Non-Equilibrium Turbulence: A Combined Empirical-Theoretical Approach Toward Improved Understanding in the Post-Kolmogorovean Era

The universal equilibrium assumption is at the very core of the classical theory of turbulence from 1941. Only recently has this assumption been questioned and subsequentlyrecognized as a primary limitation of the theory itself. The theory referred to specifically is the combined work of Lewis Fry Richardson, Andrey Nikolajevitj Kolmogorov, and George Keith Batchelor. It is a theory that has been highly successful in describing flows that are at or near equilibrium, while its predictive capabilities in non-equilibrium conditions have proven significantly more limited. Other, less influential theories exhibit different strengths and weaknesses, yet none provide a universally accurate description. These deficiencies, as outlined in the first part of this dissertation, are also reflected in the lack of effective numerical models capable of producing true predictive simulations
of turbulence.

The second part of this dissertation presents new theoretical, experimental, and numerical developments that propose an alternative description of turbulence physics, grounded in the governing equations of fluid flow and even more fundamental principles, such as Galilean invariance.

A rigorous theoretical framework, substantiated by carefully formulated hypotheses and objectives, has been developed to address the most pressing unresolved questions in turbulence research. These novel methodological concepts aim to establish a robust foundation for significantly advancing our understanding.

Single-point measurements and analyses provide valuable theoretical and empirical insight into the dynamics of turbulence, particularly regarding the nonlinear term in the Navier-Stokes equation. These investigations have illuminated the intricate, yet not necessarily overly complex, nature of turbulence. Insights gained from these studies form a crucial foundation for the subsequent research efforts described in this dissertation.

Capturing the full spatio-temporal complexity of turbulence requires four-dimensional (4D) experiments (space and time). For this purpose, a state-of-the-art laboratory has been designed and constructed, allowing for simultaneous measurement of the instantaneous dissipation rate and the nonlinear processes governing its evolution. The dissipation rate serves as a quantitative measure of non-equilibrium in turbulence, which is controlled by modulating a round turbulent jet from its near-equilibrium stationary state. Since the dissipation rate is also a key parameter in turbulence theory and modeling, this facility enables direct measurement of the full dissipation rate transport equation, making it highly relevant for turbulence modeling.

The experimental approach also examines how non-equilibrium conditions, induced through jet modulation, influence non-local interactions and drive departures from theclassical Richardson cascade. A novel theoretical framework is essential for accurately interpreting these measurements, particularly given the challenges associated with modal analysis in non-stationary turbulent flows.

We are now at a pivotal point where both technological advancements and theoretical developments enable a rigorous re-examination of the fundamental assumption of local equilibrium in turbulence. This dissertation documents research that has led to significant advancements in the field and provided novel insights into turbulence physics. Nonequilibrium turbulence remains one of the least understood types of turbulence, yet it represents the majority of real-world turbulent flows in engineering and natural systems, particularly in areas where predictive capabilities are most needed. The present work lays a combined theoretical and empirical foundation for an improved understanding of turbulence, with direct implications for scientific research and technological applications.