Annick Pouquet 教授 特別講演会

Direct numerical simulations (DNS) of three-dimensional Navier-Stokes and magnetohydrodynamic (MHD) turbulence are analyzed to study the degree to which nonlinear terms are nonlocal in Fourier space, i.e. involving widely separated scales. A sharp Fourier filter is used, and both decaying and forced flows are studied, with periodic boundary conditions. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions.

In the fluid case, roughly 20% of interactions correspond to the small scales exchanging energy with the energy-containing scale of the flow (see Phys. Rev. Lett. 95, 264503, 2005). This leads to a slow recovery of symmetries in the small scales and gives credence to subgrid modeling of turbulent flows involving entrainment by a large-scale flow, for example Rapid Distortion Theory and its variants such as the Lagrangian Averaged (alpha) model. The role of helicity (velocity-vorticity correlations) is also investigated. Finally, the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect are given.

In contrast, in MHD, the transfer itself (as opposed to triadic interactions) has strong non-local components (see Phys. Rev. E 72, 046301 and 046302, 2005), with the implication that, as soon as one exits the linear phase of exponential growth of small scales in the form of vorticity and current sheets, a plethora of structures form, with a self-similar in time growth of the maxima of current and vorticity (= t³), with a k^-3 energy spectrum at those early times and with later, a constant rate of energy dissipation.

These results will be illustrated on several flows (Taylor-Green, Beltrami (ABC), Orszag-Tang, and ABC plus random fluctuations in the small scales), up to grid resolutions of 1024³ points for NS and 1536³ in MHD. We also show that the current and vorticity sheets are spatially co-located and that, at the highest resolution, Kelvin-Helmoltz instabilities develop leading to roll-up of the sheets whereas at lower Reynolds numbers, the sheets simply fold after having been stretched.