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Exact relation for correlation functions in compressible isothermal turbulence
Sébastien Galtier1, Supratik Banerjee
1Université Paris-Sud, Institut d'Astrophysique Spatiale, UMR, Orsay, France.
Physical Review Letters
|October 27, 2011
Summary
Compressible isothermal turbulence exhibits unique energy transfer dynamics due to a novel term in its correlation functions, differing from incompressible turbulence. This suggests a modified energy cascade in high Reynolds number flows.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Statistical Mechanics
Background:
- Compressible isothermal turbulence at high Reynolds numbers presents unique challenges.
- Understanding energy transfer mechanisms is crucial for modeling turbulent flows.
- Existing models often simplify turbulence, neglecting compressibility effects.
Purpose of the Study:
- To analyze compressible isothermal turbulence under homogeneity and high Reynolds number assumptions.
- To derive exact relations for two-point correlation functions.
- To identify fundamental differences compared to incompressible turbulence.
Main Methods:
- Analysis of homogeneous, high Reynolds number compressible isothermal turbulence.
- Derivation of exact relations for two-point correlation functions.
- Application of isotropy assumption to derive specific turbulence relations.
Main Results:
- An exact relation for two-point correlation functions was derived, highlighting differences from incompressible turbulence.
- A new term was identified, acting as a source or sink for mean energy transfer in the inertial range.
- Under isotropy, a relation involving an effective energy injection rate was established.
Conclusions:
- Compressible turbulence introduces novel energy transfer mechanisms not present in incompressible flows.
- The derived relation offers new insights into the dynamics of compressible turbulence.
- A k(-5/3) spectrum may be preserved at small scales using density-weighted velocity.
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