Lagrangian coherent structures from approximate velocity data

Abstract

This paper examines whether hyperbolic Lagrangian structures—such as stable and unstable manifolds—found in model velocity data represent reliable predictions for mixing in the true fluid velocity field. The error between the model and the true velocity field may result from velocity interpolation, extrapolation, measurement imprecisions, or any other deterministic source. We find that even large velocity errors lead to reliable predictions on Lagrangian coherent structures, as long as the errors remain small in a special time-weighted norm. More specifically, we show how model predictions from the Okubo–Weiss criterion or from finite-time Lyapunov exponents can be validated. We also estimate how close the true Lagrangian coherent structures are to those predicted by models.