Non-stationary helical flows for incompressible 3D Navier–Stokes equations

摘要

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier–Stokes equations, even for 3D case of compressible gas flow. But there is an essential deficiency of non-stationary solutions indeed.In our derivation, we explore the case of non-stationary helical flow of the Navier–Stokes equations for incompressible fluids at any given initial conditions for velocity fields (it means an open choice for the space part of a solution).Such a non-stationary helical flow is proved to be decreasing exponentially in regard to the time-parameter, the extent of time-dependent exponential component is given by the coefficient of kinematic viscosity, multiplied by the square of the coefficient of proportionality between the vorticity and velocity field.