Development of enstrophy and spectra in numerical turbulence

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Abstract
Decaying isotropic turbulence with initial Taylor microscale Reynolds number (R λ≤258) is studied via direct numerical simulations (DNS), with spectral resolution ≤2563. DNS results are compared with two‐point closure, in the form of the direct interaction approximation (DIA) and the test field model (TFM). The goals of this study are to understand the time‐dependence of enstrophy and spectra as they evolve from random initial conditions, and to assess and interpret differences between DNS and closure. Two time scales are identified in the DNS. The first is that for the development of normalized enstrophy production (velocity derivative skewness) and is independent of R λ. The second is that for the saturation of the enstrophy which follows after a longer period of near exponential growth and is strongly R λ dependent. For ν≠0, the DIA represents the time development of both integral quantities, such as enstrophy and spectra, with surprising accuracy in spite of its lack of invariance to random large‐scale sweeping. The TFM has significant energy range errors, which we attribute to its Markovianization assumption.