In our research group we investigate the large scale dynamics of the oceans on the planetary scales typically going down to kilometres. Most of our efforts are directed towards the physical aspects but we also study planktonic ecosystem models and how these two interact. This research requires a solid understanding of science (physics and/or biology) and applied mathematics. We investigate idealized problems that requires first describing observations into the realm of mathematics, usually in the language of Partial Differential Equations. These equations have been well known for a long time but they are nonlinear and notoriously difficult to solve analytically. It is for this reason that numerical methods are key to accurately describe the dynamics of the ocean.