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A model for the Reynolds-number dependence of the dimensionless dissipation rate C was derived from the dimensionless Kármán-Howarth equation, resulting in C=C,+C/RL+O(1/RL2), where RL is the integral scale Reynolds number. The coefficients C and C, arise from asymptotic expansions of the dimensionless second-and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to RL=5875 (Rλ=435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law RLn with exponent value n=-1.000±0.009 and that this decay of C was actually due to the increase in the Taylor surrogate U3/L. The model equation was fitted to data from the DNS, which resulted in the value C=18.9±1.3 and in an asymptotic value for C in the infinite Reynolds-number limit of C,=0.468±0.006.
|Journal||Physical Review E - Statistical, Nonlinear and Soft Matter Physics|
|Publication status||Published - 21 Apr 2015|
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- 2 Finished
Ball, R., Berera, A., Boyle, P., Callison-Burch, C., Del Debbio, L., Gardi, E., Kennedy, A., O'Connell, D., Zwicky, R., Berera, A., Boyle, P., Buckley, A., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., Kenway, R., O'Connell, D., Smillie, J. & Zwicky, R.
1/10/14 → 30/09/18