Singularities in Fully Developed Turbulence

Abstract

Phenomenological arguments are used to explore finite-time singularity development in different physical fully-developed turbulence (FDT) situations. The role played by the cascade physics underlying this process is investigated. Such diverse aspects as the effects of spatial intermittency and fluid compressibility in three-dimensional (3D) FDT and the role of the divorticity amplification mechanism in two-dimensional (2D) FDT and quasi-2D quasi-geostrophic FDT and the advection-diffusion mechanism in magnetohydrodynamic turbulence are considered to provide physical insights into this process in variant cascade physics situations. The quasi-geostrophic FDT results connect with the 2D FDT results in the barotropic limit while they connect with 3D FDT results in the baroclinic limit (on doing the necessary interchange of vorticity in the 3D case with divorticity in the quasi-2D case); hence they seem to provide a kind of bridge between 2D FDT and 3D FDT results.