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@inbook{Holm:2024:10.1007/978-3-031-40094-0_5,
author = {Holm, DD and Hu, R and Street, OD},
booktitle = {Mathematics of Planet Earth},
doi = {10.1007/978-3-031-40094-0_5},
pages = {111--141},
publisher = {Springer Nature Switzerland},
title = {On the interactions between mean flows and inertial gravity waves in the WKB approximation},
url = {http://dx.doi.org/10.1007/978-3-031-40094-0_5},
year = {2024}
}

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TY  - CHAP
AB  - We derive a Wentzel–Kramers–Brillouin (WKB) closure of the generalised Lagrangian mean (GLM) theory by using a phase-averaged Hamilton variational principle for the Euler–Boussinesq (EB) equations. Following Gjaja and Holm 1996, we consider 3D inertial gravity waves (IGWs) in the EB approximation. The GLM closure for WKB IGWs expresses EB wave mean flow interaction (WMFI) as WKB wave motion boosted into the reference frame of the EB equations for the Lagrangian mean transport velocity. We provide both deterministic and stochastic closure models for GLM IGWs at leading order in 3D complex vector WKB wave asymptotics. This paper brings the Gjaja and Holm 1996 paper at leading order in wave amplitude asymptotics into an easily understood short form and proposes a stochastic generalisation of the WMFI equations for IGWs.
AU  - Holm,DD
AU  - Hu,R
AU  - Street,OD
DO  - 10.1007/978-3-031-40094-0_5
EP  - 141
PB  - Springer Nature Switzerland
PY  - 2024///
SN  - 9783031400933
SP  - 111
TI  - On the interactions between mean flows and inertial gravity waves in the WKB approximation
T1  - Mathematics of Planet Earth
UR  - http://dx.doi.org/10.1007/978-3-031-40094-0_5
ER  -

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