Microscale Reynolds Number Rλ Research Articles

Energy and spectral dynamics in decaying compressible turbulence

The statistical properties of decaying compressible turbulence are investigated by direct numerical simulations of flow in a periodic cube. Starting with fully developed turbulence for various microscale Reynolds numbersR λ , rms Mach numbersM, and small- and large-scale compressive ratiosr CS andr CL , we find that the kinetic energy exhibits an exponential decay in time. Interactions between the compressive and rotational components of kinetic energy are weaker than self-interactions of the respective components. The energy spectrum of rotational component obeys the same Kolmogorov similarity law as for incompressible turbulence and forced compressible turbulence. The form of the energy spectrum of the compressive component, on the other hand, depends strongly onM. As the turbulence decays freely,R λ andM decrease in time butr CS andr CL tend to some universal values.

Numerical calculation of decaying isotropic turbulence using the LET theory

The local-energy-transfer (LET) theory (McComb 1978) was used to calculate freely decaying turbulence for four different initial spectra at low-to-moderate values of microscale Reynolds numbers (Rλ up to about 40). The results for energy, dissipation and energy-transfer spectra and for skewness factor all agreed quite closely with the predictions of the well-known direct-interaction approximation (DIA: Kraichnan 1964). However, LET gave higher values of energy transfer and of evolved skewness factor than DIA. This may be related to the fact that LET yields the k−5/3 law for the energy spectrum at infinite Reynolds number.The LET equations were then integrated numerically for decaying isotropic turbulence at high Reynolds number. Values were obtained for the wavenumber spectra of energy, dissipation rate and inertial-transfer rate, along with the associated integral parameters, at an evolved microscale Reynolds number Rλ of 533. The predictions of LET agreed well with experimental results and with the Lagrangian-history theories (Herring & Kraichnan 1979). In particular, the purely Eulerian LET theory was found to agree rather closely with the strain-based Lagrangian-history approximation; and further comparisons suggested that this agreement extended to low Reynolds numbers as well.

Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar

Results of direct numerical simulations (DNS) for the decay of an initially Gaussian field of turbulence convecting a passive scalar are compared with equivalent results for the direct-interaction approximation (DIA) and the test-field model (TFM). The Taylor microscale Reynolds number Rλ and the equivalent Péclet number Pλ of the comparison ranged from 20–8 and 10–4, respectively. The Prandtl number Pr equals 0·5. Our results show a satisfactory agreement of both theories and numerical simulations, with the DIA giving better overall agreement, especially at small scales. This improved small-scale agreement - which appears to hold up to Rλ ≃ 30 - is related to the relatively long coherence times of the small scales, and to the fact that the TFM, containing as it does a built-in compliance to the fluctuation dissipation theorem, cannot properly cope with this fact. We also give a comparison of results for the velocity skewness with the experiments of Tavoularis, Bennett & Corrsin (1978).