A diftusive limit tor entrainment

An entrainment model is developed which includes the effect of the buoyancy flux by molecular diffusion across a density interface. This effect is incorporated into the conservation equation for turbulent kinetic energy through a “diffusion parameter” RiPe ^-1/2, where Ri is the bulk Richardson number and Pe the Peclet number. As RiPRiPe ^-1/2e increases and approaches a critical limiting value the net entrainment, defined as the rate of deepening of the mixed layer, becomes zero. Based on a numerical study and on results from two experiments of different scales, it is shown that the limiting value of this parameter for entrainment to occur is approximately 10 for a salt-stratified system, though this value may depend on the diffusivity of the stratified component.