Self-similar analytic solution of the two dimensional Navier-Stokes equation with a non-Newtonian type of viscosity
arXiv:1410.1303 · doi:10.3846/13926292.2016.1136901
Abstract
We investigate the two dimensional incompressible Navier-Stokes(NS) and the continuity equations in Cartesian coordinates and Eulerian description for non-Newtonian fluids. As a non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multi-dimensional generalization of the well-known self-similar Ansatz, which was already used for non-compressible and compressible viscous flow studies. The geometrical interpretations of the trial function is also discussed. We compare our recent results to the former Newtonian ones.
14 pages, 3 figures, submitted to Journal of Non-Newtonian Fluid Dynamics