Bhat, H., R. C. Fetecau, J. E Marsden, K. Mohseni, and M. West
The derivation in this paper involves averaging over a tube of trajectories centered around a given Lagrangian flow . With this tube framework, the LAE- equations are derived by following a simple procedure: start with a given action, Taylor expand in terms of small-scale fluid fluctuations , truncate, average, and then model those terms that are nonlinear functions of . Closure of the equations is provided through the use of flow rules, which prescribe the evolution of the fluctuations along the mean flow.