The dynamics of freely decaying two-dimensional turbulence

• Published in: Journal of fluid mechanics 1988-09, Vol.194 (1), p.333-349
• Main Authors: Brachet, M. E., Meneguzzi, M., Politano, H., Sulem, P. L.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112088003015

Direct numerical simulations of decaying high-Reynolds-number turbulence are presented at resolutions up to 8002 for general periodic flows and 20482 for periodic flows with large-scale symmetries. For turbulence initially excited at large scales, we characterize a transition of the inertial energy-spectrum exponent from n ≈ − 4 at early times to n ≈ − 3 when the turbulence becomes more mature. In physical space, the first regime is associated with isolated vorticity-gradient sheets, as predicted by Saffman (1971). The second regime, which is essentially statistical, corresponds to an enstrophy cascade (Kraichnan 1967; Batchelor 1969) and reflects the formation of layers resulting from the packing of vorticity-gradient sheets. In addition to these small-scale structures, the simulation displays vorticity macro-eddies which will survive long after the vorticity-gradient layers have been dissipated (McWilliams 1984). We validate the linear description of two-dimensional turbulence suggested by Weiss (1981), which predicts that coherent vortices will survive in regions where vorticity dominates strain, while vorticity-gradient sheets will be formed in regions where strain dominates. We show that this analysis remains valid even after vorticity-gradient sheets have been formed.