  In this work, we propose a single formula for the law of the wall, which is
dubbed as the logarithmic-exponential (LOG-EXP) formula, for predicting the
mean velocity profile in different regions near the wall. And then a
feedforward neural network (FNN), whose inputs and training data are based on
this new formula, is trained for the wall-modelled large-eddy simulation
(WMLES) of turbulent channel flows. The direct numerical simulation (DNS) data
of turbulent channel flows is used to evaluate the performance of both the
formula and the FNN. Compared with the Werner-Wengle (WW) model for the WMLES,
a better performance of the FNN for the WMLES is observed for predicting the
Reynolds stresses.
