Decadal Oceanic Response to Stochastic Wind Forcing

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Abstract
The low-frequency linear eigenmodes of the reduced-gravity shallow-water equations with weak friction are calculated numerically and using an analytic approximation. For basins with a large variation of the Coriolis parameter, large-scale eigenmodes emerge: the eigenfrequencies are integer multiples of the frequency for the gravest mode, which, in turn, has a period given by the transit time of the slowest long Rossby wave. The e-folding decay times are comparable to the period and independent of friction. These eigenmodes are excited by stochastic wind forcing and this leads to a weak peak in the spectral response near the frequency of the least-damped eigenmode. This decadal-frequency peak is most evident on the eastern and western boundaries and in the equatorial region of the basin. Abstract The low-frequency linear eigenmodes of the reduced-gravity shallow-water equations with weak friction are calculated numerically and using an analytic approximation. For basins with a large variation of the Coriolis parameter, large-scale eigenmodes emerge: the eigenfrequencies are integer multiples of the frequency for the gravest mode, which, in turn, has a period given by the transit time of the slowest long Rossby wave. The e-folding decay times are comparable to the period and independent of friction. These eigenmodes are excited by stochastic wind forcing and this leads to a weak peak in the spectral response near the frequency of the least-damped eigenmode. This decadal-frequency peak is most evident on the eastern and western boundaries and in the equatorial region of the basin.