The origin of organized motion in turbulence

Abstract

Energy transfer to small scales in 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 topology of the vorticity field, in particular the helicity. A perturbation of this coherence in the inertial range would induce a destruction of the vortex-line stretching mechanism and reduction, or in the extreme termination, of energy cascade to small scales. Such destruction of coherence can be achieved by a mere reshuffling of the phases connected with the relative orientation of vorticity elements. Theories of turbulence or modelling schemes based on closures, or more generally on the assumption of weak interaction between velocity harmonics which by construction are phase independent and insensitive to such perturbation, do not account for coherence and intermittency and are necessarily and fundamentally insufficient to describe this phenomenon. The destruction of small scale coherence leads to an anomalous accumulation of helicity and in anisotropic turbulent flow generation of large scale coherent vortices. It is asserted that this mechanism is responsible for violent atmospheric phenomena, such as tropical hurricanes. The theory is shown to be in satisfactory agreement with numerical simulations. Experimental data are briefly discussed.