Lagrangian averaging theories, most notably the generalized Lagrangian mean (GLM)
theory of Andrews and McIntyre, have been primarily developed in Euclidean space and …

We introduce a physically relevant stochastic representation of the rotating shallow water
equations. The derivation relies mainly on a stochastic transport principle and on a …

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our
understanding of their dynamics and their numerical approximation. This paper presents a …

Lagrangian averaging plays an important role in the analysis of wave–mean-flow
interactions and other multiscale fluid phenomena. The numerical computation of …

Lagrangian averaging has been shown to be more effective than the Eulerian mean in
separating waves from slow dynamics in two time scale flows. It also appears in many …

We describe a proof‐of‐concept development and application of a phase‐averaging
technique to the nonlinear rotating shallow‐water equations on the sphere, discretised using …

Unsteady nonlinear shallow-water flows typically emit inertia-gravity waves through a
process called “spontaneous adjustment-emission.” This process has been studied …

Anticyclonic vortices focus and trap near-inertial waves so that near-inertial energy levels
are elevated within the vortex core. Some aspects of this process, including the nonlinear …

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model.
This approximate model provides an interesting simple description of the interplay between …

Studies of ocean surface transport often invoke the" Eulerian-mean hypothesis": that wave-
agnostic general circulation models neglecting explicit surface waves effects simulate the …