  Turbulence modeling is a classical approach to address the multiscale nature
of fluid turbulence. Instead of resolving all scales of motion, which is
currently mathematically and numerically intractable, reduced models that
capture the large-scale behavior are derived. One of the most popular reduced
models is the Reynolds averaged Navier-Stokes (RANS) equations. The goal is to
solve the RANS equations for the mean velocity and pressure field. However, the
RANS equations contain a term called the Reynolds stress tensor, which is not
known in terms of the mean velocity field. Many RANS turbulence models have
been proposed to model the Reynolds stress tensor in terms of the mean velocity
field, but are usually not suitably general for all flow fields of interest.
Data-driven turbulence models have recently garnered considerable attention and
have been rapidly developed. In a seminal work, Ling et al (2016) developed the
tensor basis neural network (TBNN), which was used to learn a general Galilean
invariant model for the Reynolds stress tensor. The TBNN was applied to a
variety of flow fields with encouraging results. In the present study, the TBNN
is applied to the turbulent channel flow. Its performance is compared with
classical turbulence models as well as a neural network model that does not
preserve Galilean invariance. A sensitivity study on the TBNN reveals that the
network attempts to adjust to the dataset, but is limited by the mathematical
form that guarantees Galilean invariance.
