Physical models for small-scale structures

Dale Pullin, Graduate Aeronautical Laboratories, California Institute of Technology, USA

Attempts to model the statistical properties of small-scale turbulence using ensembles of elementary vortex structures will be discussed. These have usually consisted of exact or asymptotic solutions of the Euler or Navier-Stokes equations corresponding to either steady or evolving compact distributions of vorticity. The development of ideas using specific models such as Hills spherical vortices and Burgers vortex-sheet and vortex-tube structures will be outlined. The most successful of these, the Lundgren stretched spiral-vortex, will be analyzed in detail with applications described including velocity and passive scalar spectra, velocity-gradient statistics and velocity-structure functions.
Issues such as limitations in scale range, physical interpretation of the Kolmogorov-like scaling properties of the stretched spiral-vortex, and the successes and failures of structure-based modeling will be discussed.