In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of flui
{{Other uses}}
In
fluid dynamicsIn physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
,
turbulence or
turbulent flow is a flow regime characterized by chaotic and
stochasticStochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
property changes. This includes low
momentum diffusionMomentum diffusion refers to the diffusion, or spread of momentum between particles of matter, usually in the liquid state....
, high momentum
convectionConvection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
, and rapid variation of
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
and
velocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
in space and time. Nobel Laureate
Richard FeynmanRichard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
described turbulence as "the most important unsolved problem of classical physics." Flow in which the
kinetic energyThe kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
dies out due to the action of fluid molecular
viscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
is called
laminar flowLaminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents...
. While there is no theorem relating
Reynolds number (Re) to turbulence, flows
at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In pipe flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040; moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 3000. In turbulent flow, unsteady vortices appear on many scales and interact with each other.
DragIn fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
due to
boundary layerIn physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...
skin friction increases. The structure and location of boundary layer separation often changes, sometimes resulting in a reduction of overall drag. Although
laminar-turbulent transitionThe process of a laminar boundary layer becoming turbulent is known as boundary layer transition. This process is an extraordinarily complicated process which at present is not fully understood...
is not governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the
viscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
of the fluid is decreased, or if the
densityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of the fluid is increased.
Features
Turbulence is highly characterized by the following features:
Irregularity: Turbulent flows are always highly irregular. This is why turbulence problems are always treated statistically rather than deterministically. Turbulent flow is always chaotic but not all chaotic flows are turbulent.
DiffusivityDiffusivity can refer to:*Diffusivity of heat*Diffusivity of mass:** Molecular diffusivity ** Eddy diffusivity*Momentum diffusivity...
: Turbulence is highly associated with rapid mixing. One of the useful effects of turbulence, it tends to accelerate the homogenization of any non-uniform fluid mixture. The process which brings any non-uniform state of a system into a uniform one is called mixing and when the system is in its uniform state, the system becomes a homogeneous system. A mixing process requires sufficient input of energy which is readily available in a turbulent flow. The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is regarded as diffusivity.
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
fluxIn the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
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
RichardsonLewis Fry Richardson, FRS was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them...
's four-third power law and is governed by the
random walkA random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
principle. In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula.
A chaotic flow is never turbulent if it does not diffuse. For example, jet contrails are not turbulent as they don't diffuse even they are turbulent at the generation{{Citation needed|date=May 2011}}.
Rotationality: Turbulent flows have non-zero vorticity and are characterized by a strong three-dimensional vortex generation mechanism known as
vortex stretchingIn fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum....
. In fluid dynamics, they are essentially vortices subjected to stretching associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum. On the other hand, vortex stretching is the core mechanism on which the turbulence energy cascade relies to establish the structure function. In general, the stretching mechanism implies thinning of the vortices in the direction perpendicular to the stretching direction due to volume conservation of fluid elements. As a result, the radial length scale of the vortices decreases and the larger flow structures break down into smaller structures. The process continues until the small scale structures are small enough to the extent where their kinetic energy is overwhelmed by the fluid's molecular viscosity and dissipated into heat. This is why turbulence is always rotational and three dimensional. For example, atmospheric cyclones are rotational but their substantially two-dimensional shapes do not allow vortex generation and so are not turbulent. On the other hand, oceanic flows are dispersive but essentially non rotational and therefore are not turbulent.
DissipationIn physics, dissipation embodies the concept of a dynamical system where important mechanical models, such as waves or oscillations, lose energy over time, typically from friction or turbulence. The lost energy converts into heat, which raises the temperature of the system. Such systems are called...
: To sustain turbulent flow, a constant source of energy supply is required. Otherwise, turbulence dissipates rapidly as the kinetic energy is converted into internal energy by viscous shear stress.
Turbulence causes the formation of
eddiesIn fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid flows past an obstacle. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object...
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
inviscidIn fluid dynamics there are problems that are easily solved by using the simplifying assumption of an ideal fluid that has no viscosity. The flow of a fluid that is assumed to have no viscosity is called inviscid flow....
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 scaleKolmogorov microscales are the smallest scales in turbulent flow. They are defined bywhere \epsilon is the average rate of energy dissipation per unit mass, and \nu is the kinematic viscosity of the fluid....
.
Energy cascade: Turbulent flow can be realized as a superposition of a spectrum of velocity fluctuations and eddies on an over mean flow. The eddies are loosely defined as coherent patterns of velocity, vorticity and pressure. Turbulent flows may be viewed as made of an entire hierarchy of eddies over a wide range of length scales and the hierarchy can be described by the energy spectrum that measures the energy in velocity fluctuations for each wave number. The scales in the energy cascade are generally uncontrollable and highly non-symmetric. Nevertheless, based on these length scales these eddies can be divided into three categories.
Integral length scales: Largest scales in the energy spectrum. These eddies obtain energy from the mean flow and also from each other. Thus these are the energy production eddies which contain the most of the energy. They have the large velocity fluctuation and are low in frequency. Integral scales are highly anisotropic and are defined in terms of the normalized two-point velocity correlations. The maximum length of these scales is constrained by the characteristic length of the apparatus. For example, the largest integral length scale of pipe flow is equal to the pipe diameter. In the case of atmospheric turbulence, this length can reach up to the order of several hundreds kilometers.
Kolmogorov length scalesKolmogorov microscales are the smallest scales in turbulent flow. They are defined bywhere \epsilon is the average rate of energy dissipation per unit mass, and \nu is the kinematic viscosity of the fluid....
: Smallest scales in the spectrum that form the viscous sub-layer range. In this range, the energy input from nonlinear interactions and the energy drain from viscous dissipation are in exact balance. The small scales are in high frequency which is why turbulence is locally isotropic and homogeneous.
Taylor microscaleThe Taylor microscale is a length scale used to characterize a turbulent fluid flow. The Taylor microscale is the largest length scale at which fluid viscosity significantly affects the dynamics of turbulent eddies in the flow. This length scale is traditionally applied to turbulent flow which can...
s: The intermediate scales between the largest and the smallest scales which make the inertial subrange. Taylor micro-scales are not dissipative scale but passes down the energy from the largest to the smallest without dissipation. Some literatures do not consider Taylor micro-scales as a characteristic length scale and consider the energy cascade contains only the largest and smallest scales; while the later accommodate both the inertial sub-range and the viscous-sub layer. Nevertheless, Taylor micro-scales is often used in describing the term “turbulence” more conveniently as these Taylor micro-scales play a dominant role in energy and momentum transfer in the wavenumber space.
Although it is possible to find some particular solutions of the
Navier-Stokes equationsIn physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous...
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.
RussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Andrey KolmogorovAndrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
proposed the first statistical theory of turbulence, based on the aforementioned notion of the energy cascade (an idea originally introduced by
RichardsonLewis Fry Richardson, FRS was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them...
) and the concept of self-similarity. As a result, the
Kolmogorov microscalesKolmogorov microscales are the smallest scales in turbulent flow. They are defined bywhere \epsilon is the average rate of energy dissipation per unit mass, and \nu is the kinematic viscosity of the fluid....
were named after him. It is now known that the self-similarity is broken so the statistical description is presently modified. Still, a complete description of turbulence remains one of the
unsolved problems in physicsThis is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result...
.
According to an apocryphal story,
Werner HeisenbergWerner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
was asked what he would ask
GodGod is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....
, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why
relativityThe theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
? And why turbulence? I really believe he will have an answer for the first." A similar witticism has been attributed to
Horace LambSir Horace Lamb FRS was a British applied mathematician and author of several influential texts on classical physics, among them Hydrodynamics and Dynamical Theory of Sound...
(who had published a noted text book on Hydrodynamics)—his choice being
quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
(instead of relativity) and turbulence. Lamb was quoted as saying in a speech to the
British Association for the Advancement of Scienceframe|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...
, "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."
A more detailed presentation of turbulence with emphasis on high-Reynolds number flow, intended for a general readership of physicists and applied mathematicians, is found in the Scholarpedia articles by R. Benzi and U. Frisch. and by G. Falkovich.
Examples of turbulence
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NEWLINE- Smoke rising from a cigarette
A cigarette is a small roll of finely cut tobacco leaves wrapped in a cylinder of thin paper for smoking. The cigarette is ignited at one end and allowed to smoulder; its smoke is inhaled from the other end, which is held in or to the mouth and in some cases a cigarette holder may be used as well...
is turbulent flow-Relating to the movement of material:* Fluid dynamics, or fluid flow, the motion of a gas or liquid* Environmental flow, the amount of water necessary in a watercourse to maintain a healthy ecosystem* Flow chemistry, a chemical reaction run in a continuous stream...
. For the first few centimeters, the flow is certainly laminar. Then smoke becomes turbulent as its Reynolds number increases, as its velocity and characteristic length are both increasing. NEWLINE- Flow over a golf ball
A golf ball is a ball designed to be used in the game of golf.Under the Rules of Golf, a golf ball weighs no more than 1.620 oz , has a diameter not less than 1.680 in , and performs within specified velocity, distance, and symmetry limits...
. (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. NEWLINE- The mixing of warm and cold air in the atmosphere by wind, which causes clear-air turbulence
Clear air turbulence is the turbulent movement of air masses in the absence of any visual cues such as clouds, and is caused when bodies of air moving at widely different speeds meet....
experienced during airplane flight, as well as poor astronomical seeingAstronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index...
(the blurring of images seen through the atmosphere.) NEWLINE- Most of the terrestrial atmospheric circulation
Atmospheric circulation is the large-scale movement of air, and the means by which thermal energy is distributed on the surface of the Earth....
NEWLINE- The oceanic and atmospheric mixed layer
The oceanic or limnological mixed layer is a layer in which active turbulence has homogenized some range of depths. The surface mixed layer is a layer where this turbulence is generated by winds, cooling, or processes such as evaporation or sea ice formation which result in an increase in salinity...
s and intense oceanic currents. NEWLINE- The flow conditions in many industrial equipment (such as pipes, ducts, precipitators, gas scrubber
Scrubber systems are a diverse group of air pollution control devices that can be used to remove some particulates and/or gases from industrial exhaust streams. Traditionally, the term "scrubber" has referred to pollution control devices that use liquid to wash unwanted pollutants from a gas stream...
s, dynamic scraped surface heat exchangers, etc.) and machines (for instance, internal combustion engineThe internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber. In an internal combustion engine, the expansion of the high-temperature and high -pressure gases produced by combustion apply direct force to some component of the engine...
s and gas turbineA gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....
s). NEWLINE- The external flow over all kind of vehicles such as cars, airplanes, ships and submarines.
NEWLINE- The motions of matter in stellar atmospheres.
NEWLINE- 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.
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{{unsolved|physics|Is it possible to make a theoretical model to describe the behavior of a turbulent flow — in particular, its internal structures?}}NEWLINE
NEWLINE- Race cars unable to follow each other through fast corners due to turbulence created by the leading car causing understeer
Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle to steering. Simply put, oversteer is what occurs when a car turns by more than the amount commanded by the driver...
. NEWLINE- In windy conditions, trucks that are on the motorway gets buffeted by their wake.
NEWLINE- Bridge supports (piers) in water. In the late summer and fall, when river flow is slow, water flows smoothly around the support legs. In the spring, when the flow is faster, a higher Reynolds Number is associated with the flow. The flow may start off laminar but is quickly separated from the leg and becomes turbulent.
NEWLINE- In many geophysical flows (rivers, atmospheric boundary layer), the flow turbulence is dominated by the coherent structure activities and associated turbulent events. A turbulent event is a series of turbulent fluctuations that contain more energy than the average flow turbulence. The turbulent events are associated with coherent flow structures such as eddies and turbulent bursting, and they play a critical role in terms of sediment scour, accretion and transport in rivers as well as contaminant mixing and dispersion in rivers and estuaries, and in the atmosphere.
NEWLINE- In the medical field of cardiology
Cardiology is a medical specialty dealing with disorders of the heart . The field includes diagnosis and treatment of congenital heart defects, coronary artery disease, heart failure, valvular heart disease and electrophysiology...
, a stethoscope is used to detect heart soundsHeart sounds, or heartbeats, are the noises generated by the beating heart and the resultant flow of blood through it...
and bruits, which are due to turbulent blood flow. In normal individuals, heart sounds are a product of turbulent flow as heart valves close. However, in some conditions turbulent flow can be audible due to other reasons, some of them pathological. For example, in advanced atherosclerosisAtherosclerosis is a condition in which an artery wall thickens as a result of the accumulation of fatty materials such as cholesterol...
, bruits (and therefore turbulent flow) can be heard in some vessels that have been narrowed by the disease process.
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Heat and momentum transfer
When flow is turbulent, particles exhibit additional transverse motion which enhances the rate of energy and momentum exchange between them thus increasing the
heat transfer and the
frictionFriction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
coefficient.
Assume for a two-dimensional turbulent flow that one was able to locate a specific point in the fluid and measure the actual velocity
of every particle that passed through that point at any given time. Then one would find the actual velocity fluctuating about a mean value: