A cascade interpretation of Lundgren’s stretched spiral vortex model for turbulent fine structure

Lundgren’s [Phys. Fluids 25, 2193 (1982)] model for turbulent fine structure comprises coherent vortices which wind up vorticity variations into spiral structures; simultaneously the vortices are stretched axially by a background strain field. The model predicts a k−5/3 energy spectrum and is remarkably robust to the form of the coherent vortices and the form of the vorticity variations. To understand this the present article introduces a simple cascade argument which illuminates how the dynamical processes of vortex stretching and reduction of scale conspire to give this Kolmogorov spectrum. Some generalizations are considered.