## This content will become publicly available on June 11, 2020

## 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*remains finite for vanishing

_{T}*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. As a result, the analysis involves a formal analogy to random advection of diffusive scalars.

- Authors:

- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Danville, CA (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1529002

- Report Number(s):
- SAND-2019-5017J

Journal ID: ISSN 0022-4715; 675258

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Statistical Physics

- Additional Journal Information:
- Journal Name: Journal of Statistical Physics; Journal ID: ISSN 0022-4715

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Front propagation; Turbulence

### Citation Formats

```
Mayo, Jackson R., and Kerstein, Alan R. Log-Correlated Large-Deviation Statistics Governing Huygens Fronts in Turbulence. United States: N. p., 2019.
Web. doi:10.1007/s10955-019-02306-3.
```

```
Mayo, Jackson R., & Kerstein, Alan R. Log-Correlated Large-Deviation Statistics Governing Huygens Fronts in Turbulence. United States. doi:10.1007/s10955-019-02306-3.
```

```
Mayo, Jackson R., and Kerstein, Alan R. Tue .
"Log-Correlated Large-Deviation Statistics Governing Huygens Fronts in Turbulence". United States. doi:10.1007/s10955-019-02306-3.
```

```
@article{osti_1529002,
```

title = {Log-Correlated Large-Deviation Statistics Governing Huygens Fronts in Turbulence},

author = {Mayo, Jackson R. and Kerstein, Alan R.},

abstractNote = {Analyses have disagreed on whether the velocity uT of bulk advancement of a Huygens front in turbulence vanishes or remains finite in the limit of vanishing local front propagation speed u0. Here, a connection to the large-deviation statistics of log-correlated random processes enables a definitive determination of the correct small-u0 asymptotics. This result reconciles several theoretical and phenomenological perspectives with the conclusion that uT remains finite for vanishing u0, 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 u0 dependence of a bulk length scale associated with front geometry are predicted in this limit. As a result, the analysis involves a formal analogy to random advection of diffusive scalars.},

doi = {10.1007/s10955-019-02306-3},

journal = {Journal of Statistical Physics},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {6}

}