关于WKB近似中平均流与惯性重力波相互作用的研究
On the interactions between mean flows and inertial gravity waves in the WKB approximation
AI总结：
本文基于WKB近似推导GLM理论的闭合，将惯性重力波与平均流的相互作用表述为波运动，并给出确定性与随机闭合模型，简化并推广了Gjaja和Holm 1996年的工作。
摘要：
我们通过使用欧拉-布辛涅斯克（EB）方程的相位平均哈密顿变分原理，推导了广义拉格朗日平均（GLM）理论的Wentzel-Kramers-Brillouin（WKB）闭合。遵循Gjaja和Holm 1996年的工作，我们考虑了EB近似下的三维惯性重力波（IGWs）。WKB IGWs的GLM闭合将EB波平均流相互作用（WMFI）表示为WKB波运动，该运动被提升到拉格朗日平均输运速度的EB方程参考系中。我们在三维复矢量WKB波渐近的领先阶提供了GLM IGWs的确定性和随机闭合模型。本文将Gjaja和Holm 1996年论文在波振幅渐近领先阶的结果提炼为易于理解的简短形式，并提出了IGWs的WMFI方程的随机推广。
英文摘要：
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.
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