Rapidly oscillating asymptotic solutions of the Navier-Stokes equations, coherent structures, Fomenko invariants, Kolmogorov spectrum, and flicker noise
Виктор Павлович Маслов, А. И. Шафаревич · Russian Journal of Mathematical Physics · 2006
Asymptotic solutions of the Navier-Stokes equations describing three-phase coherent structures of the Taylor scale are constructed. These equations are related to topological invariants of the Liouville foliations on the three-dimensional torus into two-dimensional tori. The solutions turn out to be unstable with respect to small-scale perturbations, which finally leads to the appearance of perturbations of Kolmogorov scale. The flicker noise occurs at the corresponding frequencies.