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Updated: Apr 7, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Statistical energy conservation principle for inhomogeneous turbulent dynamical systems
1Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 jonjon@cims.nyu.edu.
Summary
A new theorem precisely quantifies energy exchange between mean flow and turbulent fluctuations in complex systems. This principle aids prediction and uncertainty quantification in engineering and climate science.
Area of Science:
- Turbulence Dynamics
- Fluid Mechanics
- Climate Science
Background:
- Anisotropic turbulent processes across spatiotemporal scales present a grand challenge in engineering and climate science.
- Inhomogeneous turbulent systems exhibit complex interactions between mean flow and fluctuations, impacting prediction and uncertainty quantification.
Purpose of the Study:
- To develop a systematic energy conservation principle for inhomogeneous turbulent dynamical systems.
- To precisely account for statistical energy exchange between mean flow and turbulent fluctuations.
Main Methods:
- Formulation of a Theorem based on statistical energy, defined as the sum of mean energy and the trace of turbulent covariance.
- Assessment of statistical symmetries in nonlinear interactions.
- Application of the theorem to general inhomogeneous turbulent systems.
Main Results:
- A Theorem is presented that precisely accounts for statistical energy exchange.
- Corollaries demonstrate the derivation of closed differential equalities for statistical energy over time.
- The method provides exact or bounded estimates for statistical energy under specific dissipation matrix conditions.
Conclusions:
- The developed energy principle offers a systematic approach to understanding energy dynamics in turbulent systems.
- Implications for low-order closure modeling and single-point variance estimation are discussed.
- This work advances the scientific understanding of complex turbulent phenomena.
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