Transitions of turbulent superstructures in generalized Kolmogorov flow (2102.07675v2)

Abstract: Self-organized large-scale flow structures occur in a wide range of turbulent flows. Yet, their emergence, dynamics, and interplay with small-scale turbulence are not well understood. Here, we investigate such self-organized turbulent superstructures in three-dimensional turbulent Kolmogorov flow with large-scale drag. Through extensive simulations, we uncover their low-dimensional dynamics featuring transitions between several stable and meta-stable large-scale structures as a function of the damping parameter. The main dissipation mechanism for the turbulent superstructures is the generation of small-scale turbulence, whose local structure depends strongly on the large-scale flow. Our results elucidate the generic emergence and low-dimensional dynamics of large-scale flow structures in fully developed turbulence and reveal a strong coupling of large- and small-scale flow features.

• The paper demonstrates that damping parameters induce multiple stable and metastable superstructure states in turbulent flows.
• It employs pseudo-spectral DNS to capture scale interactions, revealing that increased damping enhances energy transfer and dissipation.
• The study shows a pronounced lag between large-scale energy injection and small-scale dissipation, underscoring complex cascade dynamics.

Analysis of Turbulent Superstructures in Generalized Kolmogorov Flow

The paper titled "Transitions of Turbulent Superstructures in Generalized Kolmogorov Flow" by Cristian C. Lalescu and Michael Wilczek embarks on an in-depth simulation-based analysis of large-scale flow structures in turbulent environments. This investigation forms part of a critical effort to enhance understanding of the intricate dynamics governing turbulence, particularly in contexts where traditional Kolmogorov turbulence theories might fall short.

Background and Motivation

The research focuses on turbulent superstructures—large-scale flow features that persist in fully developed turbulence. Such superstructures are prevalent in numerous naturally occurring flows, such as oceanic currents, atmospheric patterns, and thermal convection. Historically, the emergence of these structures and their interplay with small-scale turbulence have been profoundly complex to quantify or predict. The paper leverages a generalized three-dimensional (3D) turbulent Kolmogorov flow model to mitigate boundary effects and underscore the dynamic behavior of these superstructures across varying damping scales.

Methodology

The authors employ extensive pseudo-spectral direct numerical simulations (DNS) to simulate a 3D generalized Kolmogorov flow that incorporates a large-scale drag term. This term is crucial as it allows an examination of how different scales—specifically, the interaction between large-scale superstructures and the finely detailed small-scale turbulence—are influenced by alternating damping parameters. A periodic domain was used to maintain consistency and remove boundary-induced complexities. The paper covers a wide spectrum of Reynolds numbers, up to around 18,100, providing a robust basis for analyzing turbulence in different flow regimes.

Key Findings

1. Emergence and Transition of Superstructures: The research identifies multiple stable and metastable states of large-scale turbulent superstructures that are particularly sensitive to damping parameters. For instance, flow systems characterized by strong damping most effectively resonated with shear forcing, thus maximizing energy input.
2. Energy Dynamics: The energy input into the flow sharply increases with the damping parameter, revealing a counterintuitive dynamic where higher damping results in enhanced energy transfer to the flow. This energy is primarily dissipated through 3D turbulence, corroborating a strong coupling between large-scale and small-scale dynamics.
3. Temporal and Spatial Dynamics: The temporal correlation analysis reveals significant oscillations in energy transfer across scales. Particularly, there is a notable lag between large-scale energy injection and small-scale dissipation rates, highlighting the scale-dependent energy cascade dynamics.

Theoretical and Practical Implications

The findings underscore the importance of considering both large- and small-scale dynamics in turbulent flow modelling, especially since traditional homogenous turbulence models could neglect significant scale interactions. These insights have profound implications for developing predictive models and theoretical frameworks that can better accommodate and anticipate the behaviors of geophysical and astrophysical flows.

Future Directions

The paper opens avenues for more granular investigations into energy transfer mechanisms in turbulence, including explorations of alternative force configurations or aspects of Kolmogorov flow modifications. Moreover, the discovery of low-dimensional dynamics suggests the potential for simplified models that still capture critical superstructure behaviors across various flow regimes, possibly extending into coupled systems beyond fluid mechanics, such as climate models and industrial fluid dynamics applications.

In summary, Lalescu and Wilczek's exploration of generalized Kolmogorov flow provides a significant contribution to turbulence research by elucidating the nuanced interactions between large-scale and small-scale dynamics, establishing a foundation for further investigations into complex flow systems.