Self-similar Solutions for Laminar Wall Jets

A steady three-dimensional laminar wall jet of a viscous incompressible fluid flowing out into a space submerged with the same fluid was studied numerically and experimentally in I. I. But, A. M. Gailfullin, and V. V. Zhvick, Fluid Dyn. 56, 812–823 (2021) and K. F. Adane and M. F. Tachie, ASME J. Fluids Eng. 132 (10), 1 (2010). It was found that the flow reaches a self-similar state at large values of the longitudinal coordinate with the self-similarity exponent value \(k\) close to \(1.33\) . The goal of this article is to solve this problem exploiting the fact that its dimensionality can be reduced by one. The problem is solved by means of a physically-informed neural network (PINN) implemented via PyTorch framework.