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The classic baroclinic, wind-driven, double gyre problem is considered over a range of deformation radii, wind stress amplitudes, and bottom friction coefficients with the aim of better understanding the transfer of energy across scales. In this β-plane basin setting, significant differences are found with respect to classic studies of geostrophic turbulence, which generally assume zonal periodicity and for which the β term does not play a direct role in the energy transfers. In a basin geometry, the β term can play a direct role in the transfers; for example, it can be the dominant term allowing for energy transfer between the basin scale and the baroclinic mesoscale. It is also found that barotropization of baroclinic energy forces the barotropic mode near scales at which bottom drag damps this mode. Associated with this, the barotropic, nonlinear, inverse energy cascade does not extend between mesoscale injection and large-scale dissipation wavenumbers, as is often assumed. Instead, it is part of a 'double cascade' of barotropic energy in which the nonlinear inverse cascade is nearly offset by a forward cascade associated with the β term. This is particularly evident in weak bottom drag simulations, for which a time eddy-mean decomposition of the flow reveals the double cascade to be associated with the eddy-only terms. [ABSTRACT FROM AUTHOR]

In the large eddy simulation (LES) framework for modeling a turbulent flow, when the large scale velocity field is defined by low-pass filtering the full velocity field, a Taylor series expansion of the full velocity field in terms of the large scale velocity field leads (at the leading order) to the nonlinear gradient model for the subfilter stresses. Motivated by the fact that while the nonlinear gradient model shows excellent a priori agreement in resolved simulations, the use of this model by itself is problematic, we consider two models that are related, but better behaved. The rational LES model that uses a sub-diagonal Pade approximation instead of a Taylor series expansion, and the Lagrangian averaged Navier-Stokes-α model that uses a regularization approach to modeling turbulence. In this article, we show that these two latter models are identical in two dimensions. [ABSTRACT FROM AUTHOR]

We study the modulational instability of geophysical Rossby and plasma drift waves within the Charney-Hasegawa-Mima (CHM) model both theoretically, using truncated (four-mode and three-mode) models, and numerically, using direct simulations of CHM equation in the Fourier space. We review the linear theory of Gill (Geophys. Fluid Dyn., vol. 6, 1974, p. 29) and extend it to show that for strong primary waves the most unstable modes are perpendicular to the primary wave, which correspond to generation of a zonal flow if the primary wave is purely meridional. For weak waves, the maximum growth occurs for off-zonal inclined modulations that are close to being in three-wave resonance with the primary wave. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the nonlinear jet pinching predicted by Manin & Nazarenko (Phys. Fluids, vol. 6, 1994, p. 1158). We find that, for strong primary waves, these narrow zonal jets further roll up into Kármáan-like vortex streets, and at this moment the truncated models fail. For weak primary waves, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominate primary wave, so that the truncated description holds for longer. The two-dimensional vortex streets appear to be more stable than purely one-dimensional zonal jets, and their zonal-averaged speed can reach amplitudes much stronger than is allowed by the Rayleigh-Kuo instability criterion for the one-dimensional case. In the long term, the system transitions to turbulence helped by the vortex-pairing instability (for strong waves) and the resonant wave-wave interactions (for weak waves). [ABSTRACT FROM AUTHOR]