Turbulence lecture 21

Turbulence lecture 21 - Turbulence Lecture 21 Non-linear...

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Turbulence Lecture 21 Non-linear Dynamics Strong non-linearity is a key feature of turbulence. 1. Unstable, chaotic behavior. 2. Strongly vortical (vortex stretching) 30’s & 40’s – Taylor’s work on homogeneous turbulence Kolmogorov. 60’s & 70’s – Kraichnan and followers addressed non-linear stochastic processes. Deductive theory hasn’t been developed. 1. Learned much about non-linear dynamics. 2. Theories are based on ad hoc assumptions. Simplify the problem and consider homogeneous turbulence. - Contains essential physics of the non-linear dynamics. - Simple as possible. Homogeneous in all spatial directions. If it is then: a. Energy exchange with mean flow. b. Diffusion terms are not important. Lose some large structures pathological (?) flow. (Could be too much of a simplification.) Ideas at least apply to small-scale in high Re no. flows. Can generate a homogeneous flow in a lab. 1
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Screen; mesh size, small compared to D. / U Possibly with constant mean shear to provide energy to perturbations downstream. – Not homogeneous 1. Taylor introduced the concepts in the 30’s and developed the experiment to study it. 2. Also can study homogeneous turbulence on the computer. Solve the N.-S. equations directly at a high enough Re. No. Re 1,000 λ realizable based on Taylor microscale.
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This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.

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Turbulence lecture 21 - Turbulence Lecture 21 Non-linear...

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