  Simulations of turbulent fluid flow around long cylindrical structures are
computationally expensive because of the vast range of length scales, requiring
simplifications such as dimensional reduction. Current dimensionality reduction
techniques such as strip-theory and depth-averaged methods do not take into
account the natural flow dissipation mechanism inherent in the small-scale
three-dimensional (3-D) vortical structures. We propose a novel flow
decomposition based on a local spanwise average of the flow, yielding the
spanwise-averaged Navier-Stokes (SANS) equations. The SANS equations include
closure terms accounting for the 3-D effects otherwise not considered in 2-D
formulations. A supervised machine-learning (ML) model based on a deep
convolutional neural network provides closure to the SANS system. A-priori
results show up to 92% correlation between target and predicted closure terms;
more than an order of magnitude better than the eddy viscosity model
correlation. The trained ML model is also assessed for different Reynolds
regimes and body shapes to the training case where, despite some discrepancies
in the shear-layer region, high correlation values are still observed. The new
SANS equations and ML closure model are also used for a-posteriori prediction.
While we find evidence of known stability issues with long time ML predictions
for dynamical systems, the closed SANS simulations are still capable of
predicting wake metrics and induced forces with errors from 1-10%. This results
in approximately an order of magnitude improvement over standard 2-D
simulations while reducing the computational cost of 3-D simulations by 99.5%.
