Two-dimensional-three-dimensional interactions in a thin rotating fluid: Implications for the energetics of ocean circulation

The general circulation of the ocean acts as an energy reservoir. This means that the external forcing (primarily by the wind field) is balanced by dissipation. However, the dissipation is not well understood because energy does not easily cascade forward to small scales where dissipation is active. Approximate geostrophic balance holds over much of the ocean because the advective timescale is typically long compared to the Coriolis timescale. The resulting geostrophic turbulence behaves similarly to 2D turbulence in the sense that energy is not cascaded forward to small scales. In fact, there is an inverse cascade of energy toward large scales for these "balanced" flows. One possible mechanism for dissipation of the balanced flow is nonlinear interactions with unbalanced flow. In this thesis we made an analogy between balanced flow and 2D flow for the unstratified case. We numerically integrated the hydrostatic, barotropic vorticity equation using a pseudo-spectral, triply-periodic model varying the rate of rotation and the level of 3D (corresponding to unbalanced) energy via a 3D forcing. We analysed the energetics of the 2D flow to determine the impact of rotation and the 3D energy level. We found that there is a critical Rossby number between 0.1 and 1 above which there is 2D energy drain and below which there is 2D energy gain. We found that the magnitude of the drain/gain at large scales increases with forcing up to a limiting value. A review of ocean energetics and turbulent 2D-3D interactions is also presented.