Periodic Reporting for period 4 - UniEqTURB (Universal Equilibrium and Beyond - Challenging the Richardson-Kolmogorov Paradigm)
Período documentado: 2023-10-01 hasta 2025-09-30
Turbulence is the chaotic motion we see when mixing cream into coffee or when air swirls behind an aircraft. Classical turbulence theory assumes that the smaller swirls behave in a universal and “equilibrium-like” way, largely independent of what happens at the larger scales. This assumption underpins many models used in engineering, industry, and environmental science.
However, evidence has long suggested that this analogy breaks down in many real-world flows. When gases or liquids accelerate or change rapidly in space or time—as in jet engines, wind turbine wakes, propeller flows, or fuel injection—turbulence can be pushed out of equilibrium. This “non-equilibrium turbulence” is believed to be widespread and technologically important, yet it remains the least understood regime.
The goal of the project was to determine when the classical assumptions fail and to identify how sensitive turbulence is to changes in space and time. To achieve this, the project combined three elements:
- A theoretical framework linking observed turbulent motion directly to the governing equations.
- Advanced laboratory measurements, capturing both the largest structures and the smallest, energy-dissipating scales with unprecedented precision.
- High-resolution numerical simulations, used to support the analysis and to guide the design of the experiments and laboratory facility.
A major achievement of the project was the establishment of a new experimental laboratory capable of measuring both the largest and the smallest relevant turbulent scales. This required pushing technical limits and developing new solutions.
The combined theoretical, experimental, and computational work has shown clearly that accelerations in time and space do cause turbulence to deviate from equilibrium. The exchange of energy between different scales is directly affected—as is the dissipation of energy into heat, a key parameter in all turbulence models. These findings confirm that classical equilibrium-based theories do not fully describe many flows of practical relevance.
A better understanding of non-equilibrium turbulence has broad societal importance. Turbulence influences almost every form of transportation, the performance of machines operating in air and water, and the accuracy of weather and climate predictions. Improving our ability to model turbulence, especially in non-equilibrium conditions, will therefore have a significant impact across engineering and the natural sciences.
The project concludes that non-equilibrium turbulence is not an exception but a common state of turbulent flows. The new insights and measurement capabilities developed here lay the foundation for the next generation of turbulence models and for future research into this critical, yet previously underexplored, regime.
However, evidence has long suggested that this analogy breaks down in many real-world flows. When gases or liquids accelerate or change rapidly in space or time—as in jet engines, wind turbine wakes, propeller flows, or fuel injection—turbulence can be pushed out of equilibrium. This “non-equilibrium turbulence” is believed to be widespread and technologically important, yet it remains the least understood regime.
The goal of the project was to determine when the classical assumptions fail and to identify how sensitive turbulence is to changes in space and time. To achieve this, the project combined three elements:
- A theoretical framework linking observed turbulent motion directly to the governing equations.
- Advanced laboratory measurements, capturing both the largest structures and the smallest, energy-dissipating scales with unprecedented precision.
- High-resolution numerical simulations, used to support the analysis and to guide the design of the experiments and laboratory facility.
A major achievement of the project was the establishment of a new experimental laboratory capable of measuring both the largest and the smallest relevant turbulent scales. This required pushing technical limits and developing new solutions.
The combined theoretical, experimental, and computational work has shown clearly that accelerations in time and space do cause turbulence to deviate from equilibrium. The exchange of energy between different scales is directly affected—as is the dissipation of energy into heat, a key parameter in all turbulence models. These findings confirm that classical equilibrium-based theories do not fully describe many flows of practical relevance.
A better understanding of non-equilibrium turbulence has broad societal importance. Turbulence influences almost every form of transportation, the performance of machines operating in air and water, and the accuracy of weather and climate predictions. Improving our ability to model turbulence, especially in non-equilibrium conditions, will therefore have a significant impact across engineering and the natural sciences.
The project concludes that non-equilibrium turbulence is not an exception but a common state of turbulent flows. The new insights and measurement capabilities developed here lay the foundation for the next generation of turbulence models and for future research into this critical, yet previously underexplored, regime.
From the start of the project to its conclusion, the work focused on establishing the experimental, theoretical, and computational foundations needed to investigate non-equilibrium turbulence. The project has in essence successfully completed all planned activities.
A major achievement was the creation of a new world-leading laboratory for fundamental turbulence research. The project designed and built flow-generation facilities capable of producing turbulent flows with controllable levels of non-equilibrium, and developed advanced laser-based measurement techniques required to study both the smallest and the largest relevant flow scales. Two extensive experimental campaigns were completed: one resolved the tiny dissipative scales to quantify departures from equilibrium, and one captured the global turbulence dynamics in time and all three spatial dimensions. These campaigns required significant innovation in laser diagnostics, data acquisition, and big-data handling, all of which now operate at a mature and reliable level.
In parallel, a suite of fully resolved Direct Numerical Simulations was carried out early in the project. These simulations, which compute all relevant turbulent scales directly from the governing equations, were essential for developing the theoretical framework, guiding the analysis methods, and informing the design of the experimental facilities. Their successful execution required substantial computational resources and storage capacity.
A central scientific contribution of the project is the development of a new theoretical framework for analyzing turbulence under non-equilibrium conditions. By revisiting and extending classical mathematical formulations, the project produced tools capable of describing more complex and realistic turbulent flows than those assumed in traditional equilibrium theory. Using this framework, it was possible to quantify the degree of non-equilibrium and to characterize how energy is exchanged between turbulent scales when the flow is accelerated or otherwise perturbed. Notably, the analysis revealed that even flows traditionally considered “equilibrium turbulence” exhibit subtle non-equilibrium dynamical features.
The results have been disseminated widely through invited and contributed presentations at international conferences and workshops, as well as through journal publications. The project’s scientific advances have also been consolidated in the PI’s Doctor Technices dissertation, a thesis-based degree awarded in Denmark to recognize exceptional scientific achievement and significant contributions to engineering and technological science.
Overall, the project delivered a unique combination of new experimental infrastructure, advanced theoretical tools, and high-fidelity computational data. Together, these outcomes provide a solid foundation for future turbulence modeling efforts and will facilitate continued exploitation of the results by the broader research community.
A major achievement was the creation of a new world-leading laboratory for fundamental turbulence research. The project designed and built flow-generation facilities capable of producing turbulent flows with controllable levels of non-equilibrium, and developed advanced laser-based measurement techniques required to study both the smallest and the largest relevant flow scales. Two extensive experimental campaigns were completed: one resolved the tiny dissipative scales to quantify departures from equilibrium, and one captured the global turbulence dynamics in time and all three spatial dimensions. These campaigns required significant innovation in laser diagnostics, data acquisition, and big-data handling, all of which now operate at a mature and reliable level.
In parallel, a suite of fully resolved Direct Numerical Simulations was carried out early in the project. These simulations, which compute all relevant turbulent scales directly from the governing equations, were essential for developing the theoretical framework, guiding the analysis methods, and informing the design of the experimental facilities. Their successful execution required substantial computational resources and storage capacity.
A central scientific contribution of the project is the development of a new theoretical framework for analyzing turbulence under non-equilibrium conditions. By revisiting and extending classical mathematical formulations, the project produced tools capable of describing more complex and realistic turbulent flows than those assumed in traditional equilibrium theory. Using this framework, it was possible to quantify the degree of non-equilibrium and to characterize how energy is exchanged between turbulent scales when the flow is accelerated or otherwise perturbed. Notably, the analysis revealed that even flows traditionally considered “equilibrium turbulence” exhibit subtle non-equilibrium dynamical features.
The results have been disseminated widely through invited and contributed presentations at international conferences and workshops, as well as through journal publications. The project’s scientific advances have also been consolidated in the PI’s Doctor Technices dissertation, a thesis-based degree awarded in Denmark to recognize exceptional scientific achievement and significant contributions to engineering and technological science.
Overall, the project delivered a unique combination of new experimental infrastructure, advanced theoretical tools, and high-fidelity computational data. Together, these outcomes provide a solid foundation for future turbulence modeling efforts and will facilitate continued exploitation of the results by the broader research community.
Progress beyond the state of the art:
- A measurement system for dissipation at unprecedented resolution: The project developed a unique experimental setup capable of resolving the smallest turbulent scales where energy is dissipated. This represents a significant advance in our ability to quantify non-equilibrium turbulence directly and accurately.
- Large-volume laser diagnostics for particle tracking: New laser-based measurement tools and experimental techniques were created to capture much larger flow volumes than previously possible, enabling simultaneous observation of global turbulent dynamics in three dimensions and time.
- A new theoretical framework for non-equilibrium turbulence: The project established a mathematically rigorous approach to describe and decompose turbulence under realistic, non-equilibrium conditions. This framework allows correct quantification of energy transfer between scales and extends classical theory to flows that vary in space and time.
- Quantitative characterization of non-equilibrium effects: The project produced the first detailed measurements linking varying degrees of non-equilibrium to changes in turbulent structure, energy exchange, and dissipation. These results provide new physical insight into how turbulence departs from classical equilibrium behaviour.
Since the project has been completed, all expected results have been achieved. The main outcomes - new measurement capabilities, theoretical tools, and quantitative evidence of non-equilibrium turbulence - are now fully available for use in ongoing and future research and model development.
- A measurement system for dissipation at unprecedented resolution: The project developed a unique experimental setup capable of resolving the smallest turbulent scales where energy is dissipated. This represents a significant advance in our ability to quantify non-equilibrium turbulence directly and accurately.
- Large-volume laser diagnostics for particle tracking: New laser-based measurement tools and experimental techniques were created to capture much larger flow volumes than previously possible, enabling simultaneous observation of global turbulent dynamics in three dimensions and time.
- A new theoretical framework for non-equilibrium turbulence: The project established a mathematically rigorous approach to describe and decompose turbulence under realistic, non-equilibrium conditions. This framework allows correct quantification of energy transfer between scales and extends classical theory to flows that vary in space and time.
- Quantitative characterization of non-equilibrium effects: The project produced the first detailed measurements linking varying degrees of non-equilibrium to changes in turbulent structure, energy exchange, and dissipation. These results provide new physical insight into how turbulence departs from classical equilibrium behaviour.
Since the project has been completed, all expected results have been achieved. The main outcomes - new measurement capabilities, theoretical tools, and quantitative evidence of non-equilibrium turbulence - are now fully available for use in ongoing and future research and model development.