Exploring Turbulence: An Introductory Approach

5 May 2025 • 5 minute read

Key Points

Turbulence is a widespread phenomenon that occurs across many scales, from microscopic to large-scale flows.
It involves chaotic, irregular fluid motion, typically featuring swirling structures like vortices and eddies.
Turbulence significantly influences aerodynamic drag and contributes to energy dissipation in fluid systems.

Why Study Turbulence?

Turbulent behavior in flowing fluids is one of the most intriguing and challenging problems in classical physics. Most fluid flows exhibit turbulence, which plays a pivotal role across a wide range of scales in the known universe. Its influence spans from microscopic biological processes within cells and the circulatory systems of organisms to technological devices and household appliances. Furthermore, turbulence is also present in vast geophysical and astrophysical phenomena, including planetary interiors, oceans, the atmosphere, and stellar dynamics—extending to galactic and intergalactic scales.

Throughout the 19th and 20th centuries, many prominent physicists and engineers devoted their efforts to unraveling the mysteries of turbulence. Despite the ubiquity of turbulent flow, understanding its underlying mechanisms and accurately predicting its behavior—even in simple scenarios— remains among the last great unsolved problems in classical physics. The study of turbulence is motivated by both its inherent intellectual complexity and the potential practical benefits across science and engineering.

What is Turbulence?

Turbulence is a complex, three-dimensional, unsteady phenomenon observed in fluid flows characterized by chaotic and irregular motion. In contrast to laminar flow, where fluid particles move along smooth, orderly paths, turbulent flow involves rapid fluctuations in velocity, pressure, and other flow properties. These fluctuations occur in a random manner and can lead to the formation of eddies, vortices, and swirling patterns throughout the fluid.

Effects of Turbulence

Positive Outcomes:

Enhanced heat transfer: turbulent flow improves convective heat transfer, which enables more efficient cooling or heating in applications such as heat exchangers and HVAC systems.
Energy dissipation: turbulence promotes the dissipation of kinetic energy from the fluid, helping to dampen oscillations and mitigate the impact of fluid-induced forces on structures.
Improved mixing and stability: turbulence enhances mixing, delays flow separation, and reduces form drag which is beneficial in many industrial applications.

Negative Consequences:

Increased energy losses: Turbulence in fluid flow systems results in higher frictional losses, which reduce overall efficiency. The increased shear stress within the fluid can lead to material fatigue and wear in equipment, further compromising system performance.
Unpredictable: The complexity of turbulent flow makes it challenging to predict fluid behavior, hindering the design and optimization of engineering systems. As a result, engineers often struggle to accurately model and analyze turbulent flow systems.
Unwanted mixing: While turbulence can enhance fluid mixing, this can be undesirable in applications requiring distinct fluid layers, such as chemical reactors. Conversely, the increased mixing and convective heat transfer associated with turbulent flow can affect the efficiency of heat exchangers and thermal systems, sometimes in a beneficial manner.
Uncontrollable: Turbulent flows are more difficult to control and stabilize compared to laminar flows, posing significant challenges in various fluid dynamic applications. The inherent unpredictability of turbulence makes it harder to regulate flow rates, temperatures, and pressures.
Pressure losses: Turbulent flow often leads to higher pressure drops compared to laminar flow, resulting in increased energy consumption in fluid transport systems. This can have significant implications for system design and operation.
Vibration and fatigue: Turbulence can induce vibrations in structures immersed in fluid flow, leading to structural fatigue, potential damage, and energy concerns in engineering systems. Therefore, mitigating the effects of turbulence is crucial to ensuring the safe and efficient operation of these systems.

Features of Disordered Flow Structures

Turbulent systems exhibit disorganized, chaotic, and seemingly random behavior, making it challenging to predict their exact outcomes or patterns. Because these flows are highly sensitive to initial conditions, even small variations can lead to drastically different results. This means that even small variations in the initial conditions can result in drastically different outcomes, making it impossible to reproduce the exact same behavior. Turbulence spans an extremely large range of length and time scales, from minuscule eddies to large atmospheric motions. Notably, even the smallest scales in these systems are still sufficiently large to satisfy the continuum hypothesis, which assumes that the fluid can be treated as a continuous, rather than discrete, medium.

One hallmark of turbulence is its enhanced diffusion (mixing) and energy dissipation properties due to viscosity at molecular scales. This means that turbulent systems are highly effective at mixing and dispersing substances, as well as converting kinetic energy into heat. Turbulent flows are inherently three-dimensional, time-dependent, and rotational, distinguishing them from laminar flows. In particular, the presence of rotation is a key feature of turbulent flows, as it leads to the formation of vortices and other complex structures. On the other hand, potential flows are, by definition, irrotational and therefore, cannot be turbulent. Another defining trait of turbulence is its intermittent behavior, characterized by bursts of intense activity followed by periods of relative calm, both in space and time. This irregular and uneven behavior reflects the complex dynamics that make turbulence so difficult to model and predict.

Scale Variations in Length and Time

Four primary scales are commonly identified in turbulent flows, each describing a distinct range of fluid motion. These scales are:

Large scale: This scale is determined by the geometry of the problem domain, encompassing the overall size and structure of the flow.
Integral or outer scale: This scale is approximately 10-20% of the large scale. It serves as a measure of the energy-containing eddies in the flow.
Taylor microscale: Situated between the integral scale and the smallest scale, this intermediate scale falls within Kolmogorov's inertial subrange. It characterizes the scale at which the effects of viscosity begin to influence the flow, marking a transition from the inertial range to the dissipation range.
Kolmogorov or inner scale: This is the smallest of the turbulence scales, representing the scale at which viscous forces dominate and energy is dissipated.

It is worth noting that additional scales may be relevant in turbulent flows where other physical phenomena, such as heat transfer or combustion, play important roles.

References

“Turbulent Flows” by Pope Stephen B.

“Homogeneous Isotropic Turbulence” by J.L. Lumley.

Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. (1991). A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A: Fluid Dynamics (1989-1993), 3(7), 1760- 1765.

Hunt, J. C. R., Wray, A. A., and Moin, P. (1988). Eddies, Streams, and Convergence Zones in Turbulent Flows. Proceedings of Summer Program, Stanford University: Center for Turbulence Research, 193-208