Structure functions in two-dimensional turbulence

Abstract

The “variable range decomposition” mean field type approximation is applied to the enstrophy and energy balance equations in 2D homogeneous, isotropic turbulence. Enstrophy is seen to be transferred to smaller scales, energy to larger scales. The approximate enstrophy balance equation is supplemented by an exact relation between the velocity structure functionD(r) and the vorticity structure functionDω(r) to form a closed set of equations that is used to calculateD andDω from scale zero up to the input scale.Dω is found to depend only on viscosity and the enstrophy dissipation eω and tends to the constant ≈15eω2/3 in the enstrophy inertial range.D(r) in addition to the well-knownr2-law has a second power law term ∝r4/3, which is important in the intermediate range between the viscous range and the enstrophy inertial range. All numerical constants are calculated.