A path integration formulation of stochastic-Lagrangian models of turbulent flow

In analogy with the Feynman–Kac path integration formulation of quantum mechanics, a general path integration formulation of stochastic-Lagrangian models of turbulent flow is developed with respect to the equivalence with the usual Eulerian and stochastic-Lagrangian descriptions. We then discuss efficient numerical methods for the realisation of the Lagrangian solutions via path integration which provide an effective alternative to the simpler Monte-Carlo approach.