Scale Invariant Streamline Equations and Strings of Singular Vorticity

TL;DR

This paper explores how specific flow solutions to the Navier-Stokes equations can lead to large-scale structures with singular vorticity, revealing instability and formation of curved streamline prisms at high Reynolds numbers.

Contribution

It introduces a new class of solutions involving Beltrami flows and analyzes their stability and large-scale structure formation in fluid dynamics.

Findings

Emergence of time-dependent phase and upward velocity from perturbations.

Formation of large-scale curved streamline prisms with singular vorticity.

Instability of these structures at high Reynolds numbers.

Abstract

A linear combination with constant in space amplitudes of a pair of dual anisotropic decaying Beltrami flows (the Trkal solutions)with the same eigenvalue of the curl operator and of an orthogonal constant velocity vector to the Beltrami pair,yields a triplet solution of the force-free Navier-Stokes equation. Slight space variation of the amplitudes (large scale perturbation) yields the emergence of the time depending phase between the dual Beltrami flows and of the upward velocity,which are unstable at large values of the Reynolds number as well as the formation of the large scale curved prisms of streamlines with edges being the strings of singular vorticity.