Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows

Computing and visualizing features in fluid flow often depends on the observer, or reference frame, relative to which input velocity field is given. A desired property of feature detectors therefore that they are objective, meaning independent frame. However, standard definition objectivity only given for Euclidean domains cannot be applied curved spaces. We build methods from mathematical physics Riemannian geometry generalize spaces, using powerful notion symmetry groups as basis definition. From this, we develop a general framework objective computation observer fields other computed measures become objective. An important our it works intrinsically 2D, instead 3D ambient space. This enables direct generalization 2D via optimization flat space domains, without having perform 3D. specifically case unsteady geophysical flows spheres, such Earth. Our spaces then enable well visualization time evolution scalar vector fields, automatically frames follow moving structures like vortices way makes them appear steady.