Large deviations, singularity, and lognormality of energy dissipation in turbulence

Physical Review. E
Itzhak Fouxon, Changhoon Lee

Abstract

We study implications of the assumption of power-law dependence of moments of energy dissipation in turbulence on the Reynolds number Re, holding due to intermittency. We demonstrate that at Re→∞ the dissipation's logarithm divided by lnRe converges with probability one to a negative constant. This implies that the dissipation is singular in the limit, as is known phenomenologically. The proof uses a large deviations function, whose existence is implied by the power-law assumption, and which provides the general asymptotic form of the dissipation's distribution. A similar function exists for vorticity and for velocity differences where it proves the moments representation of the multifractal model (MF). Then we observe that derivative of the scaling exponents of the dissipation, considered as a function of the order of the moment, is small at the origin. Thus the variation with the order is slow and can be described by a quadratic function. Indeed, the quadratic function, which corresponds to log-normal statistics, fits the data. Moreover, combining the lognormal scaling with the MF we derive a formula for the anomalous scaling exponents of turbulence which also fits the data. Thus lognormality, not to be confused with the Kolm...Continue Reading

References

Feb 1, 1986·Physical Review A: General Physics·T C HalseyB I Shraiman
Dec 15, 1990·Physical Review. a·M Nelkin
Feb 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P TabelingH Willaime
Jan 17, 1994·Physical Review Letters·Z S She, E Leveque
Apr 8, 1996·Physical Review Letters·M Chertkov, G Falkovich
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V Yakhot
Sep 13, 2002·Physical Review Letters·Ch RennerB Chabaud
Sep 13, 2002·Nature·G FalkovichM G Stepanov
Jul 16, 2014·Proceedings of the National Academy of Sciences of the United States of America·Jörg SchumacherKatepalli R Sreenivasan
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jonas Boschung
Mar 17, 2017·Physical Review. E·Kartik P IyerP K Yeung

❮ Previous
Next ❯

Citations

Apr 18, 2021·Physical Review. E·Itzhak FouxonMichael Mond

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
G StolovitzkyA Juneja
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
S Grossmann
© 2021 Meta ULC. All rights reserved