垂直切片模型的粒子重标对称性和Noether定理
Particle relabelling symmetries and Noether's theorem for vertical slice models
摘要：
我们考虑Cotter和Holm（Proc Roy Soc，2013）中引入的垂直切片模型的变分公式。这些模型有一个开尔文循环定理，适用于所有物质输送的闭合回路，而不仅仅是那些在位温等值面上的回路。位涡守恒可以直接从这个环流定理导出。在本文中，我们表明，这一性质是由于这些模型具有重标记对称性的每一个单一的垂直切片，保持密度的单同态，而不仅仅是那些保持位温的单同态。这是使用Cotter和Holm（计算数学基础，2012）的方法开发的。
英文摘要：
We consider the variational formulation for vertical slice models introduced in Cotter and Holm (Proc Roy Soc, 2013). These models have a Kelvin circulation theorem that holds on all materially-transported closed loops, not just those loops on isosurfaces of potential temperature. Potential vorticity conservation can be derived directly from this circulation theorem. In this paper, we show that this property is due to these models having a relabelling symmetry for every single diffeomorphism of the vertical slice that preserves the density, not just those diffeomorphisms that preserve the potential temperature. This is developed using the methodology of Cotter and Holm (Foundations of Computational Mathematics, 2012).
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