Scaling and the prediction of energy spectra in decaying hydrodynamic turbulence

P.D. Ditlevsen, M.H. Jensen and P. Olesen

Physica A: Statistical Mechanics and its Applications, 2004, vol. 342, issue 3, 471-478

Abstract: Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier–Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We find the existence of a scaling function ψ. The energy spectrum can at any time by a suitable rescaling be mapped onto this function. This indicates that the initial (primordial) energy spectrum is in principle retained in the energy spectrum observed at any later time, and the principle of permanence of large eddies is derived. The result can be seen as a restoration of the determinism of the Navier–Stokes equation in the mean. We compare our results with a windtunnel experiment and find good agreement.

Keywords: Decaying turbulence; Energy spectra; Scaling analysis (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:342:y:2004:i:3:p:471-478

DOI: 10.1016/j.physa.2004.05.076

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