A General Theorem on Angular-Momentum Changes due to Potential Vorticity Mixing and on Potential-Energy Changes due to Buoyancy Mixing
A General Theorem on Angular-Momentum Changes due to Potential Vorticity Mixing and on Potential-Energy Changes due to Buoyancy Mixing
复制标题
势涡混合引起的角动量变化和浮力混合引起的势能变化的一般定理
DOI：
10.1175/2009jas3293.1
复制
发表时间：
2009
影响因子：
3.1
通讯作者：
M. McIntyre
中科院分区：
文献类型：
--
作者：
Richard Wood;M. McIntyre
初始纬向对称的准地转位涡分布qi（y）在某个有限区域jyj，L（y为纬度）内经历完全或部分混合。考虑了初始时刻和任何以后时刻之间的总绝对角动量M的变化。对于标准准地转浅水β通道动力学，证明了对任意的qi（y），使得dqi/dy。0贯穿jyj，L，M的变化总是负的。即使在最一般的可能意义上理解“混合”，这个定理也是成立的。任意搅拌或平流重排包括，结合到任意程度的空间不均匀扩散。该定理适用于PV分布在以后的时间是否是带状对称的。同样的定理支配由于浮力混合在垂直Boussinesq位能的变化。为了使标准准地转β通道动力学有效，
An initial zonally symmetric quasigeostrophic potential vorticity (PV) distribution qi( y) is subjected to complete or partial mixing within some finite zone jyj , L, where y is latitude. The change in M, the total absolute angular momentum, between the initial and any later time is considered. For standard quasigeostrophic shallow-water beta-channel dynamics it is proved that, for any qi( y) such that dqi/dy . 0 throughout jyj , L, the change in M is always negative. This theorem holds even when ‘‘mixing’’ is understood in the most general possible sense. Arbitrary stirring or advective rearrangement is included, combined to an arbitrary extent with spatially inhomogeneous diffusion. The theorem holds whether or not the PV distribution is zonally symmetric at the later time. The same theorem governs Boussinesq potential-energy changes due to buoyancy mixing in the vertical. For the standard quasigeostrophic beta-channel dynamics to be valid the