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Statistical field theory for a passive vector model with spatially linear advection

Lukas Bentkamp* and Michael Wilczek†

  • *Contact author: lukas.bentkamp@uni-bayreuth.de
  • †Contact author: michael.wilczek@uni-bayreuth.de
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Phys. Rev. Fluids 11, 074606 – Published 23 July, 2026

DOI: https://doi.org/10.1103/wkwc-2pxt

Abstract

One challenge in developing a statistical field theory of turbulence is the analysis of the functional equations that govern the complete statistics of the flow field. Simplified models of turbulence may help to develop such a statistical framework. Here we consider the advection and stretching of an incompressible passive vector field by a spatially linear stochastic field as a model for small-scale turbulence. The model encompasses non-Gaussian statistics due to an intermittent energy flux from large scales to small scales, thereby displaying hallmark features of turbulence. We explore this model using the Hopf functional formalism, which naturally leads to a decomposition of the complex non-Gaussian statistics into Gaussian subensembles based on different realizations of the advecting field. We then characterize intermittency of the model using a numerical implementation, which takes advantage of this statistical decomposition.

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Phys. Rev. Fluids 11, 074606– Published 23 July, 2026
  • Received 17 November 2025
  • Accepted 8 June 2026
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