The origin of coherence in hydrodynamical turbulence

Abstract

It is shown that the energy transfer to small scales turbulence necessarily requires a specific phase coherence of helicity-associated fluctuations. It follows that this coherence is a sufficient cause of turbulence intermittency in physical space, while both phase coherence and intermittency are consequences of the inviscid conservation of the topology of the vorticity field, in particular the helicity. An important conclusion arrived at is that a perturbation of this coherence in the interial range results in destruction of the vortex-line stretching mechanism and reduction or, finally, termination of turbulence production at small scales. Such phase reshuffling should cost negligible energy for high Reynolds number turbulent flows. The destruction of coherence can be achieved by a mere reshuffling of the phases connected with the related orientation of vorticity elements. Thus a possibility for practical turbulence control and drag reduction is indicated by the theory. Theories of turbulence or modelling schemes based on closures, or more elaborate assumptions, such as the renormalization group theory, which by construction are phase independent, do not account for phase coherence and subsequent intermittency and are necessarily and fundamentally insufficient to describe this phenomenon. It is shown that perturbations of the vortex-line stretching mechanism may lead to an anomalous accumulation of helicity and a subsequent generation of large scale coherent vortices. Such organization of turbulence is asserted to be generic for the birth of large vortices in atmospheric phenomena. The theory is shown to be in excellent agreement with extensive numerical simulations. Experimental data are briefly discussed.