Modeling the diurnal mixed layer

The numerical model presented here is based on the one‐dimensional equations for momentum, heat, salt, and turbulent kinetic energy integrated over the diurnal mixed layer. Two noteworthy features are the inclusion of the energetics of billowing due to Kelvin‐Helmholtz instability at the base of the mixed layer, and a closure hypothesis which retains average mixed‐layer turbulent kinetic energy as an explicit variable, rather than assuming it to be a fixed proportion of external energy input. The importance of both these features is illustrated in the application of the model to the data for 1 day which included several mixing processes: a fairly calm morning with uninterrupted solar heating, followed by rapid mixed‐layer deepening during a strong afternoon sea breeze, and finally a relatively cool night with little wind. The data contain rapidly changing meteorological inputs as well as evidence of strong billow formation and collapse and thus provide an ideal test of the importance of both billow energetics and the temporal effects in the turbulent kinetic energy budget. The model does not account for processes occurring below the mixed layer nor for the effects of horizontal advection. Within these constraints, model results agree well with measured temperatures and represent an improvement over the results of a slab model without billow energetics.