In general, it is difficult to decompose a combined wave–mean motion into a mean and a wave part, especially for flows bounded by a wavy surface: e.g. in the presence of
surface gravity waves or near another undulating bounding surface (like atmospheric flow over mountainous or hilly terrain). However, this splitting of the motion in a wave and mean part is often demanded in
mathematical models, when the main interest is in the mean motion – slowly varying at scales much larger than those of the individual undulations. From a series of
postulates, arrive at the (GLM) formalism to split the flow: into a generalised Lagrangian mean flow and an oscillatory-flow part. The GLM method does not suffer from the strong drawback of the
Lagrangian specification of the flow field – following individual
fluid parcels – that Lagrangian positions which are initially close gradually drift far apart. In the Lagrangian frame of reference, it therefore becomes often difficult to attribute Lagrangian-mean values to some location in space. The specification of mean properties for the oscillatory part of the flow, like:
Stokes drift,
wave action,
pseudomomentum and
pseudoenergy – and the associated
conservation laws – arise naturally when using the GLM method. The GLM concept can also be incorporated into
variational principles of fluid flow. ==Notes==