隔声模型的变分公式
Variational formulations of sound-proof models
摘要：
我们得到一个家庭的理想（非耗散）的三维隔音流体模型，其中包括利普斯-Hemler滞弹性近似（AA）和Durran伪不可压缩近似（PIA）。这一系列的模型出现在欧拉-庞加莱框架中，涉及欧拉流体描述中表达的约束汉密尔顿原理。在这个框架中的推导建立了以下属性的每个成员的整个家庭：开尔文-诺特环流定理，守恒的流体包裹的位涡，李-泊松哈密顿制定具有保守的卡西米尔，一个保守的域积分能量和相关的变分原理满足的平衡解。\smallskip在使用约束Hamilton原理推导出3D模型之后，我们推导出这些隔音理论的相应2D垂直切片模型。
英文摘要：
We derive a family of ideal (nondissipative) 3D sound-proof fluid models that includes both the Lipps-Hemler anelastic approximation (AA) and the Durran pseudo-incompressible approximation (PIA). This family of models arises in the Euler-Poincaré framework involving a constrained Hamilton's principle expressed in the Eulerian fluid description. The derivation in this framework establishes the following properties of each member of the entire family: the Kelvin-Noether circulation theorem, conservation of potential vorticity on fluid parcels, a Lie-Poisson Hamiltonian formulation possessing conserved Casimirs, a conserved domain integrated energy and an associated variational principle satisfied by the equilibrium solutions. \smallskip Having set the stage with the derivations of 3D models using the constrained Hamilton's principle, we then derive the corresponding 2D vertical slice models for these sound-proof theories.
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