Vorticity Statistics in Fully Developed Turbulence

We study the statistical properties of fully developed hydrodynamical turbulence. To this end, a theoretical framework is established relating basic dynamical features of fluid flows to the shape and evolution of probability density functions of, for example, the vorticity. Starting from the basic equations of motion, the theory involves terms, which presently cannot be calculated from first principles. This missing information is taken from direct numerical simulations. A parallel pseudospectral code is used to to obtain well-resolved numerical simulations of homogeneous isotropic turbulence. The results yield a consistent description of the vorticity statistics and provide insights into the structure and dynamics of fully developed turbulence.