Anomalous Dissipation in Passive Scalar Transport

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Drivas, TD; Elgindi, TM; Iyer, G; Jeong, IJ

Published Date

  • March 1, 2022

Published In

Volume / Issue

  • 243 / 3

Start / End Page

  • 1151 - 1180

Electronic International Standard Serial Number (EISSN)

  • 1432-0673

International Standard Serial Number (ISSN)

  • 0003-9527

Digital Object Identifier (DOI)

  • 10.1007/s00205-021-01736-2

Citation Source

  • Scopus