# Oceanic component

The oceanic component is a shallow-water active oceanic layer superimposed on a deep ocean layer at rest. The dynamics is given by the reduced-gravity quasi-geostrophic vorticity equation.

Therefore, the equation of motion for the streamfunction $$\psi_\text{o}$$ of the ocean layer reads [OC-Pie11] [OC-DCDV16]

$\frac{\partial}{\partial t} \left( \nabla^2 \psi_\text{o} - \frac{\psi_\text{o}}{L_\text{R}^2} \right) + J(\psi_\text{o}, \nabla^2 \psi_\text{o}) + \beta \frac{\partial \psi_\text{o}}{\partial x} = -r \nabla^2 \psi_\text{o}.$

$$L_\text{R} = \sqrt{g' \, h }/ f_0$$ (LR) is the reduced Rossby deformation radius where $$g'$$ (gp) is the reduced gravity, $$h$$ is the depth of the layer (h), and $$f_0$$ is the Coriolis parameter (f0). $$r$$ (r) is the friction at the bottom of the active ocean layer.

## References

OC-DCDV16

L. De Cruz, J. Demaeyer, and S. Vannitsem. The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0. Geoscientific Model Development, 9(8):2793–2808, 2016. URL: https://www.geosci-model-dev.net/9/2793/2016/.

OC-Pie11

S. Pierini. Low-frequency variability, coherence resonance, and phase selection in a low-order model of the wind-driven ocean circulation. Journal of Physical Oceanography, 41(9):1585–1604, 2011. URL: https://journals.ametsoc.org/doi/full/10.1175/JPO-D-10-05018.1.