A Quasi-Normal Scale Elimination Theory of Turbulent Flows With Stable Stratification

The Quasi-Normal Scale Elimination (QNSE) theory is a second order spectral closure capable of dealing with host of complicated factors introduced by nonlinearity and stable stratification. The theory is based upon a mapping of the actual velocity field to a quasi-Gaussian field whose modes are governed by the Langevin equation. The parameters of the mapping are calculated using a systematic process of successive averaging over small shells of velocity and temperature modes that eliminates them from the momentum and temperature equations. Turbulence and waves are treated as one entity and the effect of waves is easily identifiable. The model shows that there exists a range of Richardson numbers, between, approximately, 0.1 and 1, in which turbulence and heat transfer undergo remarkable anisotropization; the vertical mixing becomes suppressed while the horizontal mixing is enhanced. The theory yields analytical expressions for various 1D and 3D kinetic and potential energy spectra that reflect the effects of waves and anisotropy. The model’s results are suitable for immediate use in practical applications. Partial scale elimination gives sub-grid-scale viscosities and diffusivities that can be used in large eddy simulations. The elimination of all fluctuating scales results in RANS models.