A vortex-tube model of eddies in the inertial range

A new class of geometrical models for the energy cascade within the inertial range of scales is proposed. In these models, the active eddies are portions of vortex tubes, and in this respect they are similar to tube geometries considered by Tennekes (1968) and Saffman (1968) for the dissipation range of scales. The model developed here is also a special case and an elaboration of the beta-model of Frisch et al. (1978). The structure studied represents the realization in physical space, localized in space and time, of an energy cascade to scales which are arbitrarily small. The approach relies on conservation of circulation and energy, as well as tube knottedness, in inviscid flow. Since the invariance of identifiable circulation Gamma of a tube is the key ingredient, these structures are referred to as gamma models.