Spectrum of Wind-Driven Baroclinic Fluctuations of the Ocean in the Midlatitudes

In the midlatitudes, the thermocline depth variations are largely due to Rossby waves of first baroclinic mode forced by stochastic wind stress. The frequency spectrum of this oceanic response is investigated with a simple model, with emphasis on the impact of (i) the horizontal mixing, (ii) the zonal variations of the forcing, and (iii) the nonlinearity due to variations of the Rossby wave celerity in function of the thermocline depth. Horizontal mixing, which acts here as a frequency-dependent Newtonian damping, smoothes the singularities of the spectrum computed in a linear nondissipative case and slightly increases the slope of the spectrum at periods shorter than 10 yr. Considering a wind stress with a continuous spectrum also smoothes the response spectrum and modifies the power at decadal and interdecadal frequency: it alters its dependence on the distance from the eastern boundary. A spectral peak appears when the forcing has a dominant zonal scale, but this peak disappears in more realistic cases. The nonlinearity included in Rossby wave celerity induces energy transfers from decadal frequency to annual frequency, thereby whitening the frequency spectrum at periods ranging from 0.5 to 5 yr. These features lead to a better agreement with GCM simulations and observations. 1.