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Dissipation, intermittency, and singularities in incompressible turbulent flows
P Debue1, V Shukla1, D Kuzzay1,2
1DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France.
Physical Review. E
|June 17, 2018
Summary
Singularities in fluid dynamics, specifically the incompressible Navier-Stokes equation, drive intermittency by influencing energy transfer and dissipation. This study analyzes turbulent flows to understand these connections.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Statistical Mechanics
Background:
- Intermittency in turbulent flows is a key phenomenon.
- Understanding the role of singularities in energy dissipation is crucial.
- The incompressible Navier-Stokes equation (INSE) governs fluid motion.
Purpose of the Study:
- To investigate the link between singularities/quasisingularities in INSE solutions and local energy transfer/dissipation.
- To explore how these singularities contribute to intermittency.
- To support the multifractal description of intermittency.
Main Methods:
- Analysis of velocity fields from turbulent von Kármán swirling flow experiments and INSE direct numerical simulations.
- Application of a generalized Kármán-Howarth-Monin equation for weak solutions.
- Computation of local interscale energy transfer and viscous dissipation.
Main Results:
- The formulation reveals nonzero inertial dissipation at infinite resolution in the presence of singularities.
- It provides expressions for energy transfer down to viscous scales and quantifies quasisingularity contributions to dissipation.
- Extreme energy transfer events govern intermittency corrections and align with refined similarity hypotheses.
Conclusions:
- The study provides concrete support for the multifractal description of intermittency.
- Probability distributions of extreme events are characterized by generalized Pareto distributions, indicating similarity of the second kind.
- Connections are established between topological, statistical, and multifractal properties of extreme energy transfer events.
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