Turbulence lecture 27

Turbulence lecture 27 - Turbulence Lecture 27 Kolmogorov's...

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Turbulence Lecture 27 Kolmogorov’s Universal Equilibrium Theory (Local Similarity Theory) Universal means it applies to all flows if certain requirements are met. Equilibrium – statistically stationary A. Consider possibility of Statistical Equilibrium. 1. With regard to energy containing range. Define 0 1 k = A Length scale energy containing range. Velocity Scale () 1 2 2 i qu = Time scale e q = A T , advective time Decay time if 1 e d d T T T ± Then the energy containing range is in approximate equilibrium. Homogeneous Decay (wind tunnel) 1
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1. In lab frame, most flows are statistically stationary. 2. Of more interest to follow flow, in this case turbulence decays. Experimentally 2 2 units 2 1 2 ~1 m S dA q dt A ε =− ≈    A q The decay time 2 2 1 no possibility for equilibrium d e d q T Aq q t T q A T Aq =≈ A A ∼∼ A (Still possible to force the flow to steady state, e.g. with a mean shear) 2. With regard to the smaller scale motions Observe has a maximum at
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Turbulence lecture 27 - Turbulence Lecture 27 Kolmogorov's...

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