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Geoffrey Ingram Taylor
Sir Geoffrey Ingram Taylor OM FRS FRSE (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". Early life and education 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. Career and research To students of physics, Taylor is best known for his very first paper, published ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middlesex
Middlesex (; abbreviation: Middx) is a Historic counties of England, historic county in South East England, southeast England. Its area is almost entirely within the wider urbanised area of London and mostly within the Ceremonial counties of England, ceremonial county of Greater London, with small sections in neighbouring ceremonial counties. Three rivers provide most of the county's boundaries; the River Thames, Thames in the south, the River Lea, Lea to the east and the River Colne, Hertfordshire, Colne to the west. A line of hills forms the northern boundary with Hertfordshire. Middlesex county's name derives from its origin as the Middle Saxons, Middle Saxon Province of the Anglo-Saxon England, Anglo-Saxon Kingdom of Essex, with the county of Middlesex subsequently formed from part of that territory in either the ninth or tenth century, and remaining an administrative unit until 1965. The county is the List of counties of England by area in 1831, second smallest, after Ru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Dispersion
Taylor dispersion or Taylor diffusion 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, who described the shear-induced dispersion for large Peclet numbers. The analysis was later generalized by Rutherford Aris for arbitrary values of the Peclet number. The dispersion process is sometimes also referred to as the Taylor-Aris dispersion. The canonical example is that of a simple diffusing species in uniform Poiseuille flow through a uniform circular pipe with no-flux boundary conditions. Description We use ''z'' as an axial coordinate and ''r'' as the radial coordinate, and assume axisymmetry. The pipe has radius ''a'', and the fluid velocity is: : \boldsymbol = w\hat = w_0 (1-r^2/a^2) \hat The conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rayleigh–Taylor Instability
The 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. Drazin (2002) pp. 50–51. 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 denser fluid 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–von Neumann–Sedov Blast Wave
Taylor–von Neumann–Sedov blast wave (or sometimes referred to as Sedov–von Neumann–Taylor blast wave) refers to a blast wave induced by a strong explosion. The blast wave was described by a self-similar solution independently by G. I. Taylor, John von Neumann and Leonid Sedov during World War II. History G. I. Taylor was told by the British Ministry of Home Security that it might be possible to produce a bomb in which a very large amount of energy would be released by nuclear fission and asked to report the effect of such weapons. Taylor presented his results on June 27, 1941. Exactly at the same time, in the United States, John von Neumann was working on the same problem and he presented his results on June 30, 1941. It was said that Leonid Sedov was also working on the problem around the same time in the USSR, although Sedov never confirmed any exact dates. The complete solution was published first by Sedov in 1946. von Neumann published his results in August 1947 in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Proudman Theorem
In fluid mechanics, the Taylor–Proudman theorem (after Geoffrey Ingram Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity \Omega, the fluid velocity will be uniform along any line parallel to the axis of rotation. \Omega must be large compared to the movement of the solid body in order to make the Coriolis force large compared to the acceleration terms. Derivation The Navier–Stokes equations for steady flow, with zero viscosity and a body force corresponding to the Coriolis force, are : \rho(\cdot\nabla)=-\nabla p, where is the fluid velocity, \rho is the fluid density, and p the pressure. If we assume that F=\nabla\Phi=-2\rho\mathbf\Omega\times is a scalar potential and the advective term on the left may be neglected (reasonable if the Rossby number is much less than unity) and that the flow is incompressible (density is constant), the equations become: : 2\rho\mathbf\Omega\times=-\n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Green Vortex
In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates. It is named after the British physicist and mathematician Geoffrey Ingram Taylor and his collaborator A. E. Green. Taylor, G. I. and Green, A. E., ''Mechanism of the Production of Small Eddies from Large Ones'', Proc. R. Soc. Lond. A, 158, 499–521 (1937). Original work In the original work of Taylor and Green, a particular flow is analyzed in three spatial dimensions, with the three velocity components \mathbf=(u,v,w) at time t=0 specified by : u = A \cos ax \sin by \sin cz, : v = B \sin ax \cos by \sin cz, : w = C \sin ax \sin by \cos cz. The continuity equation \nabla \cdot \mathbf=0 determines that Aa+Bb+Cc=0. The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Goldstein Equation
The 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. Formulation The equation is derived by solving a linearized version of the Navier–Stokes equation, in presence of gravity g and a mean density gradient (with gradient-length L_\rho), for the perturbation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Culick Flow
In fluid dynamics, Taylor–Culick flow describes the axisymmetric flow inside a long slender cylinder with one end closed, supplied by a constant flow injection through the sidewall. The flow is named after Geoffrey Ingram Taylor and F. E. C. Culick, since Taylor showed first in 1956 that the flow inside such a configuration is inviscid and rotational and later in 1966, Culick found a self-similar solution to the problem applied to solid-propellant rocket combustion. Although the solution is derived for inviscid equation, it satisfies the non-slip condition at the wall since as Taylor argued that the boundary layer that be supposed to exist if any at the sidewall will be blown off by flow injection. Hence, the flow is referred to as quasi-viscous. Flow description The axisymmetric inviscid equation is governed by Hicks equation, that reduces when no swirl is present (i.e., zero circulation) to :\frac - \frac \frac + \frac = -r^2 f(\psi) where \psi is the stream function, r is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Couette Flow
In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number ''Re'', the flow is steady and purely azimuthal. This basic state is known as circular Couette flow, after Maurice Marie Alfred Couette, who used this experimental device as a means to measure viscosity. Sir Geoffrey Ingram Taylor investigated the stability of Couette flow in a ground-breaking paper. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and demonstrated that the no-slip condition, which was in dispute by the scientific community at the time, was the correct boundary condition for viscous flows at a solid boundary. Taylor showed that when the angular velocity of the inner cylinder is increased above a certain threshold, Couette flow becomes unstable and a secondary steady state characterized by axisymmetric toroidal vortices, known as Taylor vortex f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schneider Flow
Schneider flow describes the axisymmetric outer flow induced by a laminar or turbulent jet having a large jet Reynolds number or by a laminar plume with a large Grashof number, in the case where the fluid domain is bounded by a wall. When the jet Reynolds number or the plume Grashof number is large, the full flow field constitutes two regions of different extent: a thin boundary-layer flow that may identified as the jet or as the plume and a slowly moving fluid in the large outer region encompassing the jet or the plume. The Schneider flow describing the latter motion is an exact solution of the Navier-Stokes equations, discovered by Wilhelm Schneider in 1981. The solution was discovered also by A. A. Golubinskii and V. V. Sychev in 1979, however, was never applied to flows entrained by jets. The solution is an extension of Taylor's potential flow solutionTaylor, G. (1958). Flow induced by jets. Journal of the Aerospace Sciences, 25(7), 464–465. to arbitrary Reynolds number. Math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beltrami Flow
In fluid dynamics, Beltrami flows are flows in which the vorticity vector \mathbf and the velocity vector \mathbf are parallel to each other. In other words, Beltrami flow is a flow where Lamb vector is zero. It is named after the Italian mathematician Eugenio Beltrami due to his derivation of the Beltrami vector field, while initial developments in fluid dynamics were done by the Russian scientist Ippolit S. Gromeka in 1881. Description Since the vorticity vector \boldsymbol and the velocity vector \mathbf are parallel to each other, we can write :\boldsymbol\times\mathbf=0, \quad \boldsymbol = \alpha(\mathbf,t) \mathbf, where \alpha(\mathbf,t) is some scalar function. One immediate consequence of Beltrami flow is that it can never be a planar or axisymmetric flow because in those flows, vorticity is always perpendicular to the velocity field. The other important consequence will be realized by looking at the incompressible vorticity equation :\frac + (\mathbf\cdot\nabla)\bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as ''glide'' or slip. The crystalline order is restored on either side of a ''glide dislocation'' but the atoms on one side have moved by one position. The crystalline order is not fully restored with a ''partial dislocation''. A dislocation defines the boundary between ''slipped'' and ''unslipped'' regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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