Dissipative Selection of Low-Frequency Modes in a Reduced-Gravity Basin

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Abstract
The spectrum of linear free modes of a reduced-gravity ocean in a closed basin with weak dissipation is examined. The constraint of total mass conservation, which in the quasigeostrophic formulation determines the pressure on the boundary as a function of time, allows the existence of selected large-scale, low-frequency basin modes that are very weakly damped in the presence of dissipation. These weakly damped modes can be quasi-resonantly excited by time-dependent forcing near the eigenperiods, or during the process of adjustment to Sverdrup balance with a steady wind from arbitrary initial conditions. In both cases the frequency of the oscillations is a multiple of 2π/t0, where t0 is the long Rossby wave transit time, which is of the order of decades for midlatitude, large-scale basins. These oscillatory modes are missed when the global mass conservation constraint is overlooked. Abstract The spectrum of linear free modes of a reduced-gravity ocean in a closed basin with weak dissipation is examined. The constraint of total mass conservation, which in the quasigeostrophic formulation determines the pressure on the boundary as a function of time, allows the existence of selected large-scale, low-frequency basin modes that are very weakly damped in the presence of dissipation. These weakly damped modes can be quasi-resonantly excited by time-dependent forcing near the eigenperiods, or during the process of adjustment to Sverdrup balance with a steady wind from arbitrary initial conditions. In both cases the frequency of the oscillations is a multiple of 2π/t0, where t0 is the long Rossby wave transit time, which is of the order of decades for midlatitude, large-scale basins. These oscillatory modes are missed when the global mass conservation constraint is overlooked.

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