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Turbulence lecture 28

# Turbulence lecture 28 - Turbulence Lecture 28 W k called...

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Turbulence Lecture 28 ( ) W k called flux of energy through wave number k. Quantities only depend on small scales. Verified experimentally U ( ) ( ) 1 1 u x Ut u t t + + ∆ Hypothesis – small scale motions are statistically independent of the large scale motions provided R A is large enough. Value of R A required needs to be determined empirically. 0 k k ε ± Small scale properties are statistically independent of large scale properties 2 , L u L C. Universal equilibrium (local similarity) if the Re is sufficiently large there is an equilibrium range of wave numbers. A. Responsible for most energy dissipation. B. Statistically steady C. Statistically isotropic D. Statistically independent of energy containing range. What does equilibrium range depend on? 1. On rate of energy removal and feed, which is the same. ( ) ( ) ( ) ( ) 2 2 0 2 2 k k T k dk W k v k E k dk v k E k dk ε = = ² = 2. On the viscosity v – gives peak.

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