Abstract
The efficacy of a simple encroachment model of mixed‐layer growth is explored by simulating two disparate days of the Wangara Experiment. The inclusion of thermal winds is shown to be essential if temperature, height and vector wind of the mixed layer are to be predicted with accuracy. In strong wind shears, additional growth due to the stress between the mixed layer and the air above evidently occurs and this is included by a new closure, invoking mean‐flow energetics (termed ‘the Froude dynamics’ approach).
Simulation of Day 12 supports the new model showing that even when averaged over (say) the central four hours of that day, the interfacial stress is expected to have been 30% larger than the surface stress. In conditions of convective heating and light winds the model predicts that negligible entrainment occurs. Growth is by encroachment only. This is confirmed by the simulation of Day 33.
Working from the turbulence kinetic energy equation, the closure problem for the Froude dynamics model is solved by a ‘catastrophe’ interpretation in which the normal state is one of no entrainment. Turbulence kinetic energy generated at the surface is dissipated and used to redistribute fluid within the mixed layer. Only when the Froude number, Fr, of the mixed layer exceeds a value of unity does entrainment occur such that the normal state is restored. Here Fr = |Δu|^2^θ~vo~/gh Δθ~V~ and Δu is the velocity jump, Δθ~v~ the virtual potential temperature jump (reference value θ~vo~) at the top of the mixed layer which is of height h; g is acceleration due to gravity. There are no adjustable or tunable parameters involved.