Anomalous Dissipation in Passive Scalar Transport
Publication
, Journal Article
Drivas, TD; Elgindi, TM; Iyer, G; Jeong, IJ
Published in: Archive for Rational Mechanics and Analysis
March 1, 2022
We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible C∞([0 , T) × Td) ∩ L1([0 , T] ; C1 -(Td)) velocity field which explicitly exhibits anomalous dissipation. As a consequence, this example also shows the non-uniqueness of solutions to the transport equation with an incompressible L1([0 , T] ; C1 -(Td)) drift, which is smooth except at one point in time. We also give a sufficient condition for anomalous dissipation based on solutions to the inviscid equation becoming singular in a controlled way. Finally, we discuss connections to the Obukhov-Corrsin monofractal theory of scalar turbulence along with other potential applications.
Duke Scholars
Published In
Archive for Rational Mechanics and Analysis
DOI
EISSN
1432-0673
ISSN
0003-9527
Publication Date
March 1, 2022
Volume
243
Issue
3
Start / End Page
1151 / 1180
Related Subject Headings
- General Physics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Drivas, T. D., Elgindi, T. M., Iyer, G., & Jeong, I. J. (2022). Anomalous Dissipation in Passive Scalar Transport. Archive for Rational Mechanics and Analysis, 243(3), 1151–1180. https://doi.org/10.1007/s00205-021-01736-2
Drivas, T. D., T. M. Elgindi, G. Iyer, and I. J. Jeong. “Anomalous Dissipation in Passive Scalar Transport.” Archive for Rational Mechanics and Analysis 243, no. 3 (March 1, 2022): 1151–80. https://doi.org/10.1007/s00205-021-01736-2.
Drivas TD, Elgindi TM, Iyer G, Jeong IJ. Anomalous Dissipation in Passive Scalar Transport. Archive for Rational Mechanics and Analysis. 2022 Mar 1;243(3):1151–80.
Drivas, T. D., et al. “Anomalous Dissipation in Passive Scalar Transport.” Archive for Rational Mechanics and Analysis, vol. 243, no. 3, Mar. 2022, pp. 1151–80. Scopus, doi:10.1007/s00205-021-01736-2.
Drivas TD, Elgindi TM, Iyer G, Jeong IJ. Anomalous Dissipation in Passive Scalar Transport. Archive for Rational Mechanics and Analysis. 2022 Mar 1;243(3):1151–1180.
Published In
Archive for Rational Mechanics and Analysis
DOI
EISSN
1432-0673
ISSN
0003-9527
Publication Date
March 1, 2022
Volume
243
Issue
3
Start / End Page
1151 / 1180
Related Subject Headings
- General Physics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics