Abstract

Abstract The classic wind-driven double-gyre problem for a homogeneous (unstratified) thin aspect ratio fluid is considered, but allowing for the flow to be depth dependent. Linear free modes for which the vertical wavenumber kz ≠ 0 are inertial oscillations, and they are excited with a large-scale stochastic forcing. This produces a background sea of near-inertial oscillations and their interaction with the vertically averaged flow is the focus of this study. In the absence of 3D forcing, the near-inertial motion vanishes and the barotropic quasigeostrophic system is recovered. With 3D forcing, 2D-to-3D energy transfers—coupled with a forward cascade of 3D energy and scale-selective dissipation—provide an energy dissipation mechanism for the gyres. The relative strength of this mechanism and a Rayleigh drag applied to the 2D flow depends on both the 3D forcing strength and the Rayleigh drag coefficient.

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