| 词条 | Generalized Lagrangian mean |
| 释义 |
In continuum mechanics, the generalized Lagrangian mean (GLM) is a formalism – developed by {{harvs|txt=yes|last1=Andrews|first1=D.G.|last2=McIntyre|year=1978a|first2=M.E.|year2=1978b}} – to unambiguously split a motion into a mean part and an oscillatory part. The method gives a mixed Eulerian–Lagrangian description for the flow field, but appointed to fixed Eulerian coordinates.[1] BackgroundIn 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, {{harvtxt|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: Stokes drift, wave action, pseudomomentum and pseudoenergy – and the associated conservation laws – arise naturally when using the GLM method.[2][3] The GLM concept can also be incorporated into variational principles of fluid flow.[4] Notes1. ^{{harvtxt|Craik|1988}} 2. ^{{harvtxt|Andrews|McIntyre|1978b}} 3. ^{{harvtxt|McIntyre|1981}} 4. ^{{harvtxt|Holm|2002}} ReferencesBy Andrews & McIntyre{{refbegin}}
| doi = 10.1017/S0022112078002773 | volume = 89 | issue = 4 | pages = 609–646 | last1 = Andrews | first1 = D. G. | last2 = McIntyre | first2 = M. E. | title = An exact theory of nonlinear waves on a Lagrangian-mean flow | journal = Journal of Fluid Mechanics | year = 1978a | url = http://www.atm.damtp.cam.ac.uk/people/mem/andrews-mcintyre-glm-jfm78.pdf | postscript = . |bibcode = 1978JFM....89..609A }}
| doi = 10.1017/S0022112078002785 | volume = 89 | issue = 4 | pages = 647–664 | last1 = Andrews | first1 = D. G. | last2 = McIntyre | first2 = M. E. | title = On wave-action and its relatives | journal = Journal of Fluid Mechanics | year = 1978b | url = http://www.atm.damtp.cam.ac.uk/people/mem/andrews-mcintyre-waveac-jfm78.pdf | postscript = . |bibcode = 1978JFM....89..647A }}
| doi = 10.1007/BF01586449 | volume = 118 | issue = 1 | pages = 152–176 | last = McIntyre | first = M. E. | title = An introduction to the generalized Lagrangian-mean description of wave, mean-flow interaction | journal = Pure and Applied Geophysics | year = 1980 | postscript = . |bibcode = 1980PApGe.118..152M }}
| doi = 10.1017/S0022112081001626 | volume = 106 | pages = 331–347 | last = Mcintyre | first = M. E. | title = On the 'wave momentum' myth | journal = Journal of Fluid Mechanics | year = 1981 | url = http://www.atm.damtp.cam.ac.uk/people/mem/papers/RECOIL/wave-momentum-myth-scanned.pdf | postscript = . |bibcode = 1981JFM...106..331M }}{{refend}} By others{{refbegin}}
| first=O. | last=Bühler | title=Waves and mean flows | publisher=Cambridge University Press | edition=2nd | year=2014 | isbn=978-1-107-66966-6 }}
| publisher = Cambridge University Press | isbn = 9780521368292 | last = Craik | first = A. D. D. | title = Wave interactions and fluid flows | year = 1988 | postscript = . }} See Chapter 12: "Generalized Lagrangian mean (GLM) formulation", pp. 105–113.
| doi = 10.1146/annurev.fl.16.010184.000303 | volume = 16 | pages = 11–44 | last = Grimshaw | first = R. | title = Wave action and wave–mean flow interaction, with application to stratified shear flows | journal = Annual Review of Fluid Mechanics | year = 1984 |bibcode = 1984AnRFM..16...11G }}
| doi = 10.1063/1.1460941 | volume = 12 | issue = 2 | pages = 518–530 | last = Holm | first = Darryl D. | title = Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics | journal = Chaos | year = 2002 | postscript = . | pmid = 12779582 |bibcode = 2002Chaos..12..518H }}{{refend}} 2 : Continuum mechanics|Concepts in physics |
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