A microscopic vortical structure in fully developed turbulence

Abstract

A microscopic vortical structure in fully developed three-dimensional turbulence is considered. The strain rates due to eddies of a certain scale stretch and shrink the vorticity field of smaller scales, whose strain rates excite the vorticity of even smaller scales. The excitation propagates toward small scales, the self-similar structure being anticipated in wavenumber space. It is indicated that a pair of oppositely oriented vortex sheets are a candidate for such a self-similar structure: the two sheets approach each other and the vorticity is enhanced during the process. The time evolution of the vorticity is expressed in the dynamical scaling form proposed previously by Nelkin and the present author [Phys. Rev. A 31, 1980(1985)] in which the higher-order structure functions and generalized dimensions in fully developed turbulence were interpreted in good agreement with experiment. Hence the derived vortical structure is expected to be responsible for the intermittent effects.