Bottleneck effect in three-dimensional turbulence simulations

Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 2):026304. doi: 10.1103/PhysRevE.68.026304. Epub 2003 Aug 12.

Abstract

At numerical resolutions around 512(3) and above, three-dimensional energy spectra from turbulence simulations begin to show noticeably shallower spectra than k(-5/3) near the dissipation wave number ("bottleneck effect"). This effect is shown to be significantly weaker in one-dimensional spectra such as those obtained in wind tunnel turbulence. The difference can be understood in terms of the transformation between the one-dimensional and three-dimensional energy spectra under the assumption that the turbulent velocity field is isotropic. Transversal and longitudinal energy spectra are similar and can both accurately be computed from the full three-dimensional spectra. Second-order structure functions are less susceptible to the bottleneck effect and may be better suited for inferring the scaling exponent from numerical simulation data.