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B. L. Hua and D. B. Haidvogel

Abstract

Direct simulations of turbulent quasi-geostrophic flow on a βplane have been performed with an emphasis on three-dimensional resolution [128 × 128] in the horizontal and up to 6 vertical modes). The statistically equilibrated turbulence is forced by baroclinic instability of a mean shear, and dissipation occurs through friction in a bottom Ekman layer. Parameters which control the vertical structure of the variability and the energy partition between the vertical modes are identified. We verity Charney's prediction of three-dimensional isotropization of quasi-geostrophic flows in the case of a constant Brunt-Väisälä profile; for a variable Brunt- Väisäl&auml stratification spectral shapes are preserved but isotropization is lost. All baroclinic modes show a tendency for a direct energy cascade, as opposed to the red cascade of purely barotropic flow. The coalescence of potential vorticity into three-dimensionally isolated structures is observed to occur; however, their vertical scale is highly dependent on whether they appear in a forced turbulent flow or in freely evolving turbulence, the latter having a larger vertical scale.

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B. Barnier, C. Le Provost, and B. L. Hua

Abstract

This paper investigates the tridimensional consistency of the resolution of eddy scales in simulating large-scale flows. The generation of classical wind-forced, eddy-driven double-gyre circulation is investigated with a multilayered quasi-geostrophic model. Six-layers on the vertical have been chosen to assure the convergence of the baroclinic instability. Emphasis is on the resolution of the high baroclinic modes and its effects on the dynamics of the midlatitude jet. Several eddy-resolving experiments, identical except for the horizontal resolution, which can be low (20 km) or high (10 km), are compared. In every experiment, the scales associated with the first and second baroclinic modes are well resolved, but those associated with the third and higher baroclinic modes are so only in 10-km experiments For a better illustration of the importance of the high vertical modes, three-layer experiments having configurations equivalent to that of the six-layer experiments have been conducted. Note that in the three-layer experiments, all the baroclinic radii of deformation that are explicitly present (the first and second) are well resolved with both 10-km or 20-km grid resolutions.

The major effect of fine resolution is to amplify the inertial mode and consequently increase the penetration scale of the midlatitude jet (by almost 40% in six-layer cases, and only 20% in three-layer cases), whereas the other indexes related to the large-scale flow are not modified by more than 10%. Our analyses show that fine (10-km) resolution produces a larger excitation of the inertial mode, and reverses the effect of numerical hyperviscosity on the stability of the jet stream, (less subgrid-scale dissipation yields a longer jet, the contrary happens when the resolution is 20-km). These latter effects are significantly more important when the vertical resolution is six-layered.

Global and local energetics indicate that the coupling between the layers is more efficient in high-resolution experiments, due to a better representation of the dynamics related to vortex stretching. Energy transfer rates show much larger amplitudes for the instability and rectification processes, which affect the large-scale flow toward a stronger jet and recirculation. Wavenumber spectra for all vertical modes show that when the resolution is six-layered, the fine resolution yields a better representation of the energy and enstrophy cascades.

The physics missing in 20-krn grid simulations can be cast in terms of a scale-dependent eddy viscosity that is negative at large-scales. The analysis of the effects of negative viscosity demonstrates the dynamical impact of the resolution of the high vertical modes; the low-resolution experiment shows a deficit in negative viscosity at large wavenumbers, because the truncation of the 20-km grid interferes with the stratified inverse cascade. This artificially damps the large scales in the low-resolution experiments, and reduces the barotropic inertial circulation.

In conclusion, the high baroclinic modes appear to play a catalytic role in eddy-driven circulations: despite their low kinetic energy level, they are strongly involved in energy transfers and are essential pathways for determining the large-scale response of turbulent ocean models. However, our calculations show that if the fine horizontal resolution significantly modifies the quantitative impact of the second and third baroclinic modes on the mean circulation, the contribution of the fourth and fifth baroclinic modes remains negligible. Therefore, the tridimensional consistency of model resolution appears to be of crucial importance in the simulation eddy-driven large-scale flows, but the number of vertical modes that require a fine resolution seems to be limited.

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