Mathematical Physics

    

Non-Stationary Helical Flows for Incompressible 3D Navier-Stokes Equations

Authors: Sergey V. Ershkov

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.

Comments: 9 Pages. Keywords: Navier-Stokes equations, non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flow

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Submission history

[v1] 2015-11-11 15:23:28
[v2] 2015-11-11 16:51:09
[v3] 2015-12-04 16:30:58

Unique-IP document downloads: 512 times

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