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Validation of a mixed‐layer closure. I: theoretical tests
Author(s) -
Lilly Douglas K.,
Stevens Bjorn
Publication year - 2008
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.184
Subject(s) - mechanics , buoyancy , dissipation , latent heat , closure (psychology) , decoupling (probability) , mixed layer , entrainment (biomusicology) , thermodynamics , radiative transfer , heat flux , physics , radiative flux , meteorology , heat transfer , engineering , optics , control engineering , rhythm , economics , acoustics , market economy
A flux closure formula introduced earlier for predicting entrainment into a mixed layer is tested through analytic solution of the kinetic energy equation and through large‐eddy simulation. For this purpose, the closure formulation and the simulation model are applied to the ‘smoke cloud’ mixed layer, that includes both radiative cooling at the cloud top and surface heating or cooling at the surface, but without the effects of latent heat. The unique aspect of the closure, height weighting of the integral of buoyancy flux, is found to be directly related to the ratio of coefficients of the dissipation and diffusion 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 are believed 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 maximum negative buoyancy flux before decoupling predicted by the flux closure and by the energy equation differ by almost a factor of 2, but it is not clear which is better. Copyright © 2008 Royal Meteorological Society