  A cylindrical and inclined jet in crossflow is studied under two distinct
velocity ratios, $r=1$ and $r=2$, using highly resolved large eddy simulations
(LES). First, an investigation of turbulent scalar mixing sheds light onto the
previously observed but unexplained phenomenon of negative turbulent
diffusivity. We identify two distinct types of counter gradient transport,
prevalent in different regions: the first, throughout the windward shear layer,
is caused by cross-gradient transport; the second, close to the wall right
after injection, is caused by non-local effects. Then, we propose a deep
learning approach for modelling the turbulent scalar flux by adapting the
tensor basis neural network previously developed to model Reynolds stresses
(Ling et al. 2016a). This approach uses a deep neural network with embedded
coordinate frame invariance to predict a tensorial turbulent diffusivity that
is not explicitly available in the high fidelity data used for training. After
ensuring analytically that the matrix diffusivity leads to a stable solution
for the advection diffusion equation, we apply this approach in the inclined
jets in crossflow under study. The results show significant improvement
compared to a simple model, particularly where cross-gradient effects play an
important role in turbulent mixing. The model proposed herein is not limited to
jets in crossflow; it can be used in any turbulent flow where the Reynolds
averaged transport of a scalar is considered.
