Exact Vorticity Solutions of the Incompressible Navier-Stokes Equations

摘要

Turbulence is found in all regions of the atmosphere, where it plays an essential role in meteorology, affects flight characteristics of vehicles, and accounts for some of the erratic behaviour of the ionosphere. The report arose out of the attempt to see whether some of the properties of turbulence could be obtained from vorticity solutions of the Navier-Stokes equations, since it is generally assumed that these equations govern the motion of turbulent fluids. For simplicity, the fluid was taken to be incompressible and of infinite extent. Exact vorticity solutions were found, which in a sense are the simplest possible ones. They have much structure in space but they lack the time-fluctuations characteristic of turbulence. Despite the failure of these solutions to describe turbulent flow, they should be of interest because they can be added to the very short list of exact vorticity solutions of fluid dynamics, and are very different from the previously known ones. (Author)