Abstract

November 3 , 2006

Title: Nonlocality of nonlinear transfer in hydrodynamic and MHD turbulence and the formation of small scales
Presented by: Annick Pouquet
Geophysical Turbulence Program
National Center for Atmospheric Research

Abstract

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, i.e. involving widely separated scales. A sharp Fourier filter is used, and both decaying and forced flows are studied, with periodic boundary conditions. In the fluid case, roughly 20% of interactions correspond to the small scales exchanging energy with the forcing scale of the flow, leading to a slow recovery of symmetries in the small scales and giving credence to models involving entrainment by a large-scale flow (Phys. Rev. Lett. 95, 264503, 2005; Phys. Rev. E 74, 056320, 2006).

In MHD, the transfer itself has strong non-local components (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 (see http://arxiv.org/abs/physics/0607269).

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 1536³ points in MHD. In that latter case, 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.

Finally, the consequences of these findings for modeling of turbulent flows, including compatibility with the Kolmogorov energy spectrum E(k) ~ k^−5/3 will be discussed.

Co-sponsored with the department of Atmospheric and Oceanic Sciences.