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

Mayo, Jackson R.; Kerstein, Alan R.

doi:10.1007/s10955-019-02306-3

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

Journal Article · Tue Jun 11 00:00:00 EDT 2019 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/s10955-019-02306-3· OSTI ID:1529002

Mayo, Jackson R. ^[1]; ^[2]

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

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 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 u_T 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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1529002

Report Number(s):: SAND--2019-5017J; 675258

Journal Information:: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 2 Vol. 17; ISSN 0022-4715

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (35)

Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov McKean, H. P. Communications on Pure and Applied Mathematics, Vol. 28, Issue 3 https://doi.org/10.1002/cpa.3160280302	journal	May 1975
Counting Function Fluctuations and Extreme Value Threshold in Multifractal Patterns: The Case Study of an Ideal 1/f Noise Fyodorov, Yan V.; Le Doussal, Pierre; Rosso, Alberto Journal of Statistical Physics, Vol. 149, Issue 5 https://doi.org/10.1007/s10955-012-0623-6	journal	November 2012
Scaling of Huygens-front speedup in weakly random media Mayo, Jackson R.; Kerstein, Alan R. Physics Letters A, Vol. 372, Issue 1 https://doi.org/10.1016/j.physleta.2007.06.078	journal	December 2007
Front propagation into unstable states Vansaarloos, W. Physics Reports, Vol. 386, Issue 2-6 https://doi.org/10.1016/j.physrep.2003.08.001	journal	November 2003
Turbulent Combustion Poinsot, Thierry European Journal of Mechanics - B/Fluids, Vol. 20, Issue 3 https://doi.org/10.1016/s0997-7546(01)01134-7	journal	May 2001
Turbulent Combustion Peters, Norbert Cambridge University Press https://doi.org/10.1017/CBO9780511612701	book	January 2010
Turbulence: The Legacy of A. N. Kolmogorov Frisch, Uriel https://doi.org/10.1017/CBO9781139170666	book	January 1996
Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity Batchelor, G. K. Journal of Fluid Mechanics, Vol. 5, Issue 01 https://doi.org/10.1017/S002211205900009X	journal	January 1959
Observation of void formation patterns in SnAg films undergoing electromigration and simulation using random walk methods Jin, Zhi; Shen, Yu-An; Zuo, Yang Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-88122-w	journal	April 2021
Fine Structure of Scalar Fields Mixed by Turbulence. I. Zero-Gradient Points and Minimal Gradient Surfaces Gibson, Carl H. Physics of Fluids, Vol. 11, Issue 11 https://doi.org/10.1063/1.1691820	journal	January 1968
Self-similarly developing, premixed, turbulent flames: A theoretical study Lipatnikov, A. N.; Chomiak, J. Physics of Fluids, Vol. 17, Issue 6 https://doi.org/10.1063/1.1921250	journal	June 2005
Scaling properties of the viscous‐convective scalar spectral subrange in turbulent jets Kerstein, Alan R. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7 https://doi.org/10.1063/1.857911	journal	July 1991
Propagation Velocity of Premixed Turbulent Flames No authors listed Combustion Science and Technology, Vol. 60, Issue 1-3 https://doi.org/10.1080/00102208808923984	journal	July 1988
One-Dimensional Propagation of a Premixed Turbulent Flame With a Balance Equation for the Flame Surface Density Fichot, Florian; Lacas, FranÇOis; Veynante, Denis Combustion Science and Technology, Vol. 90, Issue 1-4 https://doi.org/10.1080/00102209308907602	journal	April 1993
TYPE Ia SUPERNOVAE: CALCULATIONS OF TURBULENT FLAMES USING THE LINEAR EDDY MODEL Woosley, S. E.; Kerstein, A. R.; Sankaran, V. The Astrophysical Journal, Vol. 704, Issue 1 https://doi.org/10.1088/0004-637X/704/1/255	journal	September 2009
Turbulent Combustion Peters, Norbert Measurement Science and Technology, Vol. 12, Issue 11 https://doi.org/10.1088/0957-0233/12/11/708	journal	October 2001
On symmetries and averaging of the G -equation for premixed combustion Oberlack, M.; Wenzel, H.; Peters, N. Combustion Theory and Modelling, Vol. 5, Issue 3 https://doi.org/10.1088/1364-7830/5/3/307	journal	September 2001
Field equation for interface propagation in an unsteady homogeneous flow field Kerstein, Alan R.; Ashurst, William T.; Williams, Forman A. Physical Review A, Vol. 37, Issue 7 https://doi.org/10.1103/PhysRevA.37.2728	journal	April 1988
Lagrangian path integrals and fluctuations in random flow Shraiman, Boris I.; Siggia, Eric D. Physical Review E, Vol. 49, Issue 4 https://doi.org/10.1103/PhysRevE.49.2912	journal	April 1994
Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution Chertkov, M.; Falkovich, G.; Kolokolov, I. Physical Review E, Vol. 51, Issue 6 https://doi.org/10.1103/PhysRevE.51.5609	journal	June 1995
Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem Balkovsky, E.; Fouxon, A. Physical Review E, Vol. 60, Issue 4 https://doi.org/10.1103/PhysRevE.60.4164	journal	October 1999
Fronts in randomly advected and heterogeneous media and nonuniversality of Burgers turbulence: Theory and numerics Mayo, Jackson R.; Kerstein, Alan R. Physical Review E, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevE.78.056307	journal	November 2008
Spatial Intermittency of Surface Layer Wind Fluctuations at Mesoscale Range Baïle, Rachel; Muzy, Jean-François Physical Review Letters, Vol. 105, Issue 25 https://doi.org/10.1103/PhysRevLett.105.254501	journal	December 2010
Decay of Turbulence at High Reynolds Numbers Sinhuber, Michael; Bodenschatz, Eberhard; Bewley, Gregory P. Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/PhysRevLett.114.034501	journal	January 2015
Propagation rate of growing interfaces in stirred fluids Kerstein, Alan R.; Ashurst, Wm. T. Physical Review Letters, Vol. 68, Issue 7 https://doi.org/10.1103/PhysRevLett.68.934	journal	February 1992
Front Propagation Rates in Randomly Stirred Media Ronney, P. D.; Haslam, B. D.; Rhys, N. O. Physical Review Letters, Vol. 74, Issue 19 https://doi.org/10.1103/PhysRevLett.74.3804	journal	May 1995
Propagation of a Huygens Front Through Turbulent Medium Chertkov, M.; Yakhot, V. Physical Review Letters, Vol. 80, Issue 13 https://doi.org/10.1103/PhysRevLett.80.2837	journal	March 1998
Stochastic Problems in Physics and Astronomy Chandrasekhar, S. Reviews of Modern Physics, Vol. 15, Issue 1 https://doi.org/10.1103/RevModPhys.15.1	journal	January 1943
A multiresolution hierarchical approach to image segmentation based on intensity extrema Lifshitz, L. M.; Pizer, S. M. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, Issue 6 https://doi.org/10.1109/34.56189	journal	June 1990
Turbulent Combustion Peters,, N.; Kanury,, Am Applied Mechanics Reviews, Vol. 54, Issue 4 https://doi.org/10.1115/1.1383686	journal	July 2001
Level Surfaces of Gaussian Random Fields and Microemulsions Teubner, M. Europhysics Letters (EPL), Vol. 14, Issue 5 https://doi.org/10.1209/0295-5075/14/5/003	journal	March 1991
harmonic Giacomin, Giambattista; Deuschel, Jean-Dominique; Bolthausen, Erwin The Annals of Probability, Vol. 29, Issue 4 https://doi.org/10.1214/aop/1015345767	journal	October 2001
Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal $1/f$ noise Fyodorov, Yan V.; Doussal, Pierre Le; Rosso, Alberto arXiv https://doi.org/10.48550/arxiv.1207.4614	text	January 2012
Propagation of a Huygens front through turbulent medium Chertkov, M.; Yakhot, V. arXiv https://doi.org/10.48550/arxiv.chao-dyn/9709028	text	January 1997
Scaling of Huygens-front speedup in weakly random media Mayo, Jackson R.; Kerstein, Alan R. arXiv https://doi.org/10.48550/arxiv.physics/0702211	text	January 2007

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Fig. 1(p. 8)

Fig. 2(p. 20)

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