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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]
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.
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.
The Batchelor vortex is an approximate solution to the Navier–Stokes equations obtained using a boundary layer approximation. The physical reasoning behind this approximation is the assumption that the axial gradient of the flow field of interest is of much smaller magnitude than the radial gradient.
As fluid dynamics is described by non-canonical dynamics, which possess an infinite amount of Casimir invariants, an alternative formulation of Hamiltonian formulation of fluid dynamics can be introduced through the use of Nambu mechanics [1] [2]
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where ε is the average rate of dissipation of turbulence kinetic energy per unit mass, and; ν is the kinematic viscosity of the fluid.; Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, η may be much smaller.