**Sir Geoffrey Ingram Taylor** OM FRS HFRSE (7 March 1886 – 27 June 1975) was a British physicist and mathematician, and a major figure in fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century".^{[4]}^{[5]}^{[6]}^{[7]}

Taylor was born in St. John's Wood, London. His father, Edward Ingram Taylor, was an artist, and his mother, Margaret Boole, came from a family of mathematicians (his aunt was Alicia Boole Stott and his grandfather was George Boole). As a child he was fascinated by science after attending the Royal Institution Christmas Lectures, and performed experiments using paint rollers and sticky-tape. Taylor read mathematics and physics at Trinity College, Cambridge from 1905 to 1908. Then he obtained a scholarship to continue at Cambridge under J.J. Thomson.

Taylor is best known to students of physics for his very first paper,^{[8]} published while he was still an undergraduate, in which he showed that interference of visible light produced fringes even with extremely weak light sources. The interference effects were produced with light from a gas light, attenuated through a series of dark glass plates, diffracting around a sewing needle. Three months were required to produce a sufficient exposure of the photographic plate. The paper does not mention quanta of light (photons) and does not reference Einstein's 1905 paper on the photoelectric effect, but today the result can be interpreted by saying that less than one photon on average was present at a time. Once it became widely accepted ca. 1927 that the electromagnetic field was quantized, Taylor's experiment began to be presented in pedagogical treatments as evidence that interference effects with light cannot be interpreted in terms of one photon interfering with another photon—that, in fact, a *single* photon must travel through *both* slits of a double-slit apparatus. Modern understanding of the subject has shown that the conditions in Taylor's experiment were not in fact sufficient to demonstrate this, because the light source was not in fact a single-photon source, but the experiment was reproduced in 1986 using a single-photon source, and the same result was obtained.^{[9]}

He followed this up with work on shock waves, winning a Smith's Prize. In 1910 he was elected to a Fellowship at Trinity College, and the following year he was appointed to a meteorology post, becoming Reader in Dynamical Meteorology. His work on turbulence in the atmosphere led to the publication of "Turbulent motion in fluids",^{[10]} which won him the Adams Prize in 1915.

In 1913 Taylor served as a meteorologist aboard the Ice Patrol vessel *Scotia*, where his observations formed the basis of his later work on a theoretical model of mixing of the air. At the outbreak of World War I, he was sent to the Royal Aircraft Factory at Farnborough to apply his knowledge to aircraft design, working, amongst other things, on the stress on propeller shafts. Not content just to sit back and do the science, he also learned to fly aeroplanes and make parachute jumps.

After the war Taylor returned to Trinity and worked on an application of turbulent flow to oceanography. He also worked on the problem of bodies passing through a rotating fluid. In 1923 he was appointed to a Royal Society research professorship as a Yarrow Research Professor. This enabled him to stop teaching, which he had been doing for the previous four years, and which he both disliked and had no great aptitude for. It was in this period that he did his most wide-ranging work on fluid mechanics and solid mechanics, including research on the deformation of crystalline materials which followed from his war work at Farnborough. He also produced another major contribution to turbulent flow, where he introduced a new approach through a statistical study of velocity fluctuations.

In 1934, Taylor, roughly contemporarily with Michael Polanyi and Egon Orowan, realised that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations developed by Vito Volterra in 1905. The insight was critical in developing the modern science of solid mechanics.

During World War II, Taylor again applied his expertise to military problems such as the propagation of blast waves, studying both waves in air and underwater explosions. Taylor was sent to the United States in 1944–1945 as part of the British delegation to the Manhattan Project. At Los Alamos, Taylor helped solve implosion instability problems in the development of atomic weapons particularly the plutonium bomb used at Nagasaki on 9 August 1945.

In 1944 he also received his knighthood and the Copley Medal from the Royal Society.

Taylor was present at the Trinity (nuclear test), July 16, 1945, as part of General Leslie Groves' "VIP List" of just 10 people who observed the test from Compania Hill, about 20 miles (32 km) northwest of the shot tower. By a strange twist, Joan Hinton, another direct descendant of the mathematician, George Boole, had been working on the same project and witnessed the event in an unofficial capacity. They met at the time but later followed different paths: Joan, strongly opposed to nuclear weapons, to defect to Mao's China, Taylor to hold throughout his career the view that governmental policy was not within the remit of the scientist.^{[11]}

In 1950, he published two papers estimating the yield of the explosion using the Buckingham Pi theorem, and high speed photography stills from that test, bearing timestamps and physical scale of the blast radius, which had been published in Life magazine. His estimate of 22 kt was remarkably close to the accepted value of 20 kt, which was still highly classified at that time.

Taylor continued his research after the war, serving on the Aeronautical Research Committee and working on the development of supersonic aircraft. Though he officially retired in 1952, he continued research for the next twenty years, concentrating on problems that could be attacked using simple equipment. This led to such advances as a method for measuring the second coefficient of viscosity. Taylor devised an incompressible liquid with separated gas bubbles suspended in it. The dissipation of the gas in the liquid during expansion was a consequence of the shear viscosity of the liquid. Thus the bulk viscosity could easily be calculated. His other late work included the longitudinal dispersion in flow in tubes, movement through porous surfaces, and the dynamics of sheets of liquids.

Aspects of Taylor's life often found expression in his work. His over-riding interest in the movement of air and water, and by extension his studies of the movement of unicellular marine creatures and of weather, were related to his lifelong love of sailing. In the 1930s he invented the 'CQR' anchor, which was both stronger and more manageable than any in use, and which was used for all sorts of small craft including seaplanes.^{[12]}

His final research paper was published in 1969, when he was 83. In it he resumed his interest in electrical activity in thunderstorms, as jets of conducting liquid motivated by electrical fields. The cone from which such jets are observed is called the Taylor cone, after him. In the same year Taylor received the A. A. Griffith Medal and Prize and was appointed to the Order of Merit.

Taylor married Grace Stephanie Frances Ravenhill, a school teacher in 1925. They stayed together until Stephanie's death in 1965. Taylor suffered a severe stroke in 1972 which effectively put an end to his work. He died in Cambridge in 1975.

**^**Batchelor, G. K. (1976). "Geoffrey Ingram Taylor 7 March 1886 -- 27 June 1975".*Biographical Memoirs of Fellows of the Royal Society*.**22**: 565. doi:10.1098/rsbm.1976.0021.**^**O'Connor, John J.; Robertson, Edmund F., "G. I. Taylor",*MacTutor History of Mathematics archive*, University of St Andrews.**^**G. I. Taylor at the Mathematics Genealogy Project**^***The Life and Legacy of G. I. Taylor*, by George Batchelor, Cambridge University Press, 1994 ISBN 0-521-46121-9**^**Taylor, Geoffrey Ingram, Sir,*Scientific papers*. Edited by G.K. Batchelor, Cambridge University Press 1958–71. (Vol. 1. Mechanics of solids – Vol. 2. Meteorology, oceanography, and turbulent flow – Vol. 3. Aerodynamics and the mechanics of projectiles and explosions – Vol. 4. Mechanics of fluids: miscellaneous papers).**^**"G.I. Taylor as I Knew Him".*Advances in Applied Mechanics Volume 16*. Advances in Applied Mechanics.**16**. 1976. pp. xii-. doi:10.1016/S0065-2156(08)70086-3. ISBN 9780120020164.**^**Pippard, S. B. A. (1975). "Sir Geoffrey Taylor".*Physics Today*.**28**(9): 67. Bibcode:1975PhT....28i..67P. doi:10.1063/1.3069178.**^**G.I. Taylor, Interference fringes with feeble light, Proc. Camb. Phil. Soc. 15, 114-115 (1909)**^**Grangier, Roger, and Aspect, "Experimental evidence for a photon anticorrelation effect on a beamsplitter," Europhys. Lett. 1 (1986) 173**^**Taylor,G.I. 1915. Eddy Motion in the Atmosphere. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 215(A 523):1-26**^**Gerry Kennedy, The Booles and the Hintons, Atrium Press, July 2016**^**Taylor, G. I., The Holding Power of Anchors April 1934

- A Real Media stream of Taylor's Hydrodynamic demo, courtesy of MIT
- Classical Physics Through the Work of GI Taylor. Course given on Taylor's work
- Article on the course above
- G.I. Taylor Medal of the Society of Engineering Science
- Video recording of K.R. Sreenivasan's lecture on the life and work of G.I. Taylor

Andreas Acrivos (born 13 June 1928) is the Albert Einstein Professor of Science and Engineering, Emeritus at the City College of New York. He is also the director of the Benjamin Levich Institute for Physicochemical Hydrodynamics.

Blast waveIn fluid dynamics, a blast wave is the increased pressure and flow resulting from the deposition of a large amount of energy in a small, very localised volume. The flow field can be approximated as a lead shock wave, followed by a self-similar subsonic flow field. In simpler terms, a blast wave is an area of pressure expanding supersonically outward from an explosive core. It has a leading shock front of compressed gases. The blast wave is followed by a blast wind of negative pressure, which sucks items back in towards the center. The blast wave is harmful especially when one is very close to the center or at a location of constructive interference. High explosives that detonate generate blast waves.

Daniel D. JosephDaniel Donald Joseph (March 26, 1929 – May 24, 2011) was an American mechanical engineer. He was the Regents Professor Emeritus and Russell J. Penrose Professor Emeritus of Department of Aerospace Engineering and Mechanics at the University of Minnesota. He was widely known for his research in fluid dynamics.

DislocationIn materials science, a dislocation or Taylor's dislocation is a crystallographic defect or irregularity within a crystal structure. The presence of dislocations strongly influences many of the properties of materials.

The theory describing the elastic fields of the defects was originally developed by Vito Volterra in 1907,. The term 'dislocation' referring to a defect on the atomic scale was coined by G. I. Taylor in 1934. Some types of dislocations can be visualized as being caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the surrounding planes are not straight, but instead they bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. This phenomenon is analogous to the following situation related to a stack of paper: If half of a piece of paper is inserted into a stack of paper, the defect in the stack is noticeable only at the edge of the half sheet.

The two primary types of dislocations are edge dislocations and screw dislocations. Mixed dislocations are intermediate between these.

Mathematically, dislocations are a type of topological defect, sometimes called a soliton. Dislocations behave as stable particles: they can move around, but maintain their identity. Two dislocations of opposite orientation can cancel when brought together, but a single dislocation typically cannot "disappear" on its own.

Entrainment (hydrodynamics)See entrainment for other types.Entrainment is the transport of fluid across an interface between two bodies of fluid by a shear induced turbulent flux.The entrainment hypothesis was first used as a model for flow in plumes by G. I. Taylor when studying the use of oil drum fires to clear fog from aeroplane runways during World War II. It has gone on to be a common model of turbulence closure used in environmental and geophysical fluid mechanics.Entrainment is important in turbulent jets, plumes and gravity currents and is a topic of current research.Eductors or eductor-jet pumps are an example of entrainment. They are used onboard many ships to pump out flooded compartments: in the event of an accident, seawater is pumped to the eductor and forced through a jet, and any fluid at the inlet of the eductor is carried along to the outlet and up and out of the compartment. Eductors can pump out whatever can flow through them, including water, oil, and small pieces of wood. Another example is the pump-jet, which is used for marine propulsion. Jet pumps are also used to circulate reactor coolant in several designs of boiling water reactors.

In power generation, this phenomenon is used in steam jet air ejectors to maintain condenser vacuum by removing non-condensible gases from the condenser.

Franklin MedalThe Franklin Medal was a science award presented from 1915 through 1997 by the Franklin Institute located in Philadelphia, Pennsylvania, U.S. It was founded in 1914 by Samuel Insull.

The Franklin Medal was the most prestigious of the various awards presented by the Franklin Institute. Together with other historical awards, it was merged into the Benjamin Franklin Medal, initiated in 1998.

G. I. Taylor Professor of Fluid MechanicsThe G. I. Taylor Professorship of Fluid Mechanics is a professorship in fluid mechanics at the University of Cambridge. It was founded in 1992 and named in honor of G. I. Taylor.

Grigory BarenblattGrigory Isaakovich Barenblatt (Russian: Григо́рий Исаа́кович Баренблат; 10 July 1927 – 22 June 2018) was a Russian mathematician.

Homogeneous isotropic turbulenceHomogeneous isotropic turbulence is an idealized version of the realistic turbulence, but amenable to analytical studies. The concept of isotropic turbulence was first introduced by G.I. Taylor in 1935. The meaning of the turbulence is given below,

homogeneous, the statistical properties are invariant under arbitrary translations of the coordinate axes

isotropic, the statistical properties are invariant for full rotation group, which includes rotations and reflections of the coordinate axes.G.I. Taylor also suggested a way of obtaining almost homogeneous isotropic turbulence by passing fluid over a uniform grid. The theory was further developed by Theodore von Kármán and Leslie Howarth (Kármán–Howarth equation) under dynamical considerations. Kolmogorov's theory of 1941 was developed using Taylor's idea as a platform.

June 27June 27 is the 178th day of the year (179th in leap years) in the Gregorian calendar. 187 days remain until the end of the year.

March 7March 7 is the 66th day of the year (67th in leap years) in the Gregorian calendar. 299 days remain until the end of the year.

Nuclear weapon yieldThe explosive yield of a nuclear weapon is the amount of energy released when that particular nuclear weapon is detonated, usually expressed as a TNT equivalent (the standardized equivalent mass of trinitrotoluene which, if detonated, would produce the same energy discharge), either in kilotons (kt—thousands of tons of TNT), in megatons (Mt—millions of tons of TNT), or sometimes in terajoules (TJ). An explosive yield of one terajoule is equal to 0.239 kilotonnes of TNT. Because the accuracy of any measurement of the energy released by TNT has always been problematic, the conventional definition is that one kiloton of TNT is held simply to be equivalent to 1012 calories.

The yield-to-weight ratio is the amount of weapon yield compared to the mass of the weapon. The practical maximum yield-to-weight ratio for fusion weapons (thermonuclear weapons) has been estimated to six megatons of TNT per metric ton of bomb mass (25 TJ/kg). Yields of 5.2 megatons/ton and higher have been reported for large weapons constructed for single-warhead use in the early 1960s. Since then, the smaller warheads needed to achieve the increased net damage efficiency (bomb damage/bomb mass) of multiple warhead systems have resulted in decreases in the yield/mass ratio for single modern warheads.

Paul LindenPaul Frederick Linden (born 29 January 1947) is a mathematician specialising in fluid dynamics. He was the third G. I. Taylor Professor of Fluid Mechanics at the University of Cambridge and a fellow of Downing College.

Philip DrazinPhilip Gerald Drazin (25 May 1934 – 10 January 2002) was a British mathematician and a leading international expert in fluid dynamics.He completed his PhD at the University of Cambridge under G. I. Taylor in 1958. He was awarded the Smith's Prize in 1957. After leaving Cambridge, he spent two years at MIT before moving to the University of Bristol, where he stayed and became a Professor until retiring in 1999. After retiring, he lectured at the University of Oxford and the University of Bath until his death in 2002.

Drazin worked on hydrodynamic stability and the transition to turbulence. His 1974 paper On a model of instability of a slowly-varying flow introduced the concept of a global mode solution to a system of partial differential equations such as the Navier-Stokes equations. He also worked on solitons.

In 1998 he was awarded the Symons Gold Medal of the Royal Meteorological Society

Rayleigh–Taylor instabilityThe Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Examples include the behavior of water suspended above oil in the gravity of Earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear explosions, supernova explosions in which expanding core gas is accelerated into denser shell gas, instabilities in plasma fusion reactors and inertial confinement fusion.Water suspended atop oil is an everyday example of Rayleigh–Taylor instability, and it may be modeled by two completely plane-parallel layers of immiscible fluid, the more dense on top of the less dense one and both subject to the Earth's gravity. The equilibrium here is unstable to any perturbations or disturbances of the interface: if a parcel of heavier fluid is displaced downward with an equal volume of lighter fluid displaced upwards, the potential energy of the configuration is lower than the initial state. Thus the disturbance will grow and lead to a further release of potential energy, as the more dense material moves down under the (effective) gravitational field, and the less dense material is further displaced upwards. This was the set-up as studied by Lord Rayleigh. The important insight by G. I. Taylor was his realisation that this situation is equivalent to the situation when the fluids are accelerated, with the less dense fluid accelerating into the more dense fluid. This occurs deep underwater on the surface of an expanding bubble and in a nuclear explosion.As the RT instability develops, the initial perturbations progress from a linear growth phase into a non-linear growth phase, eventually developing "plumes" flowing upwards (in the gravitational buoyancy sense) and "spikes" falling downwards. In the linear phase, equations can be linearized and the amplitude of perturbations is growing exponentially with time. In the non-linear phase, perturbation amplitude is too large for the non-linear terms to be neglected. In general, the density disparity between the fluids determines the structure of the subsequent non-linear RT instability flows (assuming other variables such as surface tension and viscosity are negligible here). The difference in the fluid densities divided by their sum is defined as the Atwood number, A. For A close to 0, RT instability flows take the form of symmetric "fingers" of fluid; for A close to 1, the much lighter fluid "below" the heavier fluid takes the form of larger bubble-like plumes.This process is evident not only in many terrestrial examples, from salt domes to weather inversions, but also in astrophysics and electrohydrodynamics. RT instability structure is also evident in the Crab Nebula, in which the expanding pulsar wind nebula powered by the Crab pulsar is sweeping up ejected material from the supernova explosion 1000 years ago. The RT instability has also recently been discovered in the Sun's outer atmosphere, or solar corona, when a relatively dense solar prominence overlies a less dense plasma bubble. This latter case is a clear example of the magnetically modulated RT instability.Note that the RT instability is not to be confused with the Plateau–Rayleigh instability (also known as Rayleigh instability) of a liquid jet. This instability, sometimes called the hosepipe (or firehose) instability, occurs due to surface tension, which acts to break a cylindrical jet into a stream of droplets having the same total volume but higher surface area.

Many people have witnessed the RT instability by looking at a lava lamp, although some might claim this is more accurately described as an example of Rayleigh–Bénard convection due to the active heating of the fluid layer at the bottom of the lamp.

Steven OrszagSteven Alan Orszag (February 27, 1943 – May 1, 2011) was an American mathematician.

Taylor dispersionTaylor dispersion is an effect in fluid mechanics in which a shear flow can increase the effective diffusivity of a species. Essentially, the shear acts to smear out the concentration distribution in the direction of the flow, enhancing the rate at which it spreads in that direction. The effect is named after the British fluid dynamicist G. I. Taylor.

The canonical example is that of a simple diffusing species in uniform

Poiseuille flow through a uniform circular pipe with no-flux

boundary conditions.

Taylor–Goldstein equationThe Taylor–Goldstein equation is an ordinary differential equation used in the fields of geophysical fluid dynamics, and more generally in fluid dynamics, in presence of quasi-2D flows. It describes the dynamics of the Kelvin–Helmholtz instability, subject to buoyancy forces (e.g. gravity), for stably stratified fluids in the dissipation-less limit. Or, more generally, the dynamics of internal waves in the presence of a (continuous) density stratification and shear flow. The Taylor–Goldstein equation is derived from the 2D Euler equations, using the Boussinesq approximation.The equation is named after G.I. Taylor and S. Goldstein, who derived the equation independently from each other in 1931. The third independent derivation, also in 1931, was made by B. Haurwitz.

Tim PedleyTimothy John "Tim" Pedley (born 23 March 1942) is a British mathematician and a former G. I. Taylor Professor of Fluid Mechanics at the University of Cambridge. His principal research interest is the application of fluid mechanics to biology and medicine.He then spent three years at Johns Hopkins University as a post-doctoral fellow. From 1968 to 1973 he was a lecturer at Imperial College London, after which he moved to the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge. He remained at Cambridge until 1990 when he moved to Leeds University to be Professor of Applied Mathematics. In 1996 he returned to Cambridge and from 2000 to 2005 he was head of DAMTP.He is a fellow of Gonville and Caius College, Cambridge and a fellow of the Royal Society (elected 1995). In 2008 Pedley and Professor J. D. Murray, FRS were jointly awarded the Gold Medal of the Institute of Mathematics and its Applications in recognition of their "outstanding contributions to mathematics and its applications over a period of years".

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