On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations

• Main Authors: Sergey V. Ershkov, Roman V. Shamin, Ayrat R. Giniyatullin
• Format: Article
• Language: English
• Published: Elsevier 2020-01-01
• Series: Journal of King Saud University: Science
• Online Access: http://www.sciencedirect.com/science/article/pii/S1018364718306335

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we proceed exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids, with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of flow.The main motivation of the current research is the exploring the case when velocity field u is supposed to be perpendicular to the vector ∇α. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained, for which non-stationary helical flow with invariant Bernoulli-function is considered.The spatial part of the pressure field of the fluid flow should be determined via Bernoulli-function, if components of the velocity of the flow are already obtained. Keywords: Navier-Stokes equations, Non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flow