Abstract: The problem of bottom boundary mixed layer growth in a stratified flow is dealt with in this paper in terms of a new vertically integrated model.A parameter depending on the distribution of velocity in the vertical direction appears in a new energy balance equation. This energy balance equation is equivalent to the Richardson number closure model used byPollar et al.￣21 and Thompson￣13 when the velocity distribution is uniform in the verticaldirection within the layer.The analytic solutions are obtai...