A Note on Stochastic Wave Action
摘要
We explore a consistent derivation of the wave action conservation principle for stochastic flows. Beyond providing a proper stochastic wave action principle, this study highlights a stochastic form of the wavefront Hamilton–Jacobi equation. The stochastic framework follows the modeling under location uncertainty paradigm. Within this framework, the usual slow component of the underlying current and the fast wavy component are accordingly decomposed in terms of smooth-in-time resolved component and unresolved highly oscillating random field. The slow current is expressed as a two-dimensional evolution equation, potentially incorporating strong noise. The fast wavy components are associated with the random current but include their own noise contributions as well.