Mapping flow fields using LCS constrained regression

Mapping of unsteady flow fields from Lagrangian trajectory measurements (for example collected from ocean floats) is an important and challenging task from the perspective of navigation and guidance of mobile sensors operating within them. Some of the challenges of mapping are that we require algorithms that require a small amount of training data and make minimal assumptions of the flow field. In order for the method to generalize, we propose the use of regression on Lagrangian trajectories using a library of "Gaussian vortices'' to reconstruct the flow field. Furthermore, we enforce that the estimated flow field obeys the Lagrangian coherent structures (LCS) through linear constraints. This is useful in situations where we have knowledge of large scale coherent structures and want to resolve the entire flow field at the smaller scales. We demonstrate the effectiveness of our strategy on examples such as the double-gyre and show that by enforcing the LCS, we can reduce the amount of training data needed. Moreover, our method is not restricted to enforcing the LCS but the formulation can potentially also be used to enforce solid boundaries such as landmasses within the flow field.