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A flux closure formula introduced earlier for predicting entrainment into a mixed layer is tested throughanalytic solution of the kinetic energy equation and through large-eddy simulation. For this purpose, the closure formulationand the simulation model are applied to the ‘smoke cloud’ mixed layer, that includes both radiative cooling at the cloud topand surface heating or cooling at the surface, but without the effects of latent heat. The unique aspect of the closure, heightweighting of the integral of buoyancy flux, is found to be directly related to the ratio of coefficients of the dissipation anddiffusion terms of the energy equation.The simulation results indicate that the previous expression for predicting the entrainment flux is about 10% too small.Results of analytic solutions of the energy equation and the simulations are in general agreement. Disagreements arebelieved to be due to approximations in the energy equation and possible imperfections in the simulation model.A special issue investigated is the condition for decoupling of energy by surface radiative cooling. The maximumnegative buoyancy flux before decoupling predicted by the flux closure and by the energy equation differ by almost afactor of 2, but it is not clear which is better. Copyright 2008 Royal Meteorological Society
