Showing papers by "Peter D. Ditlevsen published in 2004"

Scaling and the prediction of energy spectra in decaying hydrodynamic turbulence

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.

Scalingand the prediction of energ y spectra in decayinghydrodynamic turbulence

Abstract: Few rig orous results are derived for fully developed turbulence. By applyingthe scalingproperties of the Navier–Stokes equation we have derived a relation for the energy spectrum valid for unforced or decayingisotropic turbulence. We 3nd the existence of a scalingfunction . 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 3nd good agreement. c