# Fluid Mechanics/Turbulent Flow

## General[edit]

Navier--Stokes equations, which govern the conservation of momentum for Newtonian fluids, have been known for more than 200 years. However, it has not been possible to solve them analytically, except for very special and also very simple flow cases with related boundary conditions. The non-linearity of this system of partial differential equations is the main barrier for its analytical solution. In principle direct numerical solutions of turbulent flow problem are possible, since the governing equations constitute a closed system. However, with increasing Reynolds number the ranges of length and temporal scales increase. Hence, more spatial and temporal resolution of the simulations are required, such that one rapidly reaches the limits of the available computer power. Therefore, it is impossible—for now and the foreseeable future—to apply direct numerical simulations for most of the turbulent flows of technological interest. Being aware of these difficulties, after Feynman, it developed into folklore to say that turbulence is the last great unsolved problem of classical physics. In spite of the difficulties related to the nature of turbulence, numerous investigations aimed at understanding turbulence and, consequently, modeling and controlling turbulent flows have been conducted. (vinii)