Statistical field theory for a passive vector model of turbulence

Developing statistical theories for turbulence starting from the equations of motion is one of the central goals of fundamental turbulence research. While this continues to be challenging for Navier-Stokes turbulence, simpler models offer the opportunity to explore conceptual aspects of statistical field theories. Here, we consider the linear stretching and advection model, a model for a passive vector advected with a spatially linear and temporally delta-correlated Gaussian velocity field, subject to viscous diffusion and driven by a large-scale forcing. The model allows for an exact computation of its spectral properties over the full range of wavenumbers. The model also features intermittency of passive vector increments. Studying its statistical properties in terms of the Hopf functional approach shows that the non-Gaussian ensemble statistics can be decomposed into Gaussian conditional statistics based on the advecting velocity field. Intermittency therefore arises from mixing Gaussian statistics with different stretching histories. In addition to reviewing the analytical properties of the model, we will present numerical simulation results.