A new class of non-helical exact solutions of the Navier–Stokes equations

Abstract

The paper presents a new class of exact solutions for the Navier–Stokes equations. These solutions describe unsteady three-dimensional in velocities and two-dimensional in coordinates for a viscous incompressible fluid flow. The procedure for constructing an exact solution generalizes Trkal's method proposed for studying screw flows. The new class of exact solutions allows to describe non-hecical flows (the velocity vector forms a nonzero angle with the vorticity vector) and fluid flows existing in a finite time.

Keywords

• navier-stokes equation
• exact solution
• trkal's method
• eigenfunctions of the laplacian
• non-helical flows
• blow-up regimes