A SMALL-SCALE TURBULENCE MODEL

A previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2-D) vortic es with internal spiral structure, each stretched by an axially symmet ric strain flow. Stretching and differential rotation produce an energ y cascade to smaller scales in which the stretching represents the eff ect of instabilities and the spiral structure is the source of dissipa tion at the end of the cascade. The energy spectrum of the resulting f low may be expressed as a time integration involving only the enstroph y spectrum of the time evolving 2-D cross-section flow, which may be o btained numerically. Examples are given in which a k-5/3 spectrum is o btained by this method. The k-5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving ran ge in the 2-D enstrophy spectrum. The results are found to be insensit ive to time dependence of the strain rate, including even intermittent on-or-off strains.