By N. peters
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A similar approach has recently been used by Oberlack (1997) to derive an equation for the dissipation tensor that is needed in Reynolds stress models. The dissipation ε plays a fundamental role in turbulence theory, as will be shown in the next section. The eddy cascade hypothesis states that it is equal to the energy transfer rate from the large eddies to the smaller eddies and therefore is invariant within the inertial subrange of turbulence. 41) one obtains Reynolds number independent solutions for free shear flows where, owing to the absence of walls, the viscous stress tensor can be neglected compared to the Reynolds stress tensor.
175 mm. 1 for the example considered above. 03 at pressures around 30 atm. In Chapter 2, dealing with premixed combustion, we will compare the thickness δ to the Kolmogorov scale η to evaluate the validity of the assumption of scale separation, on which most of the combustion models are based. In a regime called the thin reaction zones regime, we will identify the inner layer with the thin reaction zone. 101) of the oxidation layer, which is typically three times larger than δ (cf. Peters, 1991).
Therefore we will relate ε directly to the turnover velocity and the length scale of the integral scale eddies, ε ∼ v3 . 55) We now define a discrete sequence of eddies within the inertial subrange by n = 2n ≥ η, n = 1, 2, . . 56) Since ε is constant within the inertial subrange, dimensional analysis relates the turnover time tn and the velocity difference vn across the eddy n to ε in that range as ε∼ 2 v3 vn2 ∼ n ∼ 3n . 57) This relation includes the integral scales and also holds for the Kolmogorov scales as ε= vη2 tη = vη3 η .
