RANS models mean velocity

At this point, the next step is to decompose the velocity into its mean and fluctuating components, and to substitute the result into the left-hand side of (6.42). In doing so, the triple-correlation term (UiUjUk) will appear. Note that if the joint velocity PDF were known (i.e., by solving (6.19)), then the triple-correlation term could be computed exactly. This is not the case for the RANS turbulence models discussed in Section 4.4 where a model is required to close the triple-correlation term. 

RANS, under which the Reynolds-averaged Navier Stokes equations are solved using some type of closure assumption to account for the Reynolds stress terms. RANS provides the values of the mean wind velocity and estimates of the turbulence statistics within the model domain. 

All numerical models incorporate significant assumptions and approximations, and their predictions must always be regarded as estimates. Solution of the RANS equations, for example, requires some form of closure assumption dealing with the Reynolds stress terms. Since the Reynolds stress terms and the mean flow terms are coupled by the equations, inaccuracies in the closure approximations can affect the predicted mean flow fleld. Furthermore, the boundary conditions imposed on the model require the assumption of velocity profiles and momentum transport rates, which may themselves be approximated. Similar approximations are inherent in any of the various techniques used to compute the wind fleld, with further assumptions being present in each of the dispersion models. 

In the RANS-approach, turbulence or turbulent momentum transport models are required to calculate the Reynolds-stresses. This can be done starting from additional transport equations, the so-called Reynolds-stress models. Alternatively, the Reynolds-stresses can be modeled in terms of the mean values of the variables and the turbulent kinetic energy, the so-called turbulent viscosity based models. In either way, the turbulence dissipation rate has to be calculated also, as it contains essential information on the overall decay time of the velocity fluctuations. In what follows, the more popular models based on the turbulent viscosity are focused on. A detailed description of the Reynolds-stress models is given in Annex 12.5.l.A which can be downloaded from the Wiley web-page. 

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