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Universal Equilibrium and Beyond - Challenging the Richardson-Kolmogorov Paradigm

Periodic Reporting for period 1 - UniEqTURB (Universal Equilibrium and Beyond - Challenging the Richardson-Kolmogorov Paradigm)

Reporting period: 2019-04-01 to 2020-09-30

The objective of the project is to test the range of validity of the classical theory of turbulence. When e.g. mixing cream into coffee, one can observe whorls of various sizes (scales). The classical theory assumes that turbulence at the small and intermediate scales behave similarly to molecules in a thermal equilibrium, i.e. statistically they are at a state of equilibrium and even universal (same for all turbulent flows) - no matter what the dynamics at the large scales. However, the analogy halts at several instances. Not least since even molecules (that are much smaller than turbulent scales) can be pushed out of equilibrium.

Prominent examples of potentially significant non-equilibrium turbulence of technological importance is jet engines, wind turbine wakes, propeller wakes and unsteady fuel injection. However, non-equilibrium turbulence is believed to exist in much less fiercely accelerated flows.

The study is being carried out using
- a theoretical framework that describes turbulence mathematically based on the governing equations
- direct measurements. Two types of measurements are being carried out: one covering the large scales and one covering the smallest relevant scales.

The theoretical framework allows us to describe turbulence based on the governing equations, while the large scale measurements will provide the dynamics of the turbulence that can fulfill the equations. This will allow us to test whether the energy exchange between scales is in fact dominatingly between scales of similar size (as predicted by the classical theory) or if other types of energy exchange can be possible. This is particularly interesting to study in turbulence being pushed out of equilibrium. We will compare the experimental findings to further develop and understand the theoretical description.

The small scale measurements resolve the dissipative scales (where kinetic energy predominating is converted to heat through friction-based processes). This will quantify directly how much the flow is pushed out of equilibrium and provide modeling parameters that can be directly implemented.

If we can better understand and model non-equilibrium turbulence, which is of immense technological importance, then it will have a broad impact in engineering and natural science. This is very much basic research indeed, but the results will be directly applicable to analytical and computational modeling. Turbulence is omnipresent and the impact of a successfully carried out project is difficult to overestimate.
- Establishment of the laboratory (in the finalizing stage)
- Development of flow generating facilities suitable to test controllable degrees of non-equilibrium turbulence (in the finalizing stage)
- Development of new laser diagnostics tools to carry out challenging measurements pushing the limits at both the largest and the smallest relevant scales (in the finalizing stage)
- Theory-intensitve Direct Numerical Simulations (without the need to model any part of the turbulence)
- Development of the main strokes of the theoretical framework necessary to analyze measurement and simulation data
- So far, theoretical and experimental results support the hypothesis that turbulence can indeed behave very differently from the classical theory
Progress beyond state of the art:
- Development of unprecedented, sophisticated measurement system to measure dissipation (the smallest relevant turbulent scales)
- Development of laser diagnostics to cover larger volumes than previously reported in particle tracking measurements
- Development of a mathematical framework to decompose turbulence in realistic settings in a correct manner. This will allow correct analysis of energy exchange between scales.

Expected results until end of the project:
- Quantitative measurements of the effect of various degrees of non-equilibrium and an understanding of the physical processes leading to the obtained state