FLOW: Simulations of quasi-geostrophic turbulence

Two codes have been developed and implemented for use on massively parallel super computers to simulate twodimensional and quasi-geostrophic turbulence. The codes have been found to scale well with increasing resolution and width of the simulations. This has allowed for the highest resolution simulations of two-dimensional and quasigeostrophic turbulence so far reported in the literature (Vallgren & Lindborg 2010a, b & c and Lindborg & Vallgren 2010). The direct numerical simulations have focused on the statistical characteristics of turbulent cascades of energy and enstrophy, the role of coherent vortices and departures from universal scaling laws, theoretized more than 40 years ago. In particular, the investigations have concerned the enstrophy and energy cascades in forced and decaying twodimensional turbulence. Furthermore, the applicability of Charney’s hypotheses on quasi-geostrophic turbulence has been tested. The results have shed light on the flow evolution at very large Reynolds numbers. The most important results are the robustness of the enstrophy cascade in forced and decaying two-dimensional turbulence, the sensitivity to an infrared Reynolds number in the spectral scaling of the energy spectrum in the inverse energy cascade range, and the validation of Charney’s predictions on the dynamics of quasi-geostrophic turbulence. It has also been shown that the scaling of the energy spectrum in the enstrophy cascade is insensitive to intermittency in higher order statistics, but that corrections apply to the ”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipation anomalies following a classical remark by Landau (Landau & Lifshitz 1987). Another finding is that the inverse energy cascade is maintained by nonlocal triad interactions, which is in contradiction with the classical locality assumption.

Of physical interest, is now to extend the quasi-geostrophic framework to the primitive equations, which are a set of nonlinear equations used in atmospheric and oceanic modeling (Vallis 2006). The set of equations contains the momentum equations in the horizontal, the hydrostatic approximation in the vertical and is completed by the thermodynamic and continuity equations. The use of the primitive equations allows for variations of the Rossby number and deformation radius by varying the stratification, which is fixed in the framework of Charney quasigeostropy. By performing simulations of the primitive equations, we aim to explore the dynamic origins of the atmospheric energy spectrum and, perhaps most importantly, determine the origin of the high wave number k^5/3 -range in the atmospheric energy spectrum.