Variational formulations of sound-proof models Variational Sound-Proof Models
Variational formulations of sound-proof models Variational Sound-Proof Models
复制标题
隔音模型的变分公式 变分隔音模型
DOI：
10.1002/qj.2260
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发表时间：
2014
影响因子：
8.9
通讯作者：
Cotter C
中科院分区：
文献类型：
--
作者：
Cotter C
我们推导了一系列理想（非耗散）三维（3D）隔音流体模型，包括Lipps-Hemler非弹性近似（AA）和Durran伪不可压缩近似（PIA）。这类模型出现在欧拉-庞加莱格框架中，涉及欧拉流体描述中表达的受限汉密尔顿原理。在这个框架下的推导建立了整个家族中每个成员的以下性质：开尔文-诺特循环定理，流体包裹上的位涡守恒，具有守恒卡西米尔的利-泊松哈密顿公式，守恒域积分能量和平衡解满足的相关变分原理。在使用受限汉密尔顿原理推导三维模型的基础上，我们为这些隔音理论推导出相应的二维垂直切片模型。
We derive a family of ideal (non‐dissipative) three‐dimensional (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.Having set the stage with derivations of 3D models using the constrained Hamilton's principle, we then derive the corresponding 2D vertical slice models for these sound‐proof theories.