Well, spherical geometry is one obvious application. Navier Stokes can help with any kind of fluid flow which has countless applications such as weather, turbulent flows in the atmosphere, shallow/deep water waves, and if you go deep enough assuming the dynamo theory then the core is a magnetized liquid in which case we have Navier Stokes combined with Maxwell's Equations giving us the ideal MHD equations. And since you said "anything related to Earth", the ideal MHD equations can also apply to the plasma trapped in the magnetosphere. This is by NO MEANS exhaustive. There are many MANY more examples, way too much to even summarize here. Any topic in a standard applied math syllabus (excluding things like pure abstract algebra/group theory) has an application related to something you would see at an AGU meeting. If you need a connection to a particular geophysical field or if you need an application for a particular math topic, then let us know and no doubt we'll find you at least one.