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  2. Taylor microscale - Wikipedia

    en.wikipedia.org/wiki/Taylor_microscale

    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 ...

  3. Self-similar solution - Wikipedia

    en.wikipedia.org/wiki/Self-similar_solution

    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]

  4. Guderley–Landau–Stanyukovich problem - Wikipedia

    en.wikipedia.org/wiki/Guderley–Landau...

    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 ...

  5. Numerical methods for ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/Numerical_methods_for...

    Solving Ordinary Differential Equations. I. Nonstiff Problems. Springer Series in Computational Mathematics. Vol. 8 (2nd ed.). Springer-Verlag, Berlin. ISBN 3-540-56670-8. MR 1227985. Ernst Hairer and Gerhard Wanner, Solving ordinary differential equations II: Stiff and differential-algebraic problems, second edition, Springer Verlag, Berlin, 1996.

  6. Kolmogorov microscales - Wikipedia

    en.wikipedia.org/wiki/Kolmogorov_microscales

    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.

  7. Multiscale modeling - Wikipedia

    en.wikipedia.org/wiki/Multiscale_modeling

    The aforementioned DOE multiscale modeling efforts were hierarchical in nature. The first concurrent multiscale model occurred when Michael Ortiz (Caltech) took the molecular dynamics code Dynamo, developed by Mike Baskes at Sandia National Labs, and with his students embedded it into a finite element code for the first time. [18]

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  9. Taylor–Green vortex - Wikipedia

    en.wikipedia.org/wiki/Taylor–Green_vortex

    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