[Paper Review] Active Turbulence

Ricard Alert, Jaume Casademunt+1 more|arXiv (Cornell University)|Apr 5, 2021

Micro and Nano Robotics165 references4 citations

TL;DR

This review unifies the study of active turbulence across polar and nematic active fluids, with and without momentum conservation, revealing power-law scaling with universal or non-universal exponents. It contrasts chaotic flows in active systems with inertial turbulence, emphasizing the absence of energy cascades due to intrinsic length scales and self-organized energy injection.

ABSTRACT

Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the absence of inertia, chaotic active flows are reminiscent of inertial turbulence, and hence they are known as active turbulence. Here, we survey the field, providing a unified perspective over different classes of active turbulence. To this end, we divide our review in sections for systems with either polar or nematic order, and with or without momentum conservation (wet/dry). Comparing to inertial turbulence, we highlight the emergence of power-law scaling with either universal or non-universal exponents. We also contrast scenarios for the transition from steady to chaotic flows, and we discuss the absence of energy cascades. We link this feature to both the existence of intrinsic length scales and the self-organized nature of energy injection in active turbulence, which are fundamental differences with inertial turbulence. We close by outlining the emerging picture, remaining challenges, and future directions.

Motivation & Objective

• To provide a unified framework for understanding active turbulence across diverse systems such as bacterial suspensions, cytoskeletal networks, and cell tissues.
• To compare active turbulence with inertial turbulence, focusing on the absence of energy cascades and the role of intrinsic length scales.
• To analyze the transition from steady to chaotic flows in active fluids, identifying distinct scenarios in wet (momentum-conserving) and dry (momentum-non-conserving) systems.
• To clarify the role of self-organized energy injection in shaping the spatiotemporal complexity of active turbulence.
• To outline open challenges and future research directions in the field of active matter physics.

Proposed method

• Systematic classification of active turbulence into four categories: polar/nematic order and wet/dry (momentum-conserving/non-conserving) systems.
• Use of hydrodynamic equations to model active fluid dynamics, incorporating active stresses and noise terms.
• Analysis of scaling behaviors via power-law fits to correlation functions and structure factors.
• Comparison of energy transfer mechanisms, emphasizing the absence of forward energy cascades in active systems.
• Identification of intrinsic length scales from correlation functions and dynamic scaling collapse.
• Application of renormalization group and mode-coupling techniques to study critical behavior and transitions to chaos.

Experimental results

Research questions

• RQ1 How do power-law scaling exponents in active turbulence differ between universal and non-universal regimes?
• RQ2 What mechanisms govern the transition from steady to chaotic flows in active fluids?
• RQ3 Why do active turbulence systems lack energy cascades, unlike inertial turbulence?
• RQ4 How do intrinsic length scales and self-organized energy injection shape the dynamics of active turbulence?
• RQ5 What are the key differences between wet and dry active turbulence in terms of momentum conservation and flow structure?

Key findings

• Active turbulence exhibits power-law scaling in correlation functions, with exponents that can be universal or non-universal depending on system symmetry and conservation laws.
• The absence of energy cascades in active turbulence is attributed to self-organized, local energy injection and the presence of intrinsic length scales.
• Inertial turbulence features a forward energy cascade, whereas active turbulence shows no such cascade due to the absence of momentum conservation and the dominance of active stresses.
• Systems with polar order display distinct flow patterns and scaling behaviors compared to nematic systems, especially in the presence of momentum conservation.
• The transition from steady to chaotic flows in active fluids is governed by different mechanisms in wet (momentum-conserving) and dry (momentum-non-conserving) systems.
• Emergent length scales in active turbulence arise from the interplay between active stresses, hydrodynamic interactions, and noise, influencing the system's dynamic scaling.