The validity of the Boussinesq approximation in the wake behind a high-pressure turbine blade is explored. We probe the mathematical assumptions of such a relationship by employing a least-squares technique. Next, we use an evolutionary algorithm to modify the anisotropy tensor a priori using highly resolved LES data. In the latter case we build a non-linear stress-strain relationship. Results show that the standard eddy-viscosity assumption underpredicts turbulent diffusion and is theoretically invalid. By increasing the coefficient of the linear term, the far-wake prediction shows minor improvement. By using additional non-linear terms in the stress-strain coupling relationship, created by the evolutionary algorithm, the near-wake can also be improved upon. Terms created by the algorithm are scrutinized and the discussion is closed by suggesting a tentative non-linear expression for the Reynolds stress, suitable for the wake behind a high-pressure turbine blade.
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