Given the large heat capacity of the ocean as compared to the atmosphere, the dynamical system that governs the model evolution is reduced to only two degrees of freedom, the oceanic overturning thermohaline circulation and the interior north–south temperature gradient. To assess whether this instability process of oceanic origin is robust enough to cause interdecadal variability of coupled ocean–atmosphere models, a four-box ocean–atmosphere model is constructed. The proposed instability mechanism that favors surface-intensified perturbations also explains the lack of oscillations if the restoring to a surface climatology is too strong. The long-wave limit of the baroclinic instability of idealized mean flows in a three-layer model with vertical shears as observed in the GCMs demonstrates that growth rates of order one cycle per year can be produced locally, large enough to amplify thermal anomalies in the face of lateral diffusion. When the surface heat fluxes are diagnosed from a spinup in which surface temperatures are strongly restored to apparent atmospheric temperatures, the most unstable regions diagnosed by large downgradient eddy heat fluxes are located in the basin northwest corner where the surface heat losses are largest. Numerical simulations of coarse-resolution, idealized ocean basins under constant surface heat flux are analyzed to show that the interdecadal oscillations that emerge naturally in such configurations are driven by baroclinic instability of the mean state and damped by horizontal diffusion. The growth rate increases monotonically with the shear at a given wavenumber. The friction coefficient is set at 10 5 m 2 s −1. (d) for different values of the upper-layer meridional velocity (1, 2, 3, and 4 cm s −1). Growth rate variations with respect to the friction coefficient is monotonic with small growth rate associated with large friction coefficient at a given wavenumber. (c) The LR case for different values of the Laplacian friction coefficient (2.6 × 10 5, 5.1 × 10 5, 7.6 × 10 5, 10 6 m 2 s −1). Common parameter values are h 1 = 100 m, h 2 = 200 m, and h 3 = 4200 m. This must be compared with the inverse timescale associated with horizontal diffusion (dashed line). The growth rate (cycle/year) in the three-layer model (solid line) as a function of wavenumber scaled by the inverse Rossby radius of deformation ( g ′ 3 H) 1/2/ f. The oscillation index is the basin average of temperature standard deviations over a period. All of these results have been obtained with the HR configuration ( Table 1) for the solid line, but with a purely geostrophic model (no momentum dissipation but no-slip boundary conditions imposed) for the dashed line. Note that oscillations disappear for values between 20 and 25 W m −2 K −1. The mean overturning strength is plotted on the vertical axis, since the restoring atmospheric temperatures are changed along with the restoring constant. The presence (×) or absence (○) of the oscillations is indicated along with the oscillation index in the former case. Note that no oscillations are found for Peclet numbers less than 0.64 (associated with diffusivity coefficients larger than 2500 m 2 s −1) and (d) variations of the restoring constant (when the surface temperature is restored to a linear meridional temperature distribution). Abcissa is the horizontal Peclet number UΔ x/ K h with U = 1 cm s −1 and Δ x = 160 km and ordinate is the square root of the kinetic energy. Sensitivity of the interdecadal oscillations to (a) variations of the amplitude of the meridional distribution of surface heat flux (b) variations of the vertical diffusivity coefficient (log–log plot) (c) variations of the horizontal diffusivity coefficient.
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