Trkal Flows and the Emergence of Metastable Streamline-Vortex Tubes

Behavior of incompressible fluids at large values of the Reynolds number is usually considered as essentially turbulent and close to chaotic with high entropy. Nevertheless, low entropy coherent large scale structures are observed in geophysical and atmospheric phenomena, characterized by the alignment of the velocity and vorticity vectors. In his treatise on "Trkal Flows and the Emergence of Metastable Streamline-Vortex Tubes" Dr. Alexander Libin proposes a mathematical model for this phenomena,based on the asymptotic analysis at large values of the Reynolds number of the long wavelength perturbations of the Trkal solutions for 3-D Navier-Stokes equation.At the background, a dual pair of decaying Beltrami flows couples into a long-living triplet with a flow in the orthogonal direction to the dual pair plane.The plain flow is confined by a large invariant domain of a size characterized by the square root of the Reynolds number,just as the characteristic time period for the large scale plain flow stability.At these times the orthogonal flow is governed by intrinsically unstable equation,which might be considered as the manifestation of the hydrodynamic instability.