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Center for Nonlinear Studies |
Several of the numerical investigations of turbulent flows are done in a rather abstract framework: that of three-dimensional rectangular periodic boundary conditions. This has happened for several reasons, an important one of which is that one of the best existing numerical techniques for investigating turbulence has been the Orszag-Patterson pseudospectral method that relies heavily on the fast Fourier transform. Another reason is that the results of such computations appear in a form that compares easily with homogeneous and isotropic turbulence theory predictions in the Kolmogorov mold. In this talk we will discuss results from high resolution simulations of hydrodynamic turbulence with Taylor Reynolds numbers up to 1100. We have re-investigated some familiar turbulence problems with the intent of revising some of the prevailing assumptions about the locality of interactions between spatial scales in Kolmogorov theory. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. For hydrodynamic turbulence, we find that nonlinear triadic interactions are dominated by their non-local components, involving widely separated scales, even though the nonlinear transfer itself is local and the scaling for the energy spectrum is close to the classical Kolmogorov law. The large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The link between these findings and the intermittency of the small scales, and their consequences for modeling of turbulent flows are briefly discussed. Some extensions of the analysis to magnetohydrodynamic turbulence are also presented.
Host: Susan Kurien, T-7