Predicting fluids flows from Lagrangian drifter observations

A comparison of Eulerian reconstruction of the streamfunction between data assimilation algorithms and the resulting energy spectrum.

Lagrangian instruments are measurement devices that are advected by a flow. They collect real-time data as the move throughout a fluid and are a vital source of data for atmospheric and oceanic measurements. Characterization of data from such observations is crucial since Lagrangian instruments are a dominant approach in studying the atmosphere and ocean, since they can cover large distances and explore large regions compared to more costly Eulerian measurement devices, that are fixed in space.

Courant researchers M. A. Mohamad and A. J. Majda studied how such Lagrangian data can be used to recover Eulerian properties of the flow. Utilizing data assimilation techniques, they show how exact and approximate algorithms, which combine observational data with a model, can be used to predict Eulerian properties of the flow field. They assessed the skill of various data assimilations algorithms in their ability to accurately predict the Eulerian energy spectra of fluids flows, which describes how energy is distributed across various scales of the flow. The research also focused on assessing the skill of approximate algorithms for the problem, which they demonstrated has high accuracy and high computation efficiency when compared to exact methods.

Reference:

M. A. Mohamad, A. J. Majda, Recovering the Eulerian energy spectrum from noisy Lagrangian tracers, Physica D, 2019 (accepted).