# Log-Correlated Large-Deviation Statistics Governing Huygens Fronts in Turbulence

## Abstract

Analyses have disagreed on whether the velocity \(u_T\) of bulk advancement of a Huygens front in turbulence vanishes or remains finite in the limit of vanishing local front propagation speed \(u_0\). Here, a connection to the large-deviation statistics of log-correlated random processes enables a definitive determination of the correct small-\(u_0\) asymptotics. This result reconciles several theoretical and phenomenological perspectives with the conclusion that \(u_T\) remains finite for vanishing \(u_0\), which implies a propagation anomaly akin to the energy-dissipation anomaly in the limit of vanishing viscosity. Various leading-order structural properties such as a novel \(u_0\) dependence of a bulk length scale associated with front geometry are predicted in this limit. The analysis involves a formal analogy to random advection of diffusive scalars.

## Keywords

Front propagation Turbulence## Notes

### Acknowledgements

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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