Penetrative convection at the top of a growing boundary layer

Motions at an entraining interface of a growing mixed layer are ideally partitioned into large eddies, such as plumes and thermals which act to distort the interface, and smaller scale turbulence responsible for entrainment through the interface. Influences of horizontal entrainment and pressure effects on the depth of penetration of large eddies into the stratified free flow are examined. This penetration plays an important role in the initiation of cumulus at the mixed layer top and modifies the turbulence energy balance and entrainment rate there. For example, previous models predict the entrainment rate to depend on the cube of the fundamental velocity scale at a stratified interface and linearly on this velocity scale with vanishing stratification (free entrainment). The present development, which includes specific roles of penetrating elements, suggests a possible intermediate quadratic regime corresponding to weak inversion strength.