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B. Legras and M. Ghil


We consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty-five modes are retained in a spherical harmonics expansion of the streamfunction. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.

Multiple stationary solutions are obtained as a result of nonlinear interaction between waves, mean flow and orography. The number of modes retained in the analysis permits these multiple equilibria to appear for realistic values of the forcing. The equilibria exhibit blocked and zonal flow patterns bearing a marked resemblance to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows.

Wave-wave interactions influence strongly the stability properties of the equilibria and the time evolution of nonequilibrium solutions. Time-dependent solutions show persistent sequences which occur in the phase-space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby, which permits the unambiguous definition of quasi-stationary flow regimes, zonal and blocked, respectively. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.

The statistics of transitions between the two types of planetary flow regimes are computed from the model's deterministic dynamics. These transitional called breaks in statistical-synoptic long-range forecasting, are shown to be influenced by changes in model parameters. This influence is discussed in terms of the effect of anomalous boundary conditions on large-scale midlatitude atmospheric flow and on its predictability.

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C. Basdevant, B. Legras, R. Sadourny, and M. Béland


The régime flows corresponding to the barotropic nondivergent equation with forcing, drag and subgrid-scale dissipation are studied using spectral model on the plane and on the sphere. The flow régimes obtained exhibit clear evidence of the existence of an enstrophy-cascading inertial range, together with a reverse energy cascade toward small wavenumbers. It is shown, however, that the enstrophy cascade is not associated with the k −3 spectral slope expected from the Kolmogorov-Kraichnan theory of two-dimensional turbulence; the slopes obtained are significantly steeper. This apparent paradox is tentatively resolved by a phenomenological theory of space-time intermittency in two dimensions; it is further shown that such intermittency associated with steeper spectra also restores locality of the nonlinear transfers in wavenumber space. In contrast to the well-known nonlocality typical of two-dimensional non-intermittent turbulent flows. The effect of differential rotation in connection with Rossby wave propagation is also studied: the reverse energy cascade is actually inhibited, and zonal anisotropy prevails in the large scales as expected from Rhines’ theory. But it is shown that this anisotropy is in fact carried down by nonlinearity throughout the enstrophy inertial range. Finally, the predictability properties of our flows are investigated with reference to the Leith-Kraichnan theory. It is shown that the presence of Rossby waves actually increases predictability through several mechanisms: direct inhibition of the nonlinear transfers in the larger scales, concentration of energy in highly predictably large-scale zonal structures, and slowdown of error propagation in the enstrophy inertial range due to the presence of anisotropy at small and intermediate scales.

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G. Brunet, R. Vautard, B. Legras, and S. Edouard


A 25-year dataset of potential vorticity on the 315-K isentropic surface is built from the National Meteorological Center (NMC) final analysis archive. Potential vorticity is calculated from the nonlinear gradient wind balance using temperature and geopotential fields, since the wind field is not available in the early part of the archive.

The validity of this calculation is assessed by comparing the results with potential vorticity obtained directly from European Centre for Medium-Range Weather Forecasts (ECMWF) analyzed winds. The error due to the nonlinear balance approximation turns out to be smaller than the difference between ECMWF and NMC analysis.

The possibility of studying diabatic forcing as a residual of the equation of potential vorticity conservation is examined. The average potential vorticity forcing found in this way is consistent with the authors knowledge of the mean diabatic heating. The amplitude of the residual decreases through the analysis period, reflecting the improvement in the observational network and in the analysis schemes.

Next the authors demonstrate that this dataset can be used for studies of transient-mean flow interactions. The authors present diagnostics of the transient feedback by separating the contribution of vortical and thermal terms on the isentropic surface. Also, the contribution of high-frequency (periods less than 10 days) and low-frequency (periods greater than 10 days) transients is examined. On the 315-K surface, transients act mostly in reducing the potential vorticity gradient through thermal terms and accelerate the zonal flow through vortical forcing.

Finally, these diagnostics are also applied to a long ensemble of blocking events, and the authors study the anomaly of transient feedback during these events. It is found that transients have primarily an advective effect, forcing the dipole structure to retrograde westward. Thermal and vortical terms have a very distinct action on the blocking anomaly. Vortical forcing is constructive and advective, whereas thermal forcing is dissipative and makes the dipole rotate clockwise.

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