The probability density function (PDF) of velocity due to the total vorticity field is nearly Gaussian in 3D QG (kurtosis=3.08), but less Gaussian in 2D (kurtosis=3.95). In both 2D and 3D QG the velocity PDFs due to the vortex cores and the circulation cells are non-Gaussian. In 3D QG the total velocity PDF is more strongly influenced by the background, while in 2D the vortex cores are more influential. In both 2D and 3D QG turbulence, the enstrophy spectrum of the background fits the Kraichnan k-1 slope for isotropic 2D turbulence.
Our conclusion is that filamentous structures play a more dominant role in 3D QG dynamics than in 2D turbulence. In addition, two traditional measures used to quantify vorticity, the Okubo-Weiss parameter and λ2, are shown to be equivalent to each other for 2D and 3D QG fields. A point vortex model for 3D QG is derived in order to show that a collection of point vortices has a non-Gaussian probability density function, which matches the results of the numerical model.