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Turbulence lecture 29

Turbulence lecture 29 - Turbulence Lecture 29 Inertial...

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Unformatted text preview: Turbulence Lecture 29 Inertial Convective Range θ θ θ ∂ + ∇ = ∇ ∂ i ¡ 2 u D t θ θ- heat, salt, trace chemical species similar arguments hold regarding spectral transfer of θ . Equil. statistical, homogeneity, incompressible. d dt θ = − 2 1 2 D 2 i x θ ∂ = − ∂ χ χ is analogous to ε . An equilibrium range is hypothesized for large R A and u Pe D = A . (Peclet number) In this case, in equilibrium range, properties depend on χ . Main consideration is Prandtl number or Schmidt number. ν = Sc D if ν ¢ 1 D 1 If the inertial and convective ranges overlap, its called the inertial – convective range. ( ) ( ) ( ) 5 1 3 3 , ,- leads to c E k f k E k k θ θ χ ε χε − − = =∝ . “Corrsin – Obakov Spectrum” Other possibilities depending on Schmidt number. Spectral Transfer Hypothesis Equilibrium Range: T k ( ) ( ) 2 2 vk E k = E depends on 2 nd moment....
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Turbulence lecture 29 - Turbulence Lecture 29 Inertial...

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