Mean turbulent energy closure

The acronyms for closure type used in this review are as follows FVF, fluctuating velocity field MVF, mean-velocity field MVFN, Newtonian MVF MTE, mean turbulent energy MTEN, Newtonian MTE MTOS, structural MTE MTEN/L, MTEN closure with dynamical length scale equation MRS, mean Reynolds-stress MRS/L, MRS closure with dynamical length scale equation. 

Poreh, M. and Hassid, S., 1977, Mean velocity and turbulent energy closures for flows with drag reduction, Phys. Fluids 20 (10), SI93. 

The source terms on the right-hand sides of Eqs. (25)-(29) are defined as follows. In the momentum balance, g represents gravity and p is the modified pressure. The latter is found by forcing the mean velocity field to be solenoidal (V (U) = 0). In the turbulent-kinetic-energy equation (Eq. 26), Pk is the source term due to mean shear and the final term is dissipation. In the dissipation equation (Eq. 27), the source terms are closures developed on the basis of the form of the turbulent energy spectrum (Pope, 2000). Finally, the source terms... 

The k,E-model is based on a first order turbulence model closure according to Boussinesq. In analogy to laminar flows, the Reynolds stresses are assumed to be proportional to the gradients of the mean velocities. Transport equations for the turbulent kinetic energy and the turbulent dissipation are developed from the Navier-Stokes equations assuming an isotropic turbulence. The implementation of this model and the parameters used can be found in [10],... 

Here 0 denotes the mean temperature and 6 the local temperature fluctuation. The terms ufi represent transports of internal energy by turbulent motions, and it is these terms that bring the closure problem. 

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