Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws

摘要

We analyze the data stemming from a forced incompressible hydrodynamicsimulation on a grid of 2048^3 regularly spaced points, with a Taylor Reynoldsnumber of Re~1300. The forcing is given by the Taylor-Green flow, which sharessimilarities with the flow in several laboratory experiments, and thecomputation is run for ten turnover times in the turbulent steady state. Atthis Reynolds number the anisotropic large scale flow pattern, the inertialrange, the bottleneck, and the dissipative range are clearly visible, thusproviding a good test case for the study of turbulence as it appears in nature.Triadic interactions, the locality of energy fluxes, and structure functions ofthe velocity increments are computed. A comparison with runs at lower Reynoldsnumbers is performed, and shows the emergence of scaling laws for the relativeamplitude of local and non-local interactions in spectral space. The scalingsof the Kolmogorov constant, and of skewness and flatness of velocityincrements, performed as well and are consistent with previous experimentalresults. Furthermore, the accumulation of energy in the small-scales associatedwith the bottleneck seems to occur on a span of wavenumbers that is independentof the Reynolds number, possibly ruling out an inertial range explanation forit. Finally, intermittency exponents seem to depart from standard models athigh Re, leaving the interpretation of intermittency an open problem.