The unsteady horizontal motion of the ocean is well described by ocean models that are being run at increasingly higher resolution. In the vertical plane, ocean velocities are much weaker, but play a crucial role in many processes that affect our climate. Modeling this third dimension accurately remains a challenge for a system that his highly skewed due to geometry, rotation, and density stratification. Using examples, I will motivate the need for modeling vertical motion accurately, then go on to explain the mathematical and computational problems in doing so, and some approaches used in trying to address these.
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