Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws.
We analyze the data stemming from a forced incompressible hydrodynamic simulation on a grid of 2048(3) regularly spaced points, with a Taylor Reynolds number of R(lambda) ~ 1300. The forcing is given by the Taylor-Green vortex, which shares similarities with the von Kàrmàn flow used in several laboratory experiments; the computation is run for ten turnover times in the turbulent steady state. At this Reynolds number the anisotropic large scale flow pattern, the inertial range, the bottleneck, and the dissipative range are clearly visible, thus providing a good test case for the study of turbulence as it appears in nature. Triadic interactions, the locality of energy fluxes, and longitudinal structure functions of the velocity increments are computed. A comparison with runs at lower Reynolds numbers is performed and shows the emergence of scaling laws for the relative amplitude of local and nonlocal interactions in spectral space. Furthermore, the scaling of the Kolmogorov constant, and of skewness and flatness of velocity increments is consistent with previous experimental results. The accumulation of energy in the small scales associated with the bottleneck seems to occur on a span of wave numbers that is independent of the Reynolds number, possibly ruling out an inertial range explanation for it. Finally, intermittency exponents seem to depart from standard models at high R(lambda), leaving the interpretation of intermittency an open problem.
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, Argentina.
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Mininni
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Alexakis
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Pouquet