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George Keith Batchelor FRS [1] (8 March 1920 – 30 March 2000) was an Australian applied mathematician and fluid dynamicist. He was for many years a Professor of Applied Mathematics in the University of Cambridge , and was founding head of the Department of Applied Mathematics and Theoretical Physics (DAMTP).
In fluid and molecular dynamics, the Batchelor scale, determined by George Batchelor (1959), [1] describes the size of a droplet of fluid that will diffuse in the same time it takes the energy in an eddy of size η to dissipate. The Batchelor scale can be determined by: [2]
In fluid dynamics, Prandtl–Batchelor theorem states that if in a two-dimensional laminar flow at high Reynolds number closed streamlines occur, then the vorticity in the closed streamline region must be a constant. A similar statement holds true for axisymmetric flows. The theorem is named after Ludwig Prandtl and George Batchelor.
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. Below is a structured list of topics in fluid dynamics.
Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach. [2]
In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply to inviscid flows and flows where the influence of viscous forces are small and can be ignored. Helmholtz's three theorems are as follows: [1] Helmholtz's first theorem
For the next century or so vortex dynamics matured as a subfield of fluid mechanics, always commanding at least a major chapter in treatises on the subject. Thus, H. Lamb's well known Hydrodynamics (6th ed., 1932) devotes a full chapter to vorticity and vortex dynamics as does G. K. Batchelor's Introduction to Fluid Dynamics (1967). In due ...
Batchelor, G.K. (1973), An introduction to fluid dynamics, Cambridge University Press, ISBN 978-0-521-09817-5 Chanson, H. (2009), Applied Hydrodynamics: An Introduction to Ideal and Real Fluid Flows , CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 478 pages, ISBN 978-0-415-49271-3