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The Taylor microscale falls in between the large-scale eddies and the small-scale eddies, which can be seen by calculating the ratios between and the Kolmogorov microscale . Given the length scale of the larger eddies l ∝ k 3 / 2 ϵ {\displaystyle l\propto {\frac {k^{3/2}}{\epsilon }}} , and the turbulence Reynolds number Re l {\displaystyle ...
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. [1] [2]
Taylor presented his results on June 27, 1941. [3] 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. [4] 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. [5]
The description for Taylor–von Neumann–Sedov blast wave utilizes and the total energy content of the flow to develop a self-similar solution. Unlike this problem, the imploding shock wave is not self-similar throughout the entire region (the flow field near = depends on the manner in which the shock wave is generated) and thus the Guderley ...
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-by-step solution as time progresses. An exact solution in two spatial dimensions is known, and is presented below. Animation of a Taylor-Green Vortex using colour coded Lagrangian tracers
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.
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This figure represents the evolution of the Rayleigh–Taylor instability from small wavelength perturbations at the interface (a) which grow into the ubiquitous mushroom shaped spikes (fluid structures of heavy into light fluid) and bubbles (fluid structures of light into heavy fluid) (b) and these fluid structures interact due to bubble merging and competition (c) eventually developing into ...