Abstract
The dynamics of two-dimensional turbulent motions have gained considerable attention in the past owing to a combination of different phenomenology compared to three-dimensional turbulence, mathematical simplicity and its relevance to geophysical applications. As a part of the PhD-project of the first author, a fast code for two-dimensional and quasigeostrophic turbulence is under development. To begin with, we will investigate two fundamental problems of two-dimensional turbulence.
First, we will investigate the logarithmic correction of the k^-3 kinetic energy spectrum in the enstrophy inertial range. Kraichnan (1971) suggested a logarithmically corrected energy spectrum. The prediction has been supported by some studies (e.g., Bowman (1996), Ishihara and Kaneda (2001), Pasquero and Falkovich (2002)). However, under certain conditions it has been demonstrated that such a correction might be redundant (e.g., Lindborg and Alvelius (2000), Kaneda and Ishihara (2001)).
Secondly, we will investigate whether higher order vorticity statistics of the enstrophy inertial range are influenced by intermittency. Theoretical studies by e.g., Eyink (1996) and Falkovich and Lebedev (1994), suggest that there should be no such influence.
Thus, we have developed a fast pseudo-spectral forced incompressible two-dimensional code with periodic boundary conditions and Newtonian viscosity for the ultraviolet enstrophy dissipation. However, no infrared energy dissipation is introduced. The numerical scheme is based on the Runge-Kutta 4th order scheme. Furthermore, a 9/8-dealiasing is applied, since this was shown to yield sufficient accuracy, restoring a wider range of Fourier modes than the traditional 3/2-rule. To enable high resolution, the code has been parallelized with the use of a message-passing interface. Currently, simulations with resolutions up to 8192^2 are being conducted and preliminary results suggest that the enstrophy inertial range might be subject to a larger degree of intermittency than previous theoretical studies have predicted. Numerical simulations reveal that the flatness is a highly fluctuating quantity and that the flatness factor increases with decreasing r, suggesting that the vorticity field is intermittent. Furthermore, the preliminary results give little evidence for a logarithmic correction. The soon advent of a powerful turbulence super computer will allow for larger simulations than have so far been reported in the literature. The results will be presented at the workshop.