Generalized Lagrangian mean
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In
Eulerian coordinates.[1]
Background
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
postulates, Andrews & McIntyre (1978a)
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:
The GLM concept can also be incorporated into variational principles of fluid flow.[4]
Notes
References
By Andrews & McIntyre
- Andrews, D. G.; .
- Andrews, D. G.; McIntyre, M. E. (1978b), "On wave-action and its relatives" (PDF), Journal of Fluid Mechanics, 89 (4): 647–664, .
- McIntyre, M. E. (1980), "An introduction to the generalized Lagrangian-mean description of wave, mean-flow interaction", Pure and Applied Geophysics, 118 (1): 152–176, S2CID 122690944.
- McIntyre, M. E. (1981), "On the 'wave momentum' myth" (PDF), Journal of Fluid Mechanics, 106: 331–347, .
By others
- Bühler, O. (2014), Waves and mean flows (2nd ed.), Cambridge University Press, ISBN 978-1-107-66966-6
- Craik, A. D. D. (1988), Wave interactions and fluid flows, Cambridge University Press, ISBN 9780521368292. See Chapter 12: "Generalized Lagrangian mean (GLM) formulation", pp. 105–113.
- Grimshaw, R. (1984), "Wave action and wave–mean flow interaction, with application to stratified shear flows", Annual Review of Fluid Mechanics, 16: 11–44,
- PMID 12779582.