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Moffatt Eddies
Moffatt eddies are sequences of eddies that develop in corners bounded by plane walls (or sometimes between a wall and a free surface) due to an arbitrary disturbance acting at asymptotically large distances from the corner. Although the source of motion is the arbitrary disturbance at large distances, the eddies develop quite independently and thus solution of these eddies emerges from an eigenvalue problem, a self-similar solution of the second kind. The eddies are named after Keith Moffatt, who discovered these eddies in 1964, although some of the results were already obtained by William Reginald Dean and P. E. Montagnon in 1949. Lord Rayleigh also studied the problem of flow near the corner with homogeneous boundary conditions in 1911. Moffatt eddies inside cones are solved by P. N. Shankar. Flow description Near the corner, the flow can be assumed to be Stokes flow. Describing the two-dimensional planar problem by the cylindrical coordinates (r,\theta) with velocity componen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eddy (fluid Dynamics)
In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. This phenomenon is naturally observed behind large emergent rocks in swift-flowing rivers. An eddy is a movement of fluid that deviates from the general flow of the fluid. An example for an eddy is a vortex which produces such deviation. However, there are other types of eddies that are not simple vortices. For example, a Rossby wave is an eddy which is an undulation that is a deviation from mean flow, but doesn't have the local closed streamlines of a vortex. Swirl and eddies in engineering The propensity of a fluid to swirl is used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similar Solution
In the study of partial differential equations, particularly in fluid dynamics, a self-similar solution is a form of solution which is similar to itself if the independent and dependent variables are appropriately scaled. Self-similar solutions appear whenever the problem lacks a characteristic length or time scale (for example, the Blasius boundary layer of an infinite plate, but not of a finite-length plate). These include, for example, the Blasius boundary layer or the Sedov–Taylor shell. Concept A powerful tool in physics is the concept of dimensional analysis and scaling laws. By examining the physical effects present in a system, we may estimate their size and hence which, for example, might be neglected. In some cases, the system may not have a fixed natural length or time scale, while the solution depends on space or time. It is then necessary to construct a scale using space or time and the other dimensional quantities present—such as the viscosity \nu. These constru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Moffatt
Henry Keith Moffatt, FRS FRSE (born 12 April 1935) is a Scottish mathematician with research interests in the field of fluid dynamics, particularly magnetohydrodynamics and the theory of turbulence. He was Professor of Mathematical Physics at the University of Cambridge from 1980 to 2002. Early life and education Moffatt was born on 12 April 1935 to Emmeline Marchant and Frederick Henry Moffatt''.'' He was schooled at George Watson's College, Edinburgh, going on to study Mathematical Sciences at the University of Edinburgh, graduating in 1957. He then went to Trinity College, Cambridge, where he studied mathematics and, 1959, he was a Wrangler. In 1960, he was awarded a Smith's Prize while preparing his PhD. He received his PhD in 1962, the title of his dissertation was ''Magnetohydrodynamic Turbulence.'' Career After completing his PhD, Moffatt joined the staff of the Mathematics Faculty in Cambridge as an Assistant Lecturer and became a Fellow of Trinity College. He was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Fluid Mechanics
The ''Journal of Fluid Mechanics'' is a peer-reviewed scientific journal in the field of fluid mechanics. It publishes original work on theoretical, computational, and experimental aspects of the subject. The journal is published by Cambridge University Press and retains a strong association with the University of Cambridge, in particular the Department of Applied Mathematics and Theoretical Physics (DAMTP). Until January 2020, volumes were published twice a month in a single-column B5 format, but the publication is now online-only with the same frequency. The journal was established in 1956 by George Batchelor, who remained the editor-in-chief for some forty years. He started out as the sole editor, but later a team of associate editors provided assistance in arranging the review of articles. John W. Miles is the author who has most papers (117 times) appeared in this journal. Editors The following people have been editor (later, editor in chief) of the ''Journal of Fluid Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Reginald Dean
William Reginald Dean (1896–1973) was a British applied mathematician and fluid dynamicist. His research interests included Stokes flow, solid mechanics, and flow in curved channels. The Dean number bears his name. Dean carried out pioneering work in the study of fluid flow at low Reynolds numbers, by applying methods from elasticity theory. Some of his more famous results include solutions for secondary flow in curved tubes, for the perturbation to shear flow near a wall caused by a gap in the wall, and for flow in a corner. Dean was an undergraduate at Trinity College, Cambridge. He spent five years at Imperial College, and was later a fellow of Trinity College. During the war he undertook mathematical work as part of the ''Anti-Aircraft Experimental Section of M.I.D.'' He also held the Goldsmid Chair in Applied Mathematics at University College London (from which he retired in 1964), and a chair at the University of Arizona The University of Arizona (Arizona, U of A, UAr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lord Rayleigh
John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Among many honors, he received the 1904 Nobel Prize in Physics "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies." He served as president of the Royal Society from 1905 to 1908 and as chancellor of the University of Cambridge from 1908 to 1919. Rayleigh provided the first theoretical treatment of the elastic scattering of light by particles much smaller than the light's wavelength, a phenomenon now known as "Rayleigh scattering", which notably explains why the sky is blue. He studied and described transverse surface waves in solids, now known as "Rayleigh waves". He contributed extensively to fluid dynamics, with concepts such as the Rayleigh number (a dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes Flow
Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,Kim, S. & Karrila, S. J. (2005) ''Microhydrodynamics: Principles and Selected Applications'', Dover. . is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. \mathrm \ll 1. This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature this type of flow occurs in the swimming of microorganisms, sperm and the flow of lava. In technology, it occurs in paint, MEMS devices, and in the flow of viscous polymers generally. The equations of motion for Stokes flow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be solved by a number of well-known methods for linear differential equations. The primary Green's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream Function
The stream function is defined for incompressible flow, incompressible (divergence-free) fluid flow, flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can be expressed as the derivatives of the scalar field, scalar stream function. The stream function can be used to plot Streamlines, streaklines, and pathlines, streamlines, which represent the trajectories of particles in a steady flow. The two-dimensional Lagrange stream function was introduced by Joseph Louis Lagrange in 1781. The Stokes stream function is for axisymmetrical three-dimensional flow, and is named after George Gabriel Stokes. Considering the particular case of fluid dynamics, the difference between the stream function values at any two points gives the volumetric flow rate (or volumetric flux) through a line connecting the two points. Since streamlines are tangent to the flow velocity vector of the flow, the value of the stream function must be constant along ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biharmonic Equation
In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear elasticity theory and the solution of Stokes flows. Specifically, it is used in the modeling of thin structures that react elastically to external forces. Notation It is written as :\nabla^4\varphi=0 or :\nabla^2\nabla^2\varphi=0 or :\Delta^2\varphi=0 where \nabla^4, which is the fourth power of the del operator and the square of the Laplacian operator \nabla^2 (or \Delta), is known as the biharmonic operator or the bilaplacian operator. In Cartesian coordinates, it can be written in n dimensions as: : \nabla^4\varphi=\sum_^n\sum_^n\partial_i\partial_i\partial_j\partial_j \varphi =\left(\sum_^n\partial_i\partial_i\right)\left(\sum_^n \partial_j\partial_j\right) \varphi. Because the formula here contains a summation of indices, many mathematicians prefer the notation \Delta^2 over \nabla^4 because the former makes clear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Scraping Flow
In fluid dynamics, Taylor scraping flow is a type of two-dimensional corner flow occurring when one of the wall is sliding over the other with constant velocity, named after G. I. Taylor. Flow description Consider a plane wall located at \theta=0 in the cylindrical coordinates (r,\theta), moving with a constant velocity U towards the left. Consider another plane wall(scraper), at an inclined position, making an angle \alpha from the positive x direction and let the point of intersection be at r=0. This description is equivalent to moving the scraper towards right with velocity U. The problem is singular at r=0 because at the origin, the velocities are discontinuous, thus the velocity gradient is infinite there. Taylor noticed that the inertial terms are negligible as long as the region of interest is within r\ll\nu/U( or, equivalently Reynolds number Re = Ur/\nu \ll 1), thus within the region the flow is essentially a Stokes flow. For example, George Batchelor gives a typical valu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
