Small-scale-velocity-induced linear instability of large-scale turbulent flows

Analysis of a simplified equation derived previously for small-scale velocity components shows that any turbulent flow of an incompressible liquid becomes unstable against infinitesimal perturbations of small-scale velocity components if the strain rate tensor for the large-scale velocity is high. Such a statement comes into conflict with the classical stability theory, which specifically asserts that the Poiseuille flow in a circular tube is linearly stable against infinitesimal perturbations.