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Updated: Oct 6, 2025
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The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
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Remarks on anomalous dissipation for passive scalars
1Department of Mathematics, Penn State University, University Park, PA 16802, USA.
Summary
This study investigates anomalous dissipation in fluid dynamics, presenting rigorous examples of passive scalars exhibiting unique energy spectra and dissipation properties in the limit of zero diffusivity.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Partial Differential Equations
Background:
- Anomalous dissipation is a key phenomenon in turbulent flows.
- Understanding its mechanisms is crucial for modeling complex fluid behaviors.
Purpose of the Study:
- To review existing knowledge on anomalous dissipation from a mathematical perspective.
- To provide rigorous examples of passive scalars exhibiting anomalous dissipation.
Main Methods:
- Analysis of partial differential equations governing fluid flow.
- Construction of analytical examples of passive scalars.
- Examination of scalar energy spectra and diffusivity limits.
Main Results:
- Demonstrated rigorous examples of scalars with Batchelor-type energy spectra.
- Confirmed anomalous dissipation in the limit of zero scalar diffusivity.
- Connected analytical findings to established turbulence theory.
Conclusions:
- The study provides a rigorous mathematical framework for anomalous dissipation.
- The findings contribute to a deeper understanding of turbulence scaling and energy transfer.
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