turbulent flow

The motion of a fluid having local velocities and pressures that fluctuate randomly.

A fluid motion in which velocity, pressure, and other flow quantities fluctuate irregularly in time and space.See also Jet flow; Laminar flow.

Turbulence occurs nearly everywhere in nature. It is characterized by the efficient dispersion and mixing of vorticity, heat, and contaminants. In flows over solid bodies such as airplane wings or turbine blades, or in confined flows through ducts and pipelines, turbulence is responsible for increased drag and heat transfer. Turbulence is therefore a subject of great engineering interest. On the other hand, as an example of collective interaction of many coupled degrees of freedom, it is also a subject at the forefront of classical physics. See also Degree of freedom (mechanics); Diffusion; Heat transfer; Pipe flow; Pipeline.

Origin of turbulence

A central role in determining the state of fluid motion is played by the Reynolds number. In general, a given flow undergoes a succession of instabilities with increasing Reynolds number and, at some point, turbulence appears more or less abruptly. It has long been thought that the origin of turbulence can be understood by sequentially examining the instabilities. This sequence depends on the particular flow and, in many circumstances, is sensitive to a number of details. A careful analysis of the perturbed equations of motion has resulted in a good understanding of the first two instabilities in a variety of circumstances. See also Reynolds number.

Fully developed turbulence

Quite often in engineering, the detailed motion is not of interest, but only the long-time averages or means, such as the mean velocity in a boundary layer, the mean drag of an airplane or pressure loss in a pipeline, or the mean spread rate of a jet. It is therefore desirable to rewrite the Navier-Stokes equations for the mean motion. The basis for doing this is the Reynolds decomposition, which splits the overall motion into the time mean and fluctuations about the mean. These macroscopic fluctuations transport mass, momentum, and matter (in fact, by orders of magnitude more efficiently than molecular motion), and their overall effect is thus perceived to be in the form of additional transport or stress. This physical effect manifests itself as an additional stress (called the Reynolds stress) when the Navier-Stokes equations are rewritten for the mean motion (the Reynolds equations). The problem then is one of prescribing the Reynolds stress, which contains the unknown fluctuations in quadratic form. A property of turbulence is that the Reynolds stress terms are comparable to the other terms in the Reynolds equation, even when fluctuations are a small part of the overall motion. An equation for the Reynolds stress itself can be obtained by suitably manipulating the Navier-Stokes equations, but this contains third-order terms involving fluctuations, and an equation for third-order terms involves fourth-order quantities, and so forth. This is the closure problem in turbulence. The Navier-Stokes equations are themselves closed, but the presence of nonlinearity and the process of averaging result in nonclosure.

Given this situation, much of the progress in the field has been due to (1) exploratory experiments and numerical simulations of the Navier-Stokes equations at low Reynolds numbers; and (2) plausible hypotheses in conjunction with dimensional reasoning, scaling arguments, and their experimental verification.

Control of turbulent flows

Some typical objectives of flow control are the reduction of drag of an object such as an airplane wing, the suppression of combustion instabilities, and the suppression of vortex shedding behind bluff bodies. Interest in flow control has been stimulated by the discovery that some turbulent flows possess a certain degree of spatial coherence at large scales. Successful control has also been achieved through the reduction of the skin friction on a flat plate by making small longitudinal grooves, the so-called riblets, on the plate surface, imitating shark skin. See also Fluid flow.

A gustiness in the three-dimensional flow of a fluid, irregular in both space and time, and characterized by local, short-lived rotation currents known as vortices. Turbulence is hierarchical; large eddies produce smaller ones, and so on, down a series of smaller and smaller scales. In meteorology, it develops because of disturbances in air flows, the most important of which is wind shear; air parcels caught in a wind shear tend to roll over and over. The Reynolds number for turbulent flow is 2000 to 2500. In geomorphology, turbulent flow is classified according to the Froude number of a stream. Compare with laminar flow.

For more information on turbulent flow, visit Britannica.com.

The motion of a fluid in which local velocities and pressures fluctuate highly irregularly with time, in contrast to streamline flow.

The flow of a fluid in which the motion of particles at any point varies rapidly in both magnitude and direction. Turbulent flow is characterized by mixing of adjacent fluid layers.

Occurs in blood vessels where there is a stenosis or aneurysm or where there is a sudden increase in velocity; the laminar flow of normal tubes is disrupted and the fluid is randomly and completely mixed; turbulent flows have a greater apparent viscosity than laminar flows.