Inverse Energy Cascade and Intermittent Scaling in Two-Dimensional Bacterial Turbulence

Основные понятия

The collective movements of bacteria exhibit turbulence-like vortices, where the Richardson cascade plays an important role. The study examines the energy and enstrophy cascades and their associated lognormal statistics, confirming the coexistence of the inverse energy cascade and the intermittency correction of the velocity scaling in this active fluid system.

Аннотация

The content examines the energy and enstrophy cascades and their associated lognormal statistics in the context of two-dimensional bacterial turbulence.

Key highlights:

• The coherent structure observed on a large scale is due to the presence of the inverse energy cascade, while the kinetic energy is dissipated at all scales as these active movements occur below the fluid viscosity scale.
• The forward enstrophy cascade occurs with injection at all scales and may be represented by other nonlinear interactions not captured by the experimental data.
• The lognormal statistics for both energy dissipation and enstrophy fields are verified in accordance with Kolmogorov's 1962 refined theory of turbulence, with scaling exponents comparable to three-dimensional hydrodynamic turbulence.
• The joint analysis of the multifractal measures of the energy dissipation rate and enstrophy follows an ellipse model from the lognormal statistics.
• The results confirm the coexistence of the inverse energy cascade and the intermittency correction of the velocity scaling in this active fluid system.
• An inverse energy cascade diagram below the fluid viscosity is summarized to describe the observed two-dimensional bacterial turbulence.

Статистика

The global balance between energy injection and dissipation can be written as: Ein = ∫ Ein(r)dr = ∫ Bν(r)dr = ε.
In the inertial range, the asymptotic conservation relation is expected: Ein ≃ ̃Π[r] ≃ ε.

Цитаты

"The coherent structure observed on a large scale is due to the presence of the inverse energy cascade; while the kinetic energy is dissipated at all scales, since these active movements occur below the fluid viscosity scale."
"The forward enstrophy cascade occurs with injection at all scales and may be represented by other nonlinear interactions that are not captured by the existing experimental data."
"The lognormal statistics for both energy dissipation and enstrophy fields are verified in accordance with the Kolmogorov 1962 refined theory of turbulence."

Ключевые выводы из

Cascades and Kolmogorov's lognormal scaling in two-dimensional bacterial turbulence

by Yongxiang Hu... в arxiv.org 10-03-2024

https://arxiv.org/pdf/2410.01361.pdf

Дополнительные вопросы

How do the scaling exponents of the lognormal statistics in two-dimensional bacterial turbulence compare to those observed in other active fluid systems?

The scaling exponents of the lognormal statistics in two-dimensional bacterial turbulence exhibit similarities to those found in other active fluid systems, particularly in three-dimensional hydrodynamic turbulence. In the study, the lognormal statistics for both energy dissipation and enstrophy fields were verified in accordance with Kolmogorov's refined theory of turbulence, which suggests that the scaling behavior is influenced by the underlying intermittency of the flow. The intermittency parameters derived from the bacterial turbulence are comparable to those observed in three-dimensional turbulence, indicating that despite the differences in dimensionality and the nature of the active agents (bacteria versus fluid particles), the fundamental scaling laws governing energy dissipation and enstrophy remain consistent across these systems. This suggests a universal behavior in the scaling exponents, which can be attributed to the shared characteristics of turbulent flows, such as the presence of coherent structures and the bidirectional nature of energy cascades.

What are the potential limitations of the experimental data used in this study, and how might additional data or simulations help to further elucidate the underlying mechanisms of the inverse energy cascade and intermittency in this system?

The experimental data used in the study may have several limitations, including the constraints of spatial and temporal resolution, which can affect the accuracy of the measurements of velocity fields and energy dissipation rates. Additionally, the experimental setup may not fully capture the range of scales involved in the turbulence, particularly the smallest scales where dissipation occurs. The presence of noise and other environmental factors could also introduce uncertainties in the data. To address these limitations, additional data collection through high-resolution imaging techniques or advanced particle tracking methods could provide more detailed insights into the flow dynamics. Furthermore, numerical simulations could complement the experimental findings by allowing for controlled variations in parameters such as Reynolds number and forcing scales. These simulations could help to explore the mechanisms of the inverse energy cascade and intermittency in greater depth, potentially revealing new phenomena or confirming theoretical predictions that are not easily observable in experimental settings.

Given the similarities between two-dimensional bacterial turbulence and other active fluid systems, what insights from this study could be applied to understanding the dynamics of other complex, non-equilibrium systems in biology, physics, or engineering?

The insights gained from the study of two-dimensional bacterial turbulence can be broadly applied to various complex, non-equilibrium systems across different fields. The identification of dual cascades—an inverse energy cascade and a forward enstrophy cascade—highlights the importance of energy transfer mechanisms in active systems, which can be relevant in biological contexts such as cellular motility and collective behavior in swarms. The lognormal statistics observed in the energy dissipation and enstrophy fields suggest that similar scaling laws may govern other active systems, including those in ecological dynamics or fluid dynamics in engineering applications. Additionally, the study's findings on intermittency and multifractality could inform models of turbulence in atmospheric sciences or the behavior of complex fluids in industrial processes. By understanding the fundamental principles of energy cascades and scaling behaviors in bacterial turbulence, researchers can develop more accurate models and predictions for the dynamics of other non-equilibrium systems, ultimately enhancing our ability to manipulate and control these systems in practical applications.