  A novel machine learning algorithm is presented, serving as a data-driven
turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS)
simulations. This machine learning algorithm, called the Tensor Basis Random
Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while
guaranteeing Galilean invariance by making use of a tensor basis. By modifying
a random forest algorithm to accept such a tensor basis, a robust, easy to
implement, and easy to train algorithm is created. The algorithm is trained on
several flow cases using DNS/LES data, and used to predict the Reynolds stress
anisotropy tensor for new, unseen flows. The resulting predictions of
turbulence anisotropy are used as a turbulence model within a custom RANS
solver. Stabilization of this solver is necessary, and is achieved by a
continuation method and a modified $k$-equation. Results are compared to the
neural network approach of Ling et al. [J. Fluid Mech, 807(2016):155-166,
(2016)]. Results show that the TBRF algorithm is able to accurately predict the
anisotropy tensor for various flow cases, with realizable predictions close to
the DNS/LES reference data. Corresponding mean flows for a square duct flow
case and a backward facing step flow case show good agreement with DNS and
experimental data-sets. Overall, these results are seen as a next step towards
improved data-driven modelling of turbulence. This creates an opportunity to
generate custom turbulence closures for specific classes of flows, limited only
by the availability of LES/DNS data.
