Turbulence (fluid dynamics)

In fluid dynamics, turbulence is fluid motion marked by chaotic changes in pressure and flow velocity. Also known as turbulent flow, turbulence can occur in any sort of fluid, including both liquids and gases. As such, turbulence is commonly observed in everything from rapidly flowing rivers to storm clouds, smoke billowing out of a chimney, and seaside surf. Turbulence is caused by elevated levels of kinetic energy in certain parts of a fluid flow. When that kinetic energy exceeds the natural dampening effect of the fluid's viscosity, turbulence results. Turbulence is one of the most elusive concepts in physics. While the basic concept of turbulence is generally understood, turbulence remains a notoriously difficult phenomenon to explain in greater detail. Modern scientific ability to explain turbulence is largely limited to the Navier-Stokes equations and the Reynolds number, two mathematical statements that respectively describe the flow of fluids and help to predict when a fluid flow will become turbulent.

Background

To properly understand the concept of turbulence, one must first have an adequate understanding of fluid dynamics. Fluid dynamics is the scientific study of the movements of fluids and the interactions that occur when two fluids contact each other. Fluid dynamics is one of the two branches of fluid mechanics, which is the broader study of fluids and how they are affected by forces. The other branch is fluid statics, which focuses on the study of fluids at rest. Fluid dynamics is crucial to the study of phenomena like ocean currents, air flow, and blood circulation. Fluid dynamics also plays an important role in technologies like airplane engines, oil pipelines, and rockets.

The basic scientific principles involved in fluid dynamics include buoyancy, density, pressure, and viscosity. Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. As applied to fluid dynamics, density and pressure are key characteristics that determine how different fluids will interact. Viscosity is another important characteristic that determines the degree to which a given fluid is resistant to change.

Scientists who study fluid dynamics refer to the physical properties of the movement of fluid as flow. The concept of flow applies to a variety of fluid movements, including streaming through a pipe or blowing through the air. The flow of a fluid can be classified in several different ways. In the most basic sense, for example, the flow of a fluid can be described as steady or unsteady. A steady flow is one in which all properties of the flow remain constant over time. An unsteady flow has properties that change over time. While a current of water flowing through a pipe at a constant rate would be considered a steady flow, rain flowing into a gutter during a storm would be considered an unsteady flow. Different types of flows can also be differentiated based on how much contact they have with rigid boundaries or whether or not they are compressible. Where turbulence is concerned, the key factor in differentiating different flows is determining whether they are laminar or turbulent.

Overview

The terms laminar and turbulent are used to describe how a flow moves. In a laminar flow, the particles of a fluid travel along a smooth path in parallel layers and do not interfere with one another. Laminar flows also move at a constant velocity at any point within the fluid. In short, laminar flows are orderly and consistent. Turbulent flows are quite different. In a turbulent flow, excessive kinetic energy causes the particles of a fluid to interfere with one another. This causes the velocity of the flow to vary in different parts of the fluid and leads to the formation of eddies and whirlpools. Compared to laminar flows, turbulent flows are chaotic and irregular.

The specific characteristics of a flow determine whether it is laminar or turbulent. Of all the characteristic factors involved in this determination, viscosity is likely most important. Viscosity has a natural dampening effect on the flow of a fluid. Critically, if a fluid has a low viscosity, the dampening effect will be reduced. The reduced dampening effect that comes with lower viscosity makes it easier for the flow of that fluid to become turbulent.

Turbulence begins to occur when a smooth fluid flow splits into smaller eddies and whirlpools. Over time, these swirls break into smaller and smaller swirls in a cascade that allows energy to be gradually dissipated from the original flow. While some aspects of this process are clearly understood, others have yet to be adequately explained. Modern scientists also work to predict when turbulence will likely occur. The question of when a flow will transition from streamlined and laminar to turbulent can, with some precision, be answered through a calculation called the Reynolds number. The Reynolds number is a dimensionless quantity that defines the flow of a fluid as the ratio of its inertial forces to its viscous forces. By using the Reynolds number, scientists can make a reasonably accurate prediction as to when a laminar flow will become turbulent. Even so, scientists are still unable to accurately predict how a turbulent flow will evolve over time.

To a certain extent, the temporal evolution of a flow can be described using the Navier-Stokes equations. These equations take factors like the density and viscosity of a fluid, as well as the forces acting on it, into account and allow scientists to make a prediction of how the eddies and whirlpools generated in a turbulent field will behave. This prediction is limited, however. Not even the Navier-Stokes equations can accurately predict exactly how a turbulent flow will evolve over a given period of time. This is one of the greatest remaining challenges in physics. Indeed, some scientists consider it to be a "holy grail" of sorts and continue to search for an equation or other solution that can accurately and precisely illustrate how a turbulent flow will develop over the course of its existence. As it stands, however, this process simply remains too complex and irregular to be reliably predictable.

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