# Dictionary Definition

turbulent adj

1 characterized by unrest or disorder or
insubordination; "effects of the struggle will be violent and
disruptive"; "riotous times"; "these troubled areas"; "the
tumultuous years of his administration"; "a turbulent and unruly
childhood" [syn: disruptive, riotous, troubled, tumultuous]

2 (of a liquid) agitated vigorously; in a state
of turbulence; "the river's roiling current"; "turbulent rapids"
[syn: churning,
roiling, roiled, roily]

# User Contributed Dictionary

## English

### Pronunciation

### Adjective

- violently disturbed or agitated; tempestuous, tumultuous
- It is dangerous to sail in turbulent seas.

- being, or causing disturbance or unrest

## German

### Adjective

# Extensive Definition

In fluid
dynamics, turbulence or turbulent flow is a fluid regime
characterized by chaotic, stochastic property changes.
This includes low momentum
diffusion, high momentum convection, and rapid
variation of pressure
and velocity in space
and time. Flow that is not turbulent is called laminar
flow. The (dimensionless)
Reynolds
number characterizes whether flow conditions lead to laminar or
turbulent flow; e.g. for pipe flow, a Reynolds number above about
4000 (A Reynolds number between 2100 and 4000 is known as
transitional flow) will be turbulent. At very low speeds the flow
is laminar, i.e., the flow is smooth (though it may involve
vortices on a large scale). As the speed increases, at some point
the transition is made to turbulent flow. In turbulent flow,
unsteady vortices appear on many scales and interact with each
other. Drag due
to boundary
layer skin friction increases. The structure and location of
boundary layer separation often changes, sometimes resulting in a
reduction of overall drag. Because laminar-turbulent transition is
governed by Reynolds
number, the same transition occurs if the size of the object is
gradually increased, or the viscosity of the fluid is
decreased, or if the density of the fluid is
increased.

Turbulence causes the formation of eddies of many
different length scales. Most of the kinetic energy of the
turbulent motion is contained in the large scale structures. The
energy "cascades" from these large scale structures to smaller
scale structures by an inertial and essentially inviscid mechanism.
This process continues, creating smaller and smaller structures
which produces a hierarchy of eddies. Eventually this process
creates structures that are small enough that molecular diffusion
becomes important and viscous dissipation of energy finally takes
place. The scale at which this happens is the Kolmogorov
length scale.

In two dimensional turbulence (as can be
approximated in the atmosphere or ocean), energy actually flows to
larger scales. This is referred to as the inverse energy cascade
and is characterized by a k^ in the power spectrum. This is the
main reason why large scale weather features such as hurricanes
occur.

Turbulent diffusion is usually described by a
turbulent diffusion
coefficient. This turbulent diffusion coefficient is defined in
a phenomenological sense, by analogy with the molecular
diffusivities, but it does not have a true physical meaning, being
dependent on the flow conditions, and not a property of the fluid,
itself. In addition, the turbulent diffusivity concept assumes a
constitutive relation between a turbulent flux and the gradient of
a mean variable similar to the relation between flux and gradient
that exists for molecular transport. In the best case, this
assumption is only an approximation. Nevertheless, the turbulent
diffusivity is the simplest approach for quantitative analysis of
turbulent flows, and many models have been postulated to calculate
it. For instance, in large bodies of water like oceans this
coefficient can be found using Richardson's
four-third power law and is governed by the random walk
principle. In rivers and large ocean currents, the diffusion
coefficient is given by variations of Elder's formula.

When designing piping systems, turbulent flow
requires a higher input of energy from a pump (or fan) than laminar
flow. However, for applications such as heat exchangers and
reaction vessels, turbulent flow is essential for good heat
transfer and mixing.

While it is possible to find some particular
solutions of the Navier-Stokes
equations governing fluid motion, all such solutions are
unstable at large Reynolds numbers. Sensitive dependence on the
initial and boundary conditions makes fluid flow irregular both in
time and in space so that a statistical description is needed.
Russian
mathematician Andrey
Kolmogorov proposed the first statistical theory of turbulence,
based on the aforementioned notion of the energy cascade (an idea
originally introduced by Richardson) and
the concept of self-similarity. As a result, the Kolmogorov
microscales were named after him. It is now known that the
self-similarity is broken so the statistical description is
presently modified . Still, the complete description of turbulence
remains one of the
unsolved problems in physics. According to an apocryphal story
Werner
Heisenberg was asked what he would ask God, given the
opportunity. His reply was: "When I meet God, I am going to ask him
two questions: Why relativity?
And why turbulence? I really believe he will have an answer for the
first." A similar witticism has been attributed to Horace Lamb
(who had published a noted text book on Hydrodynamics)—his
choice being quantum
mechanics (instead of relativity) and turbulence. Lamb was
quoted as saying in a speech to the
British Association for the Advancement of Science, "I am an
old man now, and when I die and go to heaven there are two matters
on which I hope for enlightenment. One is quantum
electrodynamics, and the other is the turbulent motion of
fluids. And about the former I am rather optimistic."

### Examples of turbulence

- Smoke rising from a cigarette. For the first few centimeters, the flow remains laminar, and then becomes unstable and turbulent as the rising hot air accelerates upwards. Similarly, the dispersion of pollutants in the atmosphere is governed by turbulent processes.
- Flow over a golf ball. (This can be best understood by considering the golf ball to be stationary, with air flowing over it.) If the golf ball were smooth, the boundary layer flow over the front of the sphere would be laminar at typical conditions. However, the boundary layer would separate early, as the pressure gradient switched from favorable (pressure decreasing in the flow direction) to unfavorable (pressure increasing in the flow direction), creating a large region of low pressure behind the ball that creates high form drag. To prevent this from happening, the surface is dimpled to perturb the boundary layer and promote transition to turbulence. This results in higher skin friction, but moves the point of boundary layer separation further along, resulting in lower form drag and lower overall drag.
- The mixing of warm and cold air in the atmosphere by wind, which causes clear-air turbulence experienced during airplane flight, as well as poor astronomical seeing (the blurring of images seen through the atmosphere.)
- Most of the terrestrial atmospheric circulation
- The oceanic and atmospheric mixed layers and intense oceanic currents.
- The flow conditions in many industrial equipment (such as pipes, ducts, precipitators, gas scrubbers, etc.) and machines (for instance, internal combustion engines and gas turbines).
- The external flow over all kind of vehicles such as cars, airplanes, ships and submarines.
- The motions of matter in stellar atmospheres.
- A jet exhausting from a nozzle into a quiescent fluid. As the flow emerges into this external fluid, shear layers originating at the lips of the nozzle are created. These layers separate the fast moving jet from the external fluid, and at a certain critical Reynolds number they become unstable and break down to turbulence.
- Race cars unable to follow each other through fast corners due to turbulence created by the leading car causing understeer.
- In windy conditions, trucks that are on the motorway gets buffeted by their wake.
- Round bridge supports under water. In the summer when the river is flowing slowly the water goes smoothly around the support legs. In the winter the flow is faster, so a higher Reynolds Number, so the flow may start off laminar but is quickly separated from the leg and becomes turbulent.

### Kolmogorov 1941 Theory

The Richardson's notion of turbulence was that a
turbulent flow is composed by "eddies" of different sizes. The
sizes define a characteristic length scale for the eddies, which
are also characterized by velocity scales and time scales (turnover
time) dependent on the length scale. The large eddies are unstable
and eventually break up originating smaller eddies, and the kinetic
energy of the initial large eddy is divided into the smaller eddies
that stemmed from it. These smaller eddies undergo the same
process, giving rise to even smaller eddies which inherit the
energy of their predecessor eddy, and so on. In this way, the
energy is passed down from the large scales of the motion to
smaller scales until reaching a sufficiently small length scale
such that the viscosity of the fluid can effectively dissipate the
kinetic energy into internal energy.

In his original theory of 1941, Kolmogorov
postulated that for very high Reynolds number, the small scale
turbulent motions are statistically isotropic (i.e. no preferential
spatial direction could be discerned). In general, the large scales
of a flow are not isotropic, since they are determined by the
particular geometrical features of the boundaries (the size
characterizing the large scales will be denoted as L). Kolmogorov's
idea was that in the Richardson's energy cascade this geometrical
and directional information is lost, while the scale is reduced, so
that the statistics of the small scales has a universal character:
they are the same for all turbulent flows when the Reynolds number
is sufficiently high.

Thus, Kolmogorov introduced a second hypothesis:
for very high Reynolds numbers the statistics of small scales are
universally and uniquely determined by the viscosity (\nu) and the
rate of energy dissipation (\varepsilon). With only these two
parameters, the unique length that can be formed by dimensional
analysis is

\eta = (\frac)^.

This is today known as the Kolmogorov length
scale (see Kolmogorov
microscales).

A turbulent flow is characterized by a hierarchy
of scales through which the energy cascade takes place. Dissipation
of kinetic energy takes place at scales of the order of Kolmogorov
length \eta, while the input of energy into the cascade comes from
the decay of the large scales, of order L. These two scales at the
extremes of the cascade can differ by several orders of magnitude
at high Reynolds numbers. In between there is a range of scales
(each one with its own characteristic length r) that has formed at
the expense of the energy of the large ones. These scales, are very
large compared with the Kolmogorov length, but still very small
compared with the large scale of the flow (i.e. \eta \ll r \ll L).
Since eddies in this range are much larger than the dissipative
eddies that exist at Kolmogorov scales, kinetic energy is
essentially not dissipated in this range, and it is merely
transferred to smaller scales until viscous effects become
important as the order of the Kolmogorov scale is approached.
Within this range inertial effects are still much larger than
viscous effects, and it is possible to assume that viscosity does
not play a role in their internal dynamics (for this reason this
range is called "inertial range").

Hence, a third hypothesis of Kolmogorov was that
at very high Reynolds number the statistics of scales in the range
\eta \ll r \ll L are universally and uniquely determined by the
scale r and the rate of energy dissipation \varepsilon.

The way in which the kinetic energy is
distributed over the multiplicity of scales is a fundamental
characterization of a turbulent flow. For homogeneous turbulence
(i.e., statistically invariant under translations of the reference
frame) this is usually done by means of the energy spectrum
function E(k), where k is the modulus of the wavenumber vector
corresponding to some harmonics in a Fourier representation of the
flow velocity field u(x):

\mathbf(\mathbf) = \iiint_ \widehat(\mathbf)e^
\mathrm^3\mathbf,

where û(k) is the Fourier transform of the
velocity field. Thus, E(k)dk represents the contribution to the
kinetic energy from all the Fourier modes with k \mathrm =
\int_^E(k)\mathrmk.

The wavenumber k corresponding to length scale r
is k=2\pi/r. Therefore, by dimensional analysis, the only possible
form for the energy spectrum function according with the third
Kolmogorov's hypothesis is

E(k) = C \varepsilon^ k^ ,

where C would be a universal constant. This is
one of the most famous results of Kolmogorov 1941 theory, and
considerable experimental evidence has accumulated that supports
it.

In spite of this success, Kolmogorov theory is at
present under revision. This theory implicitly assumes that the
turbulence is statistically self-similar at different scales. This
essentially means that the statistics are scale-invariant in the
inertial range. A usual way of studying turbulent velocity fields
is by means of velocity increments:

\delta \mathbf(r) = \mathbf(\mathbf + \mathbf) -
\mathbf(\mathbf),

that is, the difference in velocity between
points separated by a vector r (since the turbulence is assumed
isotropic, the velocity increment depends only on the modulus of
r). Velocity increments are useful because they emphasize the
effects of scales of the order of the separation r when statistics
are computed. The statistical scale-invariance implies that the
scaling of velocity increments should occur with a unique scaling
exponent \beta, so that when r is scaled by a factor \lambda,

\delta \mathbf(\lambda r)

should have the same statistical distribution
than

\lambda^\delta \mathbf(r),

with \beta independent of the scale r. From this
fact, and other results of Kolmogorov 1941 theory, it follows that
the statistical moments of the velocity increments (known as
structure functions in turbulence) should scale as

\langle [\delta \mathbf(r)]^n \rangle = C_n
\varepsilon^ r^,

where the brackets denote the statistical
average, and the C_n would be universal constants.

There is considerable evidence that turbulent
flows deviate from this behavior. The scaling exponents deviate
from the n/3 value predicted by the theory, becoming a non-linear
function of the order n of the structure function. The universality
of the constants have also been questioned. For low orders the
discrepancy with the Kolmogorov n/3 value is very small, which
explain the success of Kolmogorov theory in regards to low order
statistical moments. In particular, it can be shown that when the
energy spectrum follows a power law

E(k) \propto k^,

with 1 , the second order structure function has
also a power law, with the form

\langle [\delta \mathbf(r)]^2 \rangle \propto r^
.

Since the experimental values obtained for the
second order structure function only deviate slightly from the 2/3
value predicted by Kolmogorov theory, the value for p is very near
to 5/3 (differences are about 2%). Thus the "Kolmogorov -5/3
spectrum" is generally observed in turbulence. However, for high
order structure functions the difference with the Kolmogorov
scaling is significant, and the breakdown of the statistical
self-similarity is clear. This behavior, and the lack of
universality of the C_n constants, are related with the phenomenon
of intermittency in turbulence. This is an important area of
research in this field, and a major goal of the modern theory of
turbulence is to understand what is really universal in the
inertial range.

## See also

## References

- Falkovich, Gregory and Sreenivasan, Katepalli R. Lessons from hydrodynamic turbulence, Physics Today, vol. 59, no. 4, pages 43-49 (April 2006).http://www.phy.olemiss.edu/~jgladden/phys510/spring06/turbulence.pdf
- U. Frisch. Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, 1995.http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521457132
- T. Bohr, M.H. Jensen, G. Paladin and A.Vulpiani. Dynamical Systems Approach to Turbulence, Cambridge University Press, 1998.http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521475143

### Original scientific research papers

- , translated into English by
- , translated into English by

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turbulent in Chinese: 湍流

# Synonyms, Antonyms and Related Words

agitated, amiss, anarchic, angry, askew, awry, blaring, blatant, blatting, blustering, blusterous, blustery, boiling, boisterous, brassy, brawling, brazen, breakaway, bustling, chaotic, clamant, clamorous, clamoursome, clanging, clangorous, clattery, cloudy, coarse, cockeyed, convulsed, cyclonic, deranged, dirty, disarranged, discomfited, discomposed, disconcerted, dislocated, disordered, disorderly, disorganized, disquieted, disturbed, excited, extreme, extremistic, factious, fast, feverish, fidgety, flurried, flustered, fluttering, fluttery, foul, frantic, frenzied, fretful, furious, fussing, fussy, haywire, hellish, howling, in disorder, infuriate, insensate, insurgent, insurrectionary,
jittery, jumpy, loudmouthed, mad, mafficking, mindless, misplaced, mutineering, mutinous, nervous, nervy, noiseful, noisy, obstreperous, on the fritz,
orgasmic, orgastic, out of gear, out of
joint, out of kelter, out of kilter, out of order, out of place,
out of tune, out of whack, pandemoniac, perturbed, quarrelsome, rackety, raging, rainy, rambunctious, raucous, ravening, raving, rebel, rebellious, restless, revolutional, revolutionary, riotous, rip-roaring, roaring, roily, roisterous, rough, roughhouse, rowdy, rowdyish, ruffled, rumbustious, seditionary, seditious, shaken, shaken up, shuffled, stirred up, storming, stormy, strepitant, strepitous, subversive, swirling, tempestuous, termagant, tornadic, traitorous, treasonable, troubled, troublous, tumultuous, turbid, typhonic, typhoonish, uncontrollable, uneasy, uninhibited, unpeaceful, unquiet, unruly, unsettled, uproarious, upset, vociferous, wild