Energy and structure of inertial range turbulence deduced from an evolution of fluid impulse

We explore numerically a very simple idea that may provide a material explanation for inertial range turbulence. We base a Lagrangian model of viscous incompressible fluid flow on an evolving ensemble of vortex doublet sheets. Initially these are randomly oriented and randomly distributed within a disk in two-dimensional space. These sheets are then actively transported (in two dimensions) according to the Oseledets equation of motion for fluid impulse. The mutual interaction of these sheets, and their diffusion, establishes a velocity fluctuation field. In a specific sense this evolution is self-affine, and we exploit this property to calculate standard statistical measures for the fluctuation field. We determine from this simple model the second-order structure function and the energy spectrum of inertial range turbulence.