Abstract
In order to better understand deviations from equilibrium in turbulent flows, it is meaningful to characterize the dynamics rather than the statistics of turbulence. To this end, the Lyapunov theory provides a useful description of turbulence through the study of the perturbation dynamics. In this work, the Lyapunov spectrum of forced homogeneous isotropic turbulent flows is computed. Using the Lyapunov exponents of a flow at different Reynolds numbers, the scaling of the dimension of the chaotic attractor for a three-dimensional homogeneous isotropic flow is obtained through direct computation. The obtained Gram-Schmidt vectors (GSVs) are analyzed. For the range of conditions studied, it is found that the chaotic response of the flow coincides with regions of large velocity gradients at lower Reynolds numbers and enstrophy at higher Reynolds numbers, but does not coincide with regions of large kinetic energy. Further, the response of the flow to perturbations is more and more localized as the Reynolds number increases. Finally, the energy spectrum of the GSVs is computed and is shown to be almost insensitive to the Lyapunov index.
11 More- Received 11 April 2019
DOI:https://doi.org/10.1103/PhysRevFluids.4.114608
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