), where kappa is the mixture-fraction diffusivity, b(s) < 0 is the buoyancy anomaly at saturation conditions chi(s) and chi(c) is the cross-over mixture fraction defining the interval of buoyancy reversing mixtures. A turbulent convection layer develops below and continuously broadens into the cloud (the lower saturated fluid). This turbulent layer approaches a self-preserving state that is characterized by the convection scales constructed from a constant reference buoyancy flux B(s) = vertical bar b(s)vertical bar w(e)/chi(s). Right underneath the inversion base, a transition or buffer zone is defined based on a strong local conversion of vertical to horizontal motion that leads to a cellular pattern and sheet-like plumes, as observed in cloud measurements and reported in other free-convection problems. The fluctuating saturation surface (instantaneous cloud top) is contained inside this intermediate region. Results show that the inversion is not broken due to the turbulent convection generated by the evaporative cooling, and the upward mean entrainment velocity w(e) is negligibly small compared to the convection velocity scale w* of the turbulent layer and the corresponding growth rate into the cloud.